A programmatic attempt at finding the optimal strategy for playing the dice game Farkle.
Originally, my hope was to learn some insight that would help me when playing the game with friends. I built a number of different simple algorithms which would determine which were the most efficient. Most Farkle players tend to be fairly conservative, and I hoped that I might find that being more aggressive would lend me an advantage.
Instead, I found the opposite. Playing more aggressive, on aggregate, is the worse play. Instead, players should take scores whenever possible, and pretty much never roll fewer than 2 dice.
The following figures are determined over 10,000 rounds for each algorithm. As you can see, there's a very high amount of variance present in each of the algorithms, and none of them have a mean time to 10K that would win most games of Farkle against live opponents.
| Player Name | Mean Rounds to 10K | Median Rounds to 10K | Standard Deviation | Minimum Rounds to 10K | Maximum Rounds to 10K |
|---|---|---|---|---|---|
| HoldOnOneHundred | 28.82 | 29 | 4.18 | 15 | 50 |
| HoldOnTwoHundred | 26.36 | 26.5 | 4.14 | 14 | 45 |
| HoldOnThreeHundred | 28.26 | 28 | 5.96 | 13 | 58 |
| HoldOnFourHundred | 29.94 | 30 | 7.01 | 11 | 60 |
| HoldOnFiveHundred | 32.13 | 32.5 | 8.11 | 12 | 70 |
| HoldOnFiveHundredUnlessSix | 34.65 | 35 | 10.03 | 10 | 81 |
| HoldOnSixHundred | 37.92 | 39 | 11.27 | 11 | 97 |
| HoldOnSevenHundred | 47.92 | 49 | 16.23 | 11 | 132 |
| HoldOnEightHundred | 57.93 | 59 | 21.11 | 12 | 191 |
| HoldOnNineHundred | 60.95 | 62 | 22.15 | 14 | 162 |
| HoldOnThousand | 61.85 | 63 | 22.51 | 11 | 190 |
| ThreeHundredRound | 25.32 | 25 | 3.65 | 14 | 41 |
| FiveHundredRound | 28.88 | 29 | 5.99 | 14 | 57 |
| SevenHundredRound | 28.63 | 29 | 7.25 | 11 | 65 |
| FifteenHundredRound | 57.14 | 58 | 23.57 | 12 | 224 |
| TwoThousandRound | 104 | 108 | 52.47 | 11 | 480 |
| HoldOnFive | 28.13 | 28 | 4.88 | 13 | 48 |
| HoldOnFour | 25.59 | 26 | 4.24 | 11 | 43 |
| HighestDiceFour | 25.6 | 26 | 4.33 | 10 | 44 |
| HoldOnThree | 23.56 | 24 | 3.83 | 9 | 40 |
| HoldOnTwo | 23.48 | 24 | 4.3 | 9 | 42 |
| HoldOnOne | 29.36 | 30 | 6.9 | 9 | 59 |
| FourIfFiveHundred | 34.53 | 35 | 10.02 | 8 | 89 |
| TwoIfFiveHundred | 44.83 | 46 | 14.1 | 9 | 124 |
| ThreeIfFiveHundred | 34.71 | 35 | 10.03 | 9 | 91 |
| TwoHundredRound | 25.89 | 26 | 3.49 | 15 | 41 |
| ThreeIfTwoHundred | 23.47 | 24 | 3.89 | 11 | 39 |
| TwoIfThreeHundred | 23.53 | 24 | 4.44 | 10 | 44 |
| FourIfSevenHundred | 56.45 | 57 | 20.09 | 12 | 165 |
| FiveIfNineHundred | 76.21 | 78 | 28.97 | 15 | 225 |
| DecreasinglyAggressive | 28.24 | 28 | 6.41 | 12 | 61 |
| IncreasinglyAggressive | 30.08 | 30 | 6.93 | 12 | 66 |