rollr
Result of 2,000 simulated games, run on 6 October 2026. In every game the three bots (Greedy, Bonus-Aware, Optimal-DP) play against each other, each with its own dice. Standard rules: 13 rounds, 35 bonus points for 63 or more points in the upper section, no extra points for a second five of a kind.
Scores and wins
| Strategy | Wins | Win rate | Avg score | ±95% | Min | Max | Bonus | Five of a kind scored | Five of a kind per turn |
|---|---|---|---|---|---|---|---|---|---|
| Greedy | 423 | 21.1% | 215.2 | 1.7 | 106 | 326 | 13.9% | 31.0% | 2.67% |
| Bonus-Aware | 437 | 21.9% | 215.7 | 1.7 | 108 | 326 | 22.9% | 30.9% | 2.68% |
| Optimal-DP | 1165 | 58.2% | 246.8 | 1.7 | 96 | 339 | 69.8% | 34.6% | 3.17% |
Wins and the bonus
| Strategy | Wins with bonus | Win rate with bonus | Win rate without bonus |
|---|---|---|---|
| Greedy | 36.9% | 56.1% | 15.5% |
| Bonus-Aware | 48.7% | 46.5% | 14.5% |
| Optimal-DP | 84.6% | 70.6% | 29.6% |
| All | 66.9% |
How to read the columns
Wins: games in which the bot had the highest score. A tie counts as a win for every bot involved, which is why the wins add up to 2,025 instead of 2,000.
±95%: half-width of the 95% confidence interval of the average score.
Bonus: share of games in which the bot reached the upper section bonus.
Five of a kind scored: share of games in which the bot scored five of a kind at least once.
Five of a kind per turn: share of all turns (13 per game) that ended with five equal dice.
Wins with bonus: share of the bot's wins in which it had the bonus.
Win rate with bonus / without bonus: share of games won among the games with and without the bonus.
The mathematical optimum for these rules is an average of 245.87 points. The Optimal-DP bot reaches 246.8 ± 1.7 points in this run, which matches the optimum within the margin of error.