0zac-cDzJwA.json

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        "text": " Hello and welcome to Let's Make a...",
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        "text": "...Deal!",
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        "text": " Behind one of these three doors is today's prize, a trip on the Coding Train Express.",
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        "text": " Behind the other two doors is a goat.",
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        "text": " It's up to you to pick one of these doors. Which one will you pick?",
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        "text": " I can hear the people of the internet shouting out to me, door number three.",
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        "text": " Ah, but before I reveal what's behind door number three, let me show you what's behind door number one.",
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        "text": " Now I'm going to offer you a one-time only chance to switch.",
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        "text": " Switch to door number two or do you want to keep door number three?",
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        "text": " Think about it.",
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        "text": " Should you switch? What is the probability that the prize is behind door number three?",
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        "text": " And what is the probability that the prize is behind door number two?",
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        "text": " This is the classic Monty Hall problem which originated in the American television show Let's Make a Deal back in the 1970s.",
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        "text": " The answer to the problem is you should absolutely switch.",
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        "text": " If you switch, you will have a two out of three chances, 66.6666666666% chance of the prize being behind door number two.",
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        "text": " This might seem counterintuitive.",
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        "text": " Shouldn't it just be 50-50? There's two of them.",
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        "text": " It's definitely not behind door number one, so it's either behind door number two or door number three.",
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        "text": " No, that is not the case.",
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        "text": " In today's coding challenge, I'm going to first explain to you why you absolutely should switch.",
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        "text": " And then I'm going to code a simple p5.js simulation of the game that you can play over and over again to test your different theories about what the proper strategy and probabilities might be.",
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        "text": " Let's recap the problem. We've got three doors.",
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        "text": " Behind one of these doors is a prize, a train.",
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        "seek": 10000,
        "start": 119,
        "temperature": 0,
        "text": " Let's say it's behind door number two.",
        "tokens": [
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          311,
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      {
        "avg_logprob": -0.15764407203311012,
        "compression_ratio": 1.6416666666666666,
        "end": 124,
        "id": 24,
        "no_speech_prob": 0.00001952557431650348,
        "seek": 10000,
        "start": 123,
        "temperature": 0,
        "text": " There, that's my train.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.15764407203311012,
        "compression_ratio": 1.6416666666666666,
        "end": 128,
        "id": 25,
        "no_speech_prob": 0.00001952557431650348,
        "seek": 10000,
        "start": 124,
        "temperature": 0,
        "text": " Then behind doors one and three is a goat.",
        "tokens": [
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      {
        "avg_logprob": -0.1643083278949444,
        "compression_ratio": 1.7025862068965518,
        "end": 130,
        "id": 26,
        "no_speech_prob": 0.00031013914849609137,
        "seek": 12800,
        "start": 128,
        "temperature": 0,
        "text": " I'm going to have to draw a goat now.",
        "tokens": [
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      {
        "avg_logprob": -0.1643083278949444,
        "compression_ratio": 1.7025862068965518,
        "end": 134,
        "id": 27,
        "no_speech_prob": 0.00031013914849609137,
        "seek": 12800,
        "start": 132,
        "temperature": 0,
        "text": " It's more like a cat, but it'll have to do.",
        "tokens": [
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      {
        "avg_logprob": -0.1643083278949444,
        "compression_ratio": 1.7025862068965518,
        "end": 141,
        "id": 28,
        "no_speech_prob": 0.00031013914849609137,
        "seek": 12800,
        "start": 134,
        "temperature": 0,
        "text": " It's important to remember that the host, played by me or Monty Hall, really, knows where the prize is.",
        "tokens": [
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        "avg_logprob": -0.1643083278949444,
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        "end": 156,
        "id": 29,
        "no_speech_prob": 0.00031013914849609137,
        "seek": 12800,
        "start": 141,
        "temperature": 0,
        "text": " Let's think about all the possible ways this game could play out and build a table describing those ways and look at how often does the player win if they switch and how often do they win if they don't switch.",
        "tokens": [
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        "temperature": 0,
        "text": " So what are the stages?",
        "tokens": [
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      },
      {
        "avg_logprob": -0.19966564902776404,
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        "end": 160,
        "id": 31,
        "no_speech_prob": 0.0065895370207726955,
        "seek": 15600,
        "start": 158,
        "temperature": 0,
        "text": " First, there's the player's pick.",
        "tokens": [
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      {
        "avg_logprob": -0.19966564902776404,
        "compression_ratio": 1.658682634730539,
        "end": 164,
        "id": 32,
        "no_speech_prob": 0.0065895370207726955,
        "seek": 15600,
        "start": 161,
        "temperature": 0,
        "text": " Then there's the door revealed by the host.",
        "tokens": [
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      {
        "avg_logprob": -0.19966564902776404,
        "compression_ratio": 1.658682634730539,
        "end": 169,
        "id": 33,
        "no_speech_prob": 0.0065895370207726955,
        "seek": 15600,
        "start": 166,
        "temperature": 0,
        "text": " Then there's the question of does the player switch or not?",
        "tokens": [
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      {
        "avg_logprob": -0.19966564902776404,
        "compression_ratio": 1.658682634730539,
        "end": 174,
        "id": 34,
        "no_speech_prob": 0.0065895370207726955,
        "seek": 15600,
        "start": 171,
        "temperature": 0,
        "text": " And of course we have the question, do they win?",
        "tokens": [
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      {
        "avg_logprob": -0.19966564902776404,
        "compression_ratio": 1.658682634730539,
        "end": 185,
        "id": 35,
        "no_speech_prob": 0.0065895370207726955,
        "seek": 15600,
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        "temperature": 0,
        "text": " All right, let's say the player starts by picking door number one.",
        "tokens": [
          51514,
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      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 193,
        "id": 36,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 185,
        "temperature": 0,
        "text": " The host then, knowing that the prize is in door number two, has to reveal door number three to show a goat.",
        "tokens": [
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      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 196,
        "id": 37,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 194,
        "temperature": 0,
        "text": " Now remember, the player's picked door number one.",
        "tokens": [
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      {
        "avg_logprob": -0.17062083653041293,
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        "end": 200,
        "id": 38,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 196,
        "temperature": 0,
        "text": " If they switch, they'll be switching to door number two.",
        "tokens": [
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      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 204,
        "id": 39,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 200,
        "temperature": 0,
        "text": " Let's just assume for the sake of argument that the player is always going to switch.",
        "tokens": [
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        "avg_logprob": -0.17062083653041293,
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        "end": 206,
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        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 204,
        "temperature": 0,
        "text": " So yes, the player switches.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 207,
        "id": 41,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 206,
        "temperature": 0,
        "text": " Did the player win?",
        "tokens": [
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      },
      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 209,
        "id": 42,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 207,
        "temperature": 0,
        "text": " Yes, the player wins.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.17062083653041293,
        "compression_ratio": 1.784037558685446,
        "end": 211,
        "id": 43,
        "no_speech_prob": 0.00006013975871610455,
        "seek": 18500,
        "start": 210,
        "temperature": 0,
        "text": " Check.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 215,
        "id": 44,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 211,
        "temperature": 0,
        "text": " Now let's look at the scenario where the player starts by picking door number two.",
        "tokens": [
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      {
        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 225,
        "id": 45,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 216,
        "temperature": 0,
        "text": " Now this is an interesting scenario because if the player has picked door number two, Monty Hall has to reveal a door that has a goat behind it.",
        "tokens": [
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        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 227,
        "id": 46,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 225,
        "temperature": 0,
        "text": " It could be either one or three.",
        "tokens": [
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        "compression_ratio": 1.9113924050632911,
        "end": 231,
        "id": 47,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 227,
        "temperature": 0,
        "text": " So let's just say that Monty Hall reveals door number three this time.",
        "tokens": [
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      {
        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 233,
        "id": 48,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 231,
        "temperature": 0,
        "text": " Again, we've got another door number three.",
        "tokens": [
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      {
        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 236,
        "id": 49,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 234,
        "temperature": 0,
        "text": " The player has picked door number two.",
        "tokens": [
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      {
        "avg_logprob": -0.16182183382803933,
        "compression_ratio": 1.9113924050632911,
        "end": 238,
        "id": 50,
        "no_speech_prob": 0.00010229468171019107,
        "seek": 21100,
        "start": 236,
        "temperature": 0,
        "text": " Should they switch to door number one?",
        "tokens": [
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        "avg_logprob": -0.19903592780084894,
        "compression_ratio": 1.7772511848341233,
        "end": 241,
        "id": 51,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 238,
        "temperature": 0,
        "text": " We know they shouldn't, but let's say in this scenario they do.",
        "tokens": [
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      {
        "avg_logprob": -0.19903592780084894,
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        "end": 245,
        "id": 52,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 241,
        "temperature": 0,
        "text": " So yes, they switch, and no, they do not win.",
        "tokens": [
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      {
        "avg_logprob": -0.19903592780084894,
        "compression_ratio": 1.7772511848341233,
        "end": 250,
        "id": 53,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 246,
        "temperature": 0,
        "text": " The last possibility here is that the player starts by picking door number three.",
        "tokens": [
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        "avg_logprob": -0.19903592780084894,
        "compression_ratio": 1.7772511848341233,
        "end": 252,
        "id": 54,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 250,
        "temperature": 0,
        "text": " They pick door number three.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.19903592780084894,
        "compression_ratio": 1.7772511848341233,
        "end": 257,
        "id": 55,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 252,
        "temperature": 0,
        "text": " Monty Hall has to reveal door number one, the only other door with a goat behind it.",
        "tokens": [
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      {
        "avg_logprob": -0.19903592780084894,
        "compression_ratio": 1.7772511848341233,
        "end": 265,
        "id": 56,
        "no_speech_prob": 0.04602669179439545,
        "seek": 23800,
        "start": 258,
        "temperature": 0,
        "text": " The player switches, switching to door number two, and yes, they win.",
        "tokens": [
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        "avg_logprob": -0.1998516863042658,
        "compression_ratio": 1.8858695652173914,
        "end": 268,
        "id": 57,
        "no_speech_prob": 0.006796713452786207,
        "seek": 26500,
        "start": 265,
        "temperature": 0,
        "text": " There's only three ways this game can play out.",
        "tokens": [
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      {
        "avg_logprob": -0.1998516863042658,
        "compression_ratio": 1.8858695652173914,
        "end": 274,
        "id": 58,
        "no_speech_prob": 0.006796713452786207,
        "seek": 26500,
        "start": 268,
        "temperature": 0,
        "text": " The player starting by picking door number one, starting by picking door number two, or starting by picking door number three.",
        "tokens": [
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      {
        "avg_logprob": -0.1998516863042658,
        "compression_ratio": 1.8858695652173914,
        "end": 281,
        "id": 59,
        "no_speech_prob": 0.006796713452786207,
        "seek": 26500,
        "start": 275,
        "temperature": 0,
        "text": " If the player always switches, the player will win two out of three times.",
        "tokens": [
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        "text": " Think about it this way.",
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        "text": " Remember, you don't know where the prizes are.",
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        "text": " You pick door number one.",
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        "text": " And I'm going to say to you now, well, would you like to keep door number one,",
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        "text": " or would you like to win if it's behind either doors two or three?",
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        "text": " Either one. You can have two doors. You don't need just one door.",
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        "temperature": 0,
        "text": " Stick with just one door, or would you like two doors?",
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        "text": " That's exactly what this problem is.",
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        "text": " You would want to pick two doors, because it's more likely two out of three times to be behind one of these two doors than the original one that you picked.",
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        "text": " Let's look at it one more way.",
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        "text": " I'm going to show you a hundred doors.",
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        "text": " All right, fine. Let's just do 50 doors. I don't feel like drawing the rest.",
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        "text": " Pick any one of these doors. There's only a prize behind one of them.",
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        "text": " This train ride, this glorious train ride you're going to win is somewhere behind one of these 50 doors.",
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        "text": " Oh, oh, you want to pick this one? Okay.",
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        "text": " You picked this one. A colored in purple to indicate it's the one you picked.",
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        "text": " Now, I'm going to reveal to you that there's a goat behind 48 other doors.",
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        "text": " Would you like now to switch to this door and see if the prize is there?",
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        "temperature": 0,
        "text": " Or would you like to keep your original door?",
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        "text": " I mean, hello, you're going to want to switch to this door, right?",
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        "text": " What's the chance that the prize happens to be your one out of 50 chance that you happen to just pick?",
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        "temperature": 0,
        "text": " Or I revealed all of these other, I mean, it could be there.",
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        "text": " There could be a goat here, but I remember, I know all of these are goats.",
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        "temperature": 0,
        "text": " So I'm going to leave one open.",
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        "text": " If you didn't pick the prize, I have to leave the one with the prize open.",
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        "text": " Would you want to switch? I think you would.",
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        "text": " There's also a very specific probability analysis known as the Bayes theorem that we could apply to show this exact two out of three probability.",
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        "temperature": 0,
        "text": " Or in this case, it would be a 49 out of 50 probability.",
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        "text": " You have a one out of 50 chance of it being your original pick.",
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        "temperature": 0,
        "text": " Or if you switch, you have a 49 out of 50 chance of winning.",
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        "text": " But you're probably not here wanting to listen to me drone on and on and diagram on the whiteboard about probability and the Monty Hall problem.",
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        "text": " We could build a P5JS sketch in code that simulates the Monty Hall problem, run it thousands of times and see if my analysis proves to be correct.",
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        "text": " Also, by the way, who is to say that the goat isn't the true prize after all?",
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        "text": " I would love to have some wonderful, beautiful goats.",
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        "text": " My usual approach to this would be to start drawing doors in the canvas and checking where the mouse is clicking.",
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        "text": " But I think I'd actually like to try this with DOM elements, meaning HTML elements that are not canvases that appear on a web page, which if you didn't know, you could also do in P5.",
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        "text": " So I'm actually going to do something quite exciting here and say no canvas.",
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        "text": " I'm going to write a little loop to create three doors.",
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        "text": " Let's make an array to hold the data for those three doors.",
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        "text": " And each door will be a div on the web page.",
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        "text": " Let's start by putting a goat in each one, and then I will pick one randomly and put the prize there.",
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        "text": " So every time I run this sketch, I see three emojis, only one of which is a train.",
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        "text": " Now, of course, they're really tiny. So let's work on some designy things.",
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        "text": " Let's create a CSS class. A CSS class is a way of designating a particular set of styles to be applied to any element on the web page.",
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        "text": " This isn't a full lesson about CSS, obviously.",
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        "text": " I have barely no CSS.",
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        "text": " But I will put resources in the video description and up on the screen here, as well as some other videos I have that go through CSS in a bit more detail.",
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        "text": " But right here in the P5 web editor, I can go over to the style.css file.",
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        "text": " I can create a door class, and I can start to add some properties to it.",
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        "text": " Now, what I'd really like to do is center those emojis in the div.",
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        "text": " Thankfully, the live Twitch chat that's watching along here has given me some tips of how to do this.",
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        "text": " Let's make the emojis a little bit bigger.",
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        "text": " Let's put a little margin between the divs.",
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        "text": " And I want to see them in a row, so I think I can add display flex to the body.",
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        "text": " Great. Now we've got our three doors there.",
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        "text": " So the tricky thing here is I want to make a div that knows whether it's a goat or a train, but I don't want to reveal that goat or train.",
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        "text": " I could create my own wrapper. Like, I could create a door class that has a div.",
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        "text": " But I think since these are just JavaScript objects, a P5 element, I can attach other properties to them.",
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        "text": " So I'm going to make the div with no text.",
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        "text": " And instead, I'll add a new property called prize, which is by default a goat.",
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        "text": " Let's call this winning door.",
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        "text": " I'll say the winning doors prize is the train.",
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        "text": " So now I have three doors. Behind the scenes, there's a variable attached to each of those divs that's holding on to either a goat or a train.",
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        "text": " But the viewer, the player, I cannot see which one is which.",
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        "text": " Now what I want to do is attach an event to each door to do something when I click on it.",
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        "text": " The clicking on the door will be the act of selecting that one.",
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        "text": " I can do this with the P5 event mouse pressed.",
        "tokens": [
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        "text": " And whenever the mouse is pressed, I want to execute a function. I'll call it reveal.",
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        "text": " One of the nice things that P5 does behind the scenes is it binds that particular function reveal to the DOM element that was triggered by the event.",
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        "text": " And that binding is embedded inside the keyword this.",
        "tokens": [
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        "text": " I have a whole video all about the this keyword and how this works.",
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        "text": " But for now, what you will see is if I just say console log this.prize, when I click on each door, we'll see the prize in the console.",
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        "text": " That one's a goat. That one's also a goat. And that one's the train.",
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        "temperature": 0,
        "text": " Running it one more time, we have train goat goat.",
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        "text": " So now I need something to keep track of the state.",
        "tokens": [
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        "text": " There's the moment I pick. There's the moment I reveal. There's the moment I switch.",
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        "text": " And then whether I win or not.",
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        "text": " So let's create a variable called state to keep track of the game state.",
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        "text": " And we're going to start with pick, meaning we're waiting for the player to pick.",
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        "text": " Now, I'm going to keep this console log here, which will help me know what's going on.",
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        "text": " And this reveal is a little bit of a misnomer, actually, because we don't want to reveal the one that we picked.",
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        "text": " We want to reveal a different one that has a goat behind it.",
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        "text": " So something that would help me a little bit is to also have each div know its index into the array.",
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        "temperature": 0,
        "text": " So here the div also has a property called index that I'm storing.",
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        "text": " Where is it in the doors array?",
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        "temperature": 0,
        "text": " So when I click, I should see 0, 1, 2.",
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        "temperature": 0,
        "text": " So once I've picked, I need Monty Hall to reveal one of the other doors.",
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        "avg_logprob": -0.20818131499820286,
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        "text": " So Monty Hall needs to know which doors can they reveal.",
        "tokens": [
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        "seek": 73800,
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        "temperature": 0,
        "text": " We'll make a new array called options.",
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        "temperature": 0,
        "text": " As long as it's not the door that the player picked, and the prize is not the train,",
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        "seek": 76400,
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        "temperature": 0,
        "text": " I can make this a little less wordy by putting the door in a separate variable.",
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        "temperature": 0,
        "text": " Oh, this, this. As long as i is not this.index, right.",
        "tokens": [
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        "temperature": 0,
        "text": " I don't know. I was so confused there.",
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        "temperature": 0,
        "text": " As long as the door I'm looking at is not the one that was clicked on,",
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        "temperature": 0,
        "text": " and that door is not the prize, then it's something that could be revealed.",
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        "seek": 78900,
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        "temperature": 0,
        "text": " Now remember, if the player didn't pick the right door in the first place,",
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        "temperature": 0,
        "text": " there's only going to be one thing left in the options.",
        "tokens": [
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        "temperature": 0,
        "text": " But I need to check all the possibilities, because if they did pick the prize,",
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        "text": " then Monty Hall can choose to reveal one of two doors.",
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        "text": " But we'll pick one of the options randomly.",
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        "text": " If there's just one, there's only one it can pick.",
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        "text": " And we will put in the div the actual prize itself.",
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        "text": " Okay, I'm going to pick door number one, and we should see a goat appear in either door two or three.",
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        "text": " What did I do wrong?",
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        "text": " Oh, I did it if it's... I have to say if it's not equal to the train.",
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        "text": " Okay, that was a disaster. Let's try this again.",
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        "text": " I'm going to pick door number one. There's that goat.",
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        "text": " Let's run it again. There's the goat.",
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        "text": " So we always will see a goat, no matter what I pick.",
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        "text": " Another thing I think I should add here is something to indicate which door was picked.",
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        "text": " So let's put a little green.",
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        "text": " So that's highlighting which one I've picked.",
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        "text": " Now is really the moment where some animation or some thoughtful interaction design would be a great addition,",
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        "text": " and I hope you, the viewer, will make a more intuitive and smooth way of playing out this game.",
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        "text": " But I'm just going to really quickly toss in a couple buttons.",
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        "text": " One button for if you want to switch doors,",
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        "text": " or a different button if you want to stay put.",
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        "text": " So when I click on any of the doors, those two buttons will now suddenly appear.",
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        "text": " Now they look a little weird here because I have this CSS display property as flex in the entire body.",
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        "text": " So probably I should make a container for the doors.",
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        "text": " So I'm going to manually put in a div called doors.",
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        "text": " Reference the ID with the hash symbol.",
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        "text": " Put the flex display there.",
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        "text": " Then I can put the door divs in the doors container by using the p5 parent function.",
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        "text": " Then my buttons look a little bit more normal there just on the next line.",
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        "text": " They are kind of small, so let me make the font size a bit bigger.",
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        "text": " And give them a little margin.",
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        "text": " Okay, again, very crude interaction design.",
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        "text": " But now I can choose whether I want to switch or stay.",
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        "text": " This is also maybe a good moment for me to, now that I've got some code worked out, kind of refactor it.",
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        "text": " Like maybe it would be nice to look at the code to see there's a pick function, a reveal function, a switch function, and then a win function.",
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        "text": " Right now I only have a reveal function, which is kind of doing both of these first two steps.",
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        "text": " So when I click on a door, what I'm really doing is picking that door.",
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        "seek": 95900,
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        "temperature": 0,
        "text": " And let's have a variable called pick door, which is set equal to this.",
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        "seek": 95900,
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        "temperature": 0,
        "text": " The div that was clicked on, which is held in the keyword this, based on p5 binding it to the mouse pressed event.",
        "tokens": [
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        "text": " Then I can call reveal.",
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        "text": " Reveal looks out of the doors and figures out what are the ones that can be revealed.",
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        "temperature": 0,
        "text": " As long as it's not the prize or the picked doors index.",
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        "temperature": 0,
        "text": " This setting it to green is really a thing we're doing when we're picking the door.",
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        "temperature": 0,
        "text": " And here we are revealing one of the other doors that has a goat.",
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        "seek": 98400,
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        "temperature": 0,
        "text": " Creating the buttons and the buttons event will be the switch function.",
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        "temperature": 0,
        "text": " I'm going to make the door that was revealed also a global variable.",
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        "text": " So if the player switches, I need to reassign pick door to the door that wasn't picked and wasn't revealed.",
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        "text": " So by switching the new pick is the door that hasn't been picked or revealed.",
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        "text": " And that is now the pick door.",
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        "text": " And then we have to check.",
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        "temperature": 0,
        "text": " Did I win?",
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        "temperature": 0,
        "text": " We'll call a function called check win and the player stay means actually you don't switch.",
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        "text": " So just go right to this check win function.",
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        "text": " And let's also reveal all the prizes.",
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        "temperature": 0,
        "text": " Here we go.",
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        "temperature": 0,
        "text": " I'm going to pick door number one.",
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        "temperature": 0,
        "text": " Oh, I got an error.",
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        "temperature": 0,
        "text": " Door reveal not being defined.",
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        "temperature": 0,
        "text": " Oh, I don't remember when I made this mistake, but I called it revealed door and then said door reveal.",
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        "text": " So the revealed door is the one that I want to put the new content in.",
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        "temperature": 0,
        "text": " Okay, here we go.",
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        "temperature": 0,
        "text": " I'm going to pick this door.",
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        "temperature": 0,
        "text": " What's going on?",
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        "avg_logprob": -0.18589228552740975,
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        "temperature": 0,
        "text": " Oh, and then reveal door.prize.",
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        "seek": 106800,
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        "temperature": 0,
        "text": " Okay, finally, I'm going to get it.",
        "tokens": [
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        "temperature": 0,
        "text": " I'm going to pick this door.",
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        "temperature": 0,
        "text": " It's showing me the goat.",
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        "temperature": 0,
        "text": " So I could switch or I could stay.",
        "tokens": [
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        "temperature": 0,
        "text": " Let's try switching.",
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      },
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        "avg_logprob": -0.18589228552740975,
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        "temperature": 0,
        "text": " And I won.",
        "tokens": [
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        "seek": 109700,
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        "temperature": 0,
        "text": " So this, what, let's, let's, I think this should be a different color.",
        "tokens": [
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        "seek": 109700,
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        "temperature": 0,
        "text": " I'm going to make this blue just to show that I've selected green meaning I won.",
        "tokens": [
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        "end": 1109,
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        "no_speech_prob": 0.000029311255275388248,
        "seek": 109700,
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        "temperature": 0,
        "text": " Pick this door.",
        "tokens": [
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        "avg_logprob": -0.17667732598646632,
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        "end": 1112,
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        "temperature": 0,
        "text": " I'm going to switch and I won.",
        "tokens": [
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        "end": 1115,
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        "seek": 109700,
        "start": 1112,
        "temperature": 0,
        "text": " And let's get rid of the blue after I switch.",
        "tokens": [
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        "text": " I think I have everything now.",
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        "text": " I'm going to pick a door.",
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        "text": " I'm going to switch and I lost.",
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        "text": " I'm going to play again.",
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        "text": " I'm going to pick a door.",
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        "text": " I'm going to switch and I won.",
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        "text": " It's working.",
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        "text": " Could use a lot of improvement.",
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        "text": " Let's clean up just a few things.",
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        "text": " One is I have this wonderful state variable that I never bothered to change.",
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        "text": " So the moment I pick the door, I should change the state.",
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        "text": " And I made it a const for some reason, which it shouldn't be.",
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        "text": " So I'm changing the state to reveal.",
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        "text": " The reason why this is important is that picking event should only happen if the state is pick.",
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        "text": " So now if I were to click again in the middle of the game, it wouldn't change anything that's happening.",
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        "text": " This code would not execute.",
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        "text": " I am probably overusing global variables here, but it would be helpful to actually have these buttons be global variables that I could just show or hide as needed.",
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        "text": " So I'm actually going to take these and put them in setup.",
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        "text": " Hide them and then just show them when it's time to prompt the user.",
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        "text": " Then after the player has either chosen to switch or stay, I can hide those buttons again.",
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        "text": " Pick a door, switch, and I won.",
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        "text": " Let's add some CSS for the you win message.",
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        "text": " And let's create a play again button.",
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        "text": " Now, of course, a lot of these DOM elements don't need to be generated with P5 functions.",
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        "text": " In a properly designed page, you might want to do all of this with HTML and CSS.",
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        "text": " But this is just a quick way that I'm doing it to get this going.",
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        "text": " That said, to finish off this play again button, I need to write the start over function.",
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        "text": " What do we do to start over?",
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        "text": " Well, we need to pick a new prize again.",
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        "text": " Start them all off as goats.",
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        "text": " Pick a random one to be the winner.",
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        "text": " Now that I've done this, I actually don't need to do this here in setup anymore.",
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        "text": " I can just say start over.",
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        "text": " I should also make sure I clear any background color or text that was in the div.",
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        "text": " And hide the play again button.",
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        "text": " All right, let's see if this works.",
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        "text": " I'm going to pick door number one.",
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        "text": " I'm going to switch.",
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        "seek": 126400,
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        "temperature": 0,
        "text": " I think I forgot to show the play again button.",
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      {
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        "compression_ratio": 1.7190476190476192,
        "end": 1287,
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        "seek": 126400,
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        "temperature": 0,
        "text": " Play again dot show.",
        "tokens": [
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      {
        "avg_logprob": -0.1788578206842596,
        "compression_ratio": 1.7190476190476192,
        "end": 1288,
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        "temperature": 0,
        "text": " One more time.",
        "tokens": [
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      {
        "avg_logprob": -0.1788578206842596,
        "compression_ratio": 1.7190476190476192,
        "end": 1291,
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        "seek": 126400,
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        "temperature": 0,
        "text": " Let's pick door number three and let's switch.",
        "tokens": [
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        "end": 1293,
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        "temperature": 0,
        "text": " I won. Let's play again.",
        "tokens": [
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        "seek": 129400,
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        "temperature": 0,
        "text": " Still says you win there.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.18081829848798733,
        "compression_ratio": 1.6130434782608696,
        "end": 1299,
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        "seek": 129400,
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        "temperature": 0,
        "text": " I need a permanent place for the win or lose message.",
        "tokens": [
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        "avg_logprob": -0.18081829848798733,
        "compression_ratio": 1.6130434782608696,
        "end": 1303,
        "id": 276,
        "no_speech_prob": 0.00003705284325405955,
        "seek": 129400,
        "start": 1300,
        "temperature": 0,
        "text": " Call that outcome P for outcome paragraph.",
        "tokens": [
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        "end": 1308,
        "id": 277,
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        "seek": 129400,
        "start": 1304,
        "temperature": 0,
        "text": " Definitely need to clear it when we start over.",
        "tokens": [
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      {
        "avg_logprob": -0.18081829848798733,
        "compression_ratio": 1.6130434782608696,
        "end": 1312,
        "id": 278,
        "no_speech_prob": 0.00003705284325405955,
        "seek": 129400,
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        "temperature": 0,
        "text": " In setup, you need to create it.",
        "tokens": [
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      {
        "avg_logprob": -0.18081829848798733,
        "compression_ratio": 1.6130434782608696,
        "end": 1317,
        "id": 279,
        "no_speech_prob": 0.00003705284325405955,
        "seek": 129400,
        "start": 1312,
        "temperature": 0,
        "text": " And then the message, instead of creating a new paragraph, we just put it in the existing one.",
        "tokens": [
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        "seek": 129400,
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        "temperature": 0,
        "text": " All right, ready for this?",
        "tokens": [
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        "temperature": 0,
        "text": " All right, I'm going to pick door number two.",
        "tokens": [
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        "temperature": 0,
        "text": " I never seem to pick door number two to start.",
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        "temperature": 0,
        "text": " The goat is revealed as door number three.",
        "tokens": [
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        "end": 1330,
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        "temperature": 0,
        "text": " Should I switch? Should I stay?",
        "tokens": [
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      {
        "avg_logprob": -0.15774452429023578,
        "compression_ratio": 1.9908675799086757,
        "end": 1331,
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        "temperature": 0,
        "text": " I'm going to switch.",
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        "seek": 132300,
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        "temperature": 0,
        "text": " Whoops. What just happened there?",
        "tokens": [
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        "temperature": 0,
        "text": " Nice little typo there.",
        "tokens": [
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      },
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        "temperature": 0,
        "text": " I would have lost.",
        "tokens": [
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        "temperature": 0,
        "text": " So good thing I got that error.",
        "tokens": [
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        "temperature": 0,
        "text": " I'm going to pick door number two.",
        "tokens": [
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        "temperature": 0,
        "text": " The goat is revealed as door number one.",
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        "temperature": 0,
        "text": " I'm going to switch.",
        "tokens": [
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        "temperature": 0,
        "text": " And I won. Let's play again.",
        "tokens": [
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        "end": 1348,
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        "temperature": 0,
        "text": " I'm going to pick door number three.",
        "tokens": [
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        "temperature": 0,
        "text": " No, it's not working.",
        "tokens": [
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        "temperature": 0,
        "text": " Oh, I've got to set the state back to pick.",
        "tokens": [
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        "seek": 135000,
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        "temperature": 0,
        "text": " So ultimately, I don't know if I really needed this state variable,",
        "tokens": [
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        "seek": 135000,
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        "temperature": 0,
        "text": " or I'm certainly not using it very effectively,",
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        "end": 1362,
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        "temperature": 0,
        "text": " because I only have it as pick or not pick, essentially.",
        "tokens": [
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        "compression_ratio": 1.7751937984496124,
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        "id": 300,
        "no_speech_prob": 0.011868538334965706,
        "seek": 135000,
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        "temperature": 0,
        "text": " But I'll let you figure out how to improve that in your own version of this.",
        "tokens": [
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        "no_speech_prob": 0.011868538334965706,
        "seek": 135000,
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        "temperature": 0,
        "text": " But when I start over, I definitely need to set the state back to pick.",
        "tokens": [
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        "end": 1372,
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        "seek": 135000,
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        "temperature": 0,
        "text": " Here we go.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.1689865482387258,
        "compression_ratio": 1.7751937984496124,
        "end": 1374,
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        "no_speech_prob": 0.011868538334965706,
        "seek": 135000,
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        "temperature": 0,
        "text": " I'm going to pick door number two.",
        "tokens": [
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      {
        "avg_logprob": -0.1689865482387258,
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        "end": 1377,
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        "no_speech_prob": 0.011868538334965706,
        "seek": 135000,
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        "temperature": 0,
        "text": " I'm going to switch.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.1689865482387258,
        "compression_ratio": 1.7751937984496124,
        "end": 1379,
        "id": 305,
        "no_speech_prob": 0.011868538334965706,
        "seek": 135000,
        "start": 1377,
        "temperature": 0,
        "text": " I'm going to play again.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.14601079723503016,
        "compression_ratio": 2.007575757575758,
        "end": 1380,
        "id": 306,
        "no_speech_prob": 0.008984770625829697,
        "seek": 137900,
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        "temperature": 0,
        "text": " I'm going to pick door number one.",
        "tokens": [
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      {
        "avg_logprob": -0.14601079723503016,
        "compression_ratio": 2.007575757575758,
        "end": 1382,
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        "seek": 137900,
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        "temperature": 0,
        "text": " I'm going to switch.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.14601079723503016,
        "compression_ratio": 2.007575757575758,
        "end": 1384,
        "id": 308,
        "no_speech_prob": 0.008984770625829697,
        "seek": 137900,
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        "temperature": 0,
        "text": " I'm going to play again and pick door number three.",
        "tokens": [
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        "text": " I'm going to switch.",
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        "text": " I'm going to play again.",
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        "text": " Door one. Switch.",
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        "text": " I am just winning over and over again.",
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        "text": " I am so good at this game.",
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        "text": " I'm ready to wrap this up.",
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        "text": " I mean, what I really would like to do,",
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        "text": " and I'll create a version of it that just picks automatically and switches automatically,",
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        "text": " running it hundreds of times per second.",
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        "text": " And I'm showing that to you right now over here.",
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        "text": " But what I'm going to do in this video itself",
        "tokens": [
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        "text": " is just add some code to track the win rate for switching",
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        "text": " and the win rate for staying put.",
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        "text": " And if the math that I demonstrated at the beginning of the video is correct,",
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        "text": " we should see a win rate of approximately two out of three times for switching",
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        "text": " and one out of three times for staying put.",
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        "text": " So I need a variable for total plays,",
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        "text": " total switches.",
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        "text": " Actually, I don't need the total plays.",
        "tokens": [
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        "text": " I need to know how many times did I switch and how many times did I stay.",
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        "end": 1440,
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        "text": " So I'll call that total switch plays.",
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        "seek": 143300,
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        "temperature": 0,
        "text": " Awkward variable names.",
        "tokens": [
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      },
      {
        "avg_logprob": -0.18389551827077116,
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        "end": 1447,
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        "temperature": 0,
        "text": " Then I need switch wins and stay wins.",
        "tokens": [
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      {
        "avg_logprob": -0.18389551827077116,
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        "end": 1456,
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        "temperature": 0,
        "text": " Every time the player switches, I need to increase the number of switch plays.",
        "tokens": [
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        "text": " Every time the player stays, ah, but I don't have a function for staying.",
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        "text": " So let me actually go and put that in.",
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        "text": " So instead of when you stay going directly to check win,",
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        "text": " let's write a player stay function.",
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        "text": " And the only thing that happens in that function is",
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      {
        "avg_logprob": -0.14269682339259557,
        "compression_ratio": 1.6416666666666666,
        "end": 1480,
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        "text": " we increase the number of total stay plays and then go to check wins.",
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        "text": " Oh, but when I check the win, how do I know whether I switched or not?",
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        "temperature": 0,
        "text": " And this is a typo here.",
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        "text": " All right, again, so much to refactor later.",
        "tokens": [
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        "end": 1492,
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        "temperature": 0,
        "text": " But let's introduce another variable.",
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        "end": 1495,
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        "temperature": 0,
        "text": " Oh, no, no, I don't need another variable.",
        "tokens": [
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        "avg_logprob": -0.1771597181047712,
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        "text": " I know exactly what to do.",
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        "avg_logprob": -0.1771597181047712,
        "compression_ratio": 1.8229166666666667,
        "end": 1500,
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        "temperature": 0,
        "text": " The check win function can receive an argument.",
        "tokens": [
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        "end": 1502,
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        "no_speech_prob": 0.00017674463742878288,
        "seek": 149000,
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        "temperature": 0,
        "text": " Did the player switch or not?",
        "tokens": [
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        "temperature": 0,
        "text": " So when the player stays, we can say check win false.",
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        "temperature": 0,
        "text": " When the player switches, we can say check win true.",
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        "seek": 149000,
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        "text": " If the player switch, maybe it should be player switched.",
        "tokens": [
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        "seek": 151600,
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        "temperature": 0,
        "text": " If the player switched, total switch wins, plus plus.",
        "tokens": [
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        "text": " Otherwise, total stay wins, plus plus.",
        "tokens": [
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        "seek": 151600,
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        "temperature": 0,
        "text": " And then if the player loses, I'm not keeping track of the number of losses.",
        "tokens": [
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        "text": " By definition, that's the difference between the total plays and the number of wins.",
        "tokens": [
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        "seek": 151600,
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        "temperature": 0,
        "text": " So I think I'm good. I just need to put the stats on the page itself.",
        "tokens": [
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        "seek": 151600,
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        "temperature": 0,
        "text": " So another paragraph element, call it results.",
        "tokens": [
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        "temperature": 0,
        "text": " And here, let's show the win rates.",
        "tokens": [
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        "seek": 154400,
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        "temperature": 0,
        "text": " The switch rate is the total switch wins divided by the total switch plays.",
        "tokens": [
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        "temperature": 0,
        "text": " The stay rate is the total stay wins divided by the total stay plays.",
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        "avg_logprob": -0.18691739400227864,
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        "seek": 154400,
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        "temperature": 0,
        "text": " Then I can use a nice template literal to display a nicely formatted message",
        "tokens": [
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        "avg_logprob": -0.18691739400227864,
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        "seek": 154400,
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        "temperature": 0,
        "text": " with the data that is in those variables.",
        "tokens": [
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        "temperature": 0,
        "text": " And for the win rates, I want those to appear as percentages,",
        "tokens": [
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        "temperature": 0,
        "text": " so I'll multiply them by 100.",
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        "seek": 157400,
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        "temperature": 0,
        "text": " And then I can use the P5 number format function to only show it to two decimal places.",
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        "seek": 157400,
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        "temperature": 0,
        "text": " All right, I think we might be finished with this.",
        "tokens": [
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        "avg_logprob": -0.20906641128215384,
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        "seek": 157400,
        "start": 1595,
        "temperature": 0,
        "text": " Let's see if I have any errors.",
        "tokens": [
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        "seek": 157400,
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        "temperature": 0,
        "text": " I'm going to pick door number one.",
        "tokens": [
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        "avg_logprob": -0.20906641128215384,
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        "end": 1600,
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        "temperature": 0,
        "text": " I'm going to switch.",
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        "seek": 160000,
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        "temperature": 0,
        "text": " I forgot that this is HTML, so even though I put these nice line breaks in here,",
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        "temperature": 0,
        "text": " that means absolutely nothing. I need to put actual line breaks.",
        "tokens": [
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        "end": 1614,
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        "seek": 160000,
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        "temperature": 0,
        "text": " Let's give myself more space to see the canvas.",
        "tokens": [
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        "seek": 160000,
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        "temperature": 0,
        "text": " And here we go.",
        "tokens": [
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        "avg_logprob": -0.3360675018612701,
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        "seek": 160000,
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        "temperature": 0,
        "text": " I'm going to just play this a lot of times now.",
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        "avg_logprob": -0.3360675018612701,
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        "end": 1623,
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        "seek": 160000,
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        "temperature": 0,
        "text": " I'm going to play this a lot of times now.",
        "tokens": [
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        "temperature": 0,
        "text": " I'm going to play this a lot of times now.",
        "tokens": [
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        "seek": 162500,
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        "temperature": 0,
        "text": " I'm going to just play this a lot of times now.",
        "tokens": [
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        "seek": 162500,
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        "temperature": 0,
        "text": " After playing 44 times, I switched 22 times, I stayed 22 times.",
        "tokens": [
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        "temperature": 0,
        "text": " You can see my switch win rate is about 68%, and my stay win rate is about 41%.",
        "tokens": [
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        "temperature": 0,
        "text": " So obviously I've gotten extra lucky on both.",
        "tokens": [
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        "text": " Quite a bit luckier for staying. That should really be at one third.",
        "tokens": [
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        "avg_logprob": -0.16349020160612512,
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        "text": " 68 is quite close to two thirds.",
        "tokens": [
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        "avg_logprob": -0.16349020160612512,
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        "seek": 165200,
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        "temperature": 0,
        "text": " But the math that we started with is what we're seeing play out here",
        "tokens": [
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        "avg_logprob": -0.16349020160612512,
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        "temperature": 0,
        "text": " in playing the game over and over again.",
        "tokens": [
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        "temperature": 0,
        "text": " This would also be, by the way, a really great opportunity to use local storage.",
        "tokens": [
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        "temperature": 0,
        "text": " So if I stop the sketch and start it up again,",
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        "seek": 165200,
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        "temperature": 0,
        "text": " I would then see all of the plays that I did before.",
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        "text": " I did happen to just make a whole tutorial about local storage.",
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        "text": " So if you want to go watch that, then come back to this.",
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        "text": " I'll leave it as an exercise to the viewer.",
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        "text": " And I will add an extra code example for this video with local storage implemented.",
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        "text": " Also, if I haven't actually played a game, I get a divide by zero error.",
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        "text": " That's probably something that I should address.",
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        "text": " But as long as I play one switch and one stay, the error will go away.",
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        "temperature": 0,
        "text": " Before I leave you, let me attempt to tie everything I've done to Bayes' theorem.",
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        "text": " This is the famous Bayes' probability theorem.",
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        "text": " Let me first address what is meant by the notation here.",
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        "text": " So if we say something like P of A,",
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        "text": " this is the probability of the event A occurring.",
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        "text": " So if I'm flipping a coin and the event A is it landing on heads,",
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        "text": " the probability of A is 50 percent, one out of two times.",
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        "text": " This notation here, P A line B, this is known as conditional probability.",
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        "text": " Meaning there are two events, A and B.",
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        "text": " What's the probability of A occurring given B occurring?",
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        "text": " Bayesian inference is the idea of determining what is the probability of one of the events occurring",
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        "text": " given prior knowledge of a previous event.",
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        "text": " Now I'd like to try to tie this formula to the Monty Hall problem itself.",
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        "text": " Let's create the three doors and actually label them A, B, and C.",
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        "text": " So I'm going to start by picking door C.",
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        "text": " Monty Hall is going to reveal door B.",
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        "text": " What is the probability then that I win if I switch to A?",
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        "temperature": 0,
        "text": " Given the event that Monty Hall reveals door B,",
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        "text": " what is the probability that A is the winner?",
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        "text": " That is what this part of the formula is describing.",
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        "text": " Now we just need to figure out each of these three components.",
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        "text": " Well, let's start with the easiest one first.",
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        "text": " The prior probability, just given nothing, no information whatsoever,",
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        "text": " that the winner, the prize is under door A is one out of three.",
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        "temperature": 0,
        "text": " P of B, B is the event that Monty Hall reveals door B.",
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        "temperature": 0,
        "text": " What is the probability that Monty Hall will reveal door B if the prize is under A?",
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        "text": " Well, that's 100%. 100%.",
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        "text": " Because if I picked C and the prize is under A, Monty Hall has to show door B.",
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        "text": " So that's 100% or one.",
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        "text": " Now we've got a slightly trickier one.",
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        "text": " Given no information, what's the probability that Monty Hall reveals door B?",
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        "text": " So I've picked C, but I don't know the prize is not necessarily under A.",
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        "text": " We don't have that prior information.",
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        "text": " So the probability that Monty Hall reveals door B in this case is just a flip of a coin, 50%.",
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        "text": " Maybe it's going to be A, maybe it's going to be B.",
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        "text": " We don't have any information to tell us one or the other.",
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        "text": " So now one times one third divided by one half.",
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        "text": " Guess what that is?",
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        "text": " Two thirds.",
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        "text": " The probability, if I started with C, that A is the winner given Monty Hall revealing B is two out of three.",
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        "text": " There's a lot more to be said about this kind of probability analysis.",
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        "text": " I will include some excellent references to Bayes' theorem and the Monty Hall problem in the video's description if you want to take a look at those.",
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        "text": " One thing that I really missed that would be fun to try is could you make the number of doors a variable?",
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        "text": " So suddenly you have a version of this with 10 doors or 100 doors and how many doors are revealed?",
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        "text": " Oh, so many possibilities.",
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        "text": " Board the train, make your own creative twist on this, share it with me, and I will see you next time.",
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        "text": " Bye.",
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    "transcription": " Hello and welcome to Let's Make a......Deal! Behind one of these three doors is today's prize, a trip on the Coding Train Express. Behind the other two doors is a goat. It's up to you to pick one of these doors. Which one will you pick? I can hear the people of the internet shouting out to me, door number three. Ah, but before I reveal what's behind door number three, let me show you what's behind door number one. Now I'm going to offer you a one-time only chance to switch. Switch to door number two or do you want to keep door number three? Think about it. Should you switch? What is the probability that the prize is behind door number three? And what is the probability that the prize is behind door number two? This is the classic Monty Hall problem which originated in the American television show Let's Make a Deal back in the 1970s. The answer to the problem is you should absolutely switch. If you switch, you will have a two out of three chances, 66.6666666666% chance of the prize being behind door number two. This might seem counterintuitive. Shouldn't it just be 50-50? There's two of them. It's definitely not behind door number one, so it's either behind door number two or door number three. No, that is not the case. In today's coding challenge, I'm going to first explain to you why you absolutely should switch. And then I'm going to code a simple p5.js simulation of the game that you can play over and over again to test your different theories about what the proper strategy and probabilities might be. Let's recap the problem. We've got three doors. Behind one of these doors is a prize, a train. Let's say it's behind door number two. There, that's my train. Then behind doors one and three is a goat. I'm going to have to draw a goat now. It's more like a cat, but it'll have to do. It's important to remember that the host, played by me or Monty Hall, really, knows where the prize is. Let's think about all the possible ways this game could play out and build a table describing those ways and look at how often does the player win if they switch and how often do they win if they don't switch. So what are the stages? First, there's the player's pick. Then there's the door revealed by the host. Then there's the question of does the player switch or not? And of course we have the question, do they win? All right, let's say the player starts by picking door number one. The host then, knowing that the prize is in door number two, has to reveal door number three to show a goat. Now remember, the player's picked door number one. If they switch, they'll be switching to door number two. Let's just assume for the sake of argument that the player is always going to switch. So yes, the player switches. Did the player win? Yes, the player wins. Check. Now let's look at the scenario where the player starts by picking door number two. Now this is an interesting scenario because if the player has picked door number two, Monty Hall has to reveal a door that has a goat behind it. It could be either one or three. So let's just say that Monty Hall reveals door number three this time. Again, we've got another door number three. The player has picked door number two. Should they switch to door number one? We know they shouldn't, but let's say in this scenario they do. So yes, they switch, and no, they do not win. The last possibility here is that the player starts by picking door number three. They pick door number three. Monty Hall has to reveal door number one, the only other door with a goat behind it. The player switches, switching to door number two, and yes, they win. There's only three ways this game can play out. The player starting by picking door number one, starting by picking door number two, or starting by picking door number three. If the player always switches, the player will win two out of three times. Think about it this way. Remember, you don't know where the prizes are. You pick door number one. And I'm going to say to you now, well, would you like to keep door number one, or would you like to win if it's behind either doors two or three? Either one. You can have two doors. You don't need just one door. Stick with just one door, or would you like two doors? That's exactly what this problem is. You would want to pick two doors, because it's more likely two out of three times to be behind one of these two doors than the original one that you picked. Let's look at it one more way. I'm going to show you a hundred doors. All right, fine. Let's just do 50 doors. I don't feel like drawing the rest. Pick any one of these doors. There's only a prize behind one of them. This train ride, this glorious train ride you're going to win is somewhere behind one of these 50 doors. Oh, oh, you want to pick this one? Okay. You picked this one. A colored in purple to indicate it's the one you picked. Now, I'm going to reveal to you that there's a goat behind 48 other doors. Would you like now to switch to this door and see if the prize is there? Or would you like to keep your original door? I mean, hello, you're going to want to switch to this door, right? What's the chance that the prize happens to be your one out of 50 chance that you happen to just pick? Or I revealed all of these other, I mean, it could be there. There could be a goat here, but I remember, I know all of these are goats. So I'm going to leave one open. If you didn't pick the prize, I have to leave the one with the prize open. Would you want to switch? I think you would. There's also a very specific probability analysis known as the Bayes theorem that we could apply to show this exact two out of three probability. Or in this case, it would be a 49 out of 50 probability. You have a one out of 50 chance of it being your original pick. Or if you switch, you have a 49 out of 50 chance of winning. But you're probably not here wanting to listen to me drone on and on and diagram on the whiteboard about probability and the Monty Hall problem. We could build a P5JS sketch in code that simulates the Monty Hall problem, run it thousands of times and see if my analysis proves to be correct. Also, by the way, who is to say that the goat isn't the true prize after all? I would love to have some wonderful, beautiful goats. My usual approach to this would be to start drawing doors in the canvas and checking where the mouse is clicking. But I think I'd actually like to try this with DOM elements, meaning HTML elements that are not canvases that appear on a web page, which if you didn't know, you could also do in P5. So I'm actually going to do something quite exciting here and say no canvas. I'm going to write a little loop to create three doors. Let's make an array to hold the data for those three doors. And each door will be a div on the web page. Let's start by putting a goat in each one, and then I will pick one randomly and put the prize there. So every time I run this sketch, I see three emojis, only one of which is a train. Now, of course, they're really tiny. So let's work on some designy things. Let's create a CSS class. A CSS class is a way of designating a particular set of styles to be applied to any element on the web page. This isn't a full lesson about CSS, obviously. I have barely no CSS. But I will put resources in the video description and up on the screen here, as well as some other videos I have that go through CSS in a bit more detail. But right here in the P5 web editor, I can go over to the style.css file. I can create a door class, and I can start to add some properties to it. Now, what I'd really like to do is center those emojis in the div. Thankfully, the live Twitch chat that's watching along here has given me some tips of how to do this. Let's make the emojis a little bit bigger. Let's put a little margin between the divs. And I want to see them in a row, so I think I can add display flex to the body. Great. Now we've got our three doors there. So the tricky thing here is I want to make a div that knows whether it's a goat or a train, but I don't want to reveal that goat or train. I could create my own wrapper. Like, I could create a door class that has a div. But I think since these are just JavaScript objects, a P5 element, I can attach other properties to them. So I'm going to make the div with no text. And instead, I'll add a new property called prize, which is by default a goat. Let's call this winning door. I'll say the winning doors prize is the train. So now I have three doors. Behind the scenes, there's a variable attached to each of those divs that's holding on to either a goat or a train. But the viewer, the player, I cannot see which one is which. Now what I want to do is attach an event to each door to do something when I click on it. The clicking on the door will be the act of selecting that one. I can do this with the P5 event mouse pressed. And whenever the mouse is pressed, I want to execute a function. I'll call it reveal. One of the nice things that P5 does behind the scenes is it binds that particular function reveal to the DOM element that was triggered by the event. And that binding is embedded inside the keyword this. I have a whole video all about the this keyword and how this works. But for now, what you will see is if I just say console log this.prize, when I click on each door, we'll see the prize in the console. That one's a goat. That one's also a goat. And that one's the train. Running it one more time, we have train goat goat. So now I need something to keep track of the state. There's the moment I pick. There's the moment I reveal. There's the moment I switch. And then whether I win or not. So let's create a variable called state to keep track of the game state. And we're going to start with pick, meaning we're waiting for the player to pick. Now, I'm going to keep this console log here, which will help me know what's going on. And this reveal is a little bit of a misnomer, actually, because we don't want to reveal the one that we picked. We want to reveal a different one that has a goat behind it. So something that would help me a little bit is to also have each div know its index into the array. So here the div also has a property called index that I'm storing. Where is it in the doors array? So when I click, I should see 0, 1, 2. So once I've picked, I need Monty Hall to reveal one of the other doors. So Monty Hall needs to know which doors can they reveal. We'll make a new array called options. As long as it's not the door that the player picked, and the prize is not the train, I can make this a little less wordy by putting the door in a separate variable. Oh, this, this. As long as i is not this.index, right. I don't know. I was so confused there. As long as the door I'm looking at is not the one that was clicked on, and that door is not the prize, then it's something that could be revealed. Now remember, if the player didn't pick the right door in the first place, there's only going to be one thing left in the options. But I need to check all the possibilities, because if they did pick the prize, then Monty Hall can choose to reveal one of two doors. But we'll pick one of the options randomly. If there's just one, there's only one it can pick. And we will put in the div the actual prize itself. Okay, I'm going to pick door number one, and we should see a goat appear in either door two or three. What did I do wrong? Oh, I did it if it's... I have to say if it's not equal to the train. Okay, that was a disaster. Let's try this again. I'm going to pick door number one. There's that goat. Let's run it again. There's the goat. So we always will see a goat, no matter what I pick. Another thing I think I should add here is something to indicate which door was picked. So let's put a little green. So that's highlighting which one I've picked. Now is really the moment where some animation or some thoughtful interaction design would be a great addition, and I hope you, the viewer, will make a more intuitive and smooth way of playing out this game. But I'm just going to really quickly toss in a couple buttons. One button for if you want to switch doors, or a different button if you want to stay put. So when I click on any of the doors, those two buttons will now suddenly appear. Now they look a little weird here because I have this CSS display property as flex in the entire body. So probably I should make a container for the doors. So I'm going to manually put in a div called doors. Reference the ID with the hash symbol. Put the flex display there. Then I can put the door divs in the doors container by using the p5 parent function. Then my buttons look a little bit more normal there just on the next line. They are kind of small, so let me make the font size a bit bigger. And give them a little margin. Okay, again, very crude interaction design. But now I can choose whether I want to switch or stay. This is also maybe a good moment for me to, now that I've got some code worked out, kind of refactor it. Like maybe it would be nice to look at the code to see there's a pick function, a reveal function, a switch function, and then a win function. Right now I only have a reveal function, which is kind of doing both of these first two steps. So when I click on a door, what I'm really doing is picking that door. And let's have a variable called pick door, which is set equal to this. The div that was clicked on, which is held in the keyword this, based on p5 binding it to the mouse pressed event. Then I can call reveal. Reveal looks out of the doors and figures out what are the ones that can be revealed. As long as it's not the prize or the picked doors index. This setting it to green is really a thing we're doing when we're picking the door. And here we are revealing one of the other doors that has a goat. Creating the buttons and the buttons event will be the switch function. I'm going to make the door that was revealed also a global variable. So if the player switches, I need to reassign pick door to the door that wasn't picked and wasn't revealed. So by switching the new pick is the door that hasn't been picked or revealed. And that is now the pick door. And then we have to check. Did I win? We'll call a function called check win and the player stay means actually you don't switch. So just go right to this check win function. And let's also reveal all the prizes. Here we go. I'm going to pick door number one. Oh, I got an error. Door reveal not being defined. Oh, I don't remember when I made this mistake, but I called it revealed door and then said door reveal. So the revealed door is the one that I want to put the new content in. Okay, here we go. I'm going to pick this door. What's going on? Oh, and then reveal door.prize. Okay, finally, I'm going to get it. I'm going to pick this door. It's showing me the goat. So I could switch or I could stay. Let's try switching. And I won. So this, what, let's, let's, I think this should be a different color. I'm going to make this blue just to show that I've selected green meaning I won. Pick this door. I'm going to switch and I won. And let's get rid of the blue after I switch. I think I have everything now. I'm going to pick a door. I'm going to switch and I lost. I'm going to play again. I'm going to pick a door. I'm going to switch and I won. It's working. Could use a lot of improvement. Let's clean up just a few things. One is I have this wonderful state variable that I never bothered to change. So the moment I pick the door, I should change the state. And I made it a const for some reason, which it shouldn't be. So I'm changing the state to reveal. The reason why this is important is that picking event should only happen if the state is pick. So now if I were to click again in the middle of the game, it wouldn't change anything that's happening. This code would not execute. I am probably overusing global variables here, but it would be helpful to actually have these buttons be global variables that I could just show or hide as needed. So I'm actually going to take these and put them in setup. Hide them and then just show them when it's time to prompt the user. Then after the player has either chosen to switch or stay, I can hide those buttons again. Pick a door, switch, and I won. Let's add some CSS for the you win message. And let's create a play again button. Now, of course, a lot of these DOM elements don't need to be generated with P5 functions. In a properly designed page, you might want to do all of this with HTML and CSS. But this is just a quick way that I'm doing it to get this going. That said, to finish off this play again button, I need to write the start over function. What do we do to start over? Well, we need to pick a new prize again. Start them all off as goats. Pick a random one to be the winner. Now that I've done this, I actually don't need to do this here in setup anymore. I can just say start over. I should also make sure I clear any background color or text that was in the div. And hide the play again button. All right, let's see if this works. I'm going to pick door number one. I'm going to switch. I think I forgot to show the play again button. Play again dot show. One more time. Let's pick door number three and let's switch. I won. Let's play again. Still says you win there. I need a permanent place for the win or lose message. Call that outcome P for outcome paragraph. Definitely need to clear it when we start over. In setup, you need to create it. And then the message, instead of creating a new paragraph, we just put it in the existing one. All right, ready for this? All right, I'm going to pick door number two. I never seem to pick door number two to start. The goat is revealed as door number three. Should I switch? Should I stay? I'm going to switch. Whoops. What just happened there? Nice little typo there. I would have lost. So good thing I got that error. I'm going to pick door number two. The goat is revealed as door number one. I'm going to switch. And I won. Let's play again. I'm going to pick door number three. No, it's not working. Oh, I've got to set the state back to pick. So ultimately, I don't know if I really needed this state variable, or I'm certainly not using it very effectively, because I only have it as pick or not pick, essentially. But I'll let you figure out how to improve that in your own version of this. But when I start over, I definitely need to set the state back to pick. Here we go. I'm going to pick door number two. I'm going to switch. I'm going to play again. I'm going to pick door number one. I'm going to switch. I'm going to play again and pick door number three. I'm going to switch. I'm going to play again. Door one. Switch. I am just winning over and over again. I am so good at this game. I'm ready to wrap this up. I mean, what I really would like to do, and I'll create a version of it that just picks automatically and switches automatically, running it hundreds of times per second. And I'm showing that to you right now over here. But what I'm going to do in this video itself is just add some code to track the win rate for switching and the win rate for staying put. And if the math that I demonstrated at the beginning of the video is correct, we should see a win rate of approximately two out of three times for switching and one out of three times for staying put. So I need a variable for total plays, total switches. Actually, I don't need the total plays. I need to know how many times did I switch and how many times did I stay. So I'll call that total switch plays. Awkward variable names. Then I need switch wins and stay wins. Every time the player switches, I need to increase the number of switch plays. Every time the player stays, ah, but I don't have a function for staying. So let me actually go and put that in. So instead of when you stay going directly to check win, let's write a player stay function. And the only thing that happens in that function is we increase the number of total stay plays and then go to check wins. Oh, but when I check the win, how do I know whether I switched or not? And this is a typo here. All right, again, so much to refactor later. But let's introduce another variable. Oh, no, no, I don't need another variable. I know exactly what to do. The check win function can receive an argument. Did the player switch or not? So when the player stays, we can say check win false. When the player switches, we can say check win true. If the player switch, maybe it should be player switched. If the player switched, total switch wins, plus plus. Otherwise, total stay wins, plus plus. And then if the player loses, I'm not keeping track of the number of losses. By definition, that's the difference between the total plays and the number of wins. So I think I'm good. I just need to put the stats on the page itself. So another paragraph element, call it results. And here, let's show the win rates. The switch rate is the total switch wins divided by the total switch plays. The stay rate is the total stay wins divided by the total stay plays. Then I can use a nice template literal to display a nicely formatted message with the data that is in those variables. And for the win rates, I want those to appear as percentages, so I'll multiply them by 100. And then I can use the P5 number format function to only show it to two decimal places. All right, I think we might be finished with this. Let's see if I have any errors. I'm going to pick door number one. I'm going to switch. I forgot that this is HTML, so even though I put these nice line breaks in here, that means absolutely nothing. I need to put actual line breaks. Let's give myself more space to see the canvas. And here we go. I'm going to just play this a lot of times now. I'm going to play this a lot of times now. I'm going to play this a lot of times now. I'm going to just play this a lot of times now. After playing 44 times, I switched 22 times, I stayed 22 times. You can see my switch win rate is about 68%, and my stay win rate is about 41%. So obviously I've gotten extra lucky on both. Quite a bit luckier for staying. That should really be at one third. 68 is quite close to two thirds. But the math that we started with is what we're seeing play out here in playing the game over and over again. This would also be, by the way, a really great opportunity to use local storage. So if I stop the sketch and start it up again, I would then see all of the plays that I did before. I did happen to just make a whole tutorial about local storage. So if you want to go watch that, then come back to this. I'll leave it as an exercise to the viewer. And I will add an extra code example for this video with local storage implemented. Also, if I haven't actually played a game, I get a divide by zero error. That's probably something that I should address. But as long as I play one switch and one stay, the error will go away. Before I leave you, let me attempt to tie everything I've done to Bayes' theorem. This is the famous Bayes' probability theorem. Let me first address what is meant by the notation here. So if we say something like P of A, this is the probability of the event A occurring. So if I'm flipping a coin and the event A is it landing on heads, the probability of A is 50 percent, one out of two times. This notation here, P A line B, this is known as conditional probability. Meaning there are two events, A and B. What's the probability of A occurring given B occurring? Bayesian inference is the idea of determining what is the probability of one of the events occurring given prior knowledge of a previous event. Now I'd like to try to tie this formula to the Monty Hall problem itself. Let's create the three doors and actually label them A, B, and C. So I'm going to start by picking door C. Monty Hall is going to reveal door B. What is the probability then that I win if I switch to A? Given the event that Monty Hall reveals door B, what is the probability that A is the winner? That is what this part of the formula is describing. Now we just need to figure out each of these three components. Well, let's start with the easiest one first. The prior probability, just given nothing, no information whatsoever, that the winner, the prize is under door A is one out of three. P of B, B is the event that Monty Hall reveals door B. What is the probability that Monty Hall will reveal door B if the prize is under A? Well, that's 100%. 100%. Because if I picked C and the prize is under A, Monty Hall has to show door B. So that's 100% or one. Now we've got a slightly trickier one. Given no information, what's the probability that Monty Hall reveals door B? So I've picked C, but I don't know the prize is not necessarily under A. We don't have that prior information. So the probability that Monty Hall reveals door B in this case is just a flip of a coin, 50%. Maybe it's going to be A, maybe it's going to be B. We don't have any information to tell us one or the other. So now one times one third divided by one half. Guess what that is? Two thirds. The probability, if I started with C, that A is the winner given Monty Hall revealing B is two out of three. There's a lot more to be said about this kind of probability analysis. I will include some excellent references to Bayes' theorem and the Monty Hall problem in the video's description if you want to take a look at those. One thing that I really missed that would be fun to try is could you make the number of doors a variable? So suddenly you have a version of this with 10 doors or 100 doors and how many doors are revealed? Oh, so many possibilities. Board the train, make your own creative twist on this, share it with me, and I will see you next time. Bye.",
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