Yatzy odds
Two kinds of numbers. The first table is exact: the probability of making each box within one turn when you keep the right dice every time, computed over every possible roll. The second comes from simulated games and tells you what a normal total looks like.
Box odds are exact: every possible roll is counted. Score averages come from simulated games. What to keep →
Yatzy: chance of making each box in one turn
| Box | First roll | First roll, exact | Within 3 rolls | Odds |
|---|---|---|---|---|
| One pair | 90.7 % | 49/54 | 99.9 % | more likely than not |
| Two pairs | 27.0 % | 175/648 | 74.2 % | more likely than not |
| Three of a kind | 21.3 % | 23/108 | 74.3 % | more likely than not |
| Four of a kind | 2.0 % | 13/648 | 29.1 % | 1 in 3.4 |
| Small straight | 1.5 % | 5/324 | 19.7 % | 1 in 5.1 |
| Large straight | 1.5 % | 5/324 | 19.7 % | 1 in 5.1 |
| Full house | 3.9 % | 25/648 | 36.3 % | 1 in 2.8 |
| Yatzy | 0.077 % | 1/1296 | 4.6 % | 1 in 22 |
American 13-category: chance of making each box in one turn
| Box | First roll | First roll, exact | Within 3 rolls | Odds |
|---|---|---|---|---|
| Three of a kind | 21.3 % | 23/108 | 74.3 % | more likely than not |
| Four of a kind | 2.0 % | 13/648 | 29.1 % | 1 in 3.4 |
| Full house | 3.9 % | 25/648 | 36.3 % | 1 in 2.8 |
| Small straight | 15.4 % | 25/162 | 61.5 % | more likely than not |
| Large straight | 3.1 % | 5/162 | 26.1 % | 1 in 3.8 |
| Yatzy | 0.077 % | 1/1296 | 4.6 % | 1 in 22 |
Maxi Yatzy: chance of making each box in one turn
| Box | First roll | First roll, exact | Within 3 rolls | Odds |
|---|---|---|---|---|
| One pair | 98.5 % | 319/324 | 100.0 % | more likely than not |
| Two pairs | 55.6 % | 4325/7776 | 94.9 % | more likely than not |
| Three pairs | 3.9 % | 25/648 | 27.3 % | 1 in 3.7 |
| Three of a kind | 36.7 % | 119/324 | 88.9 % | more likely than not |
| Four of a kind | 5.2 % | 203/3888 | 50.1 % | more likely than not |
| Five of a kind | 0.40 % | 31/7776 | 15.7 % | 1 in 6.4 |
| Small straight | 5.4 % | 35/648 | 43.7 % | 1 in 2.3 |
| Large straight | 5.4 % | 35/648 | 43.7 % | 1 in 2.3 |
| Full straight | 1.5 % | 5/324 | 19.7 % | 1 in 5.1 |
| Full house | 17.0 % | 1325/7776 | 76.1 % | more likely than not |
| Villa | 0.64 % | 25/3888 | 16.3 % | 1 in 6.2 |
| Tower | 0.96 % | 25/2592 | 19.5 % | 1 in 5.1 |
| Yatzy | 0.013 % | 1/7776 | 2.0 % | 1 in 49 |
Good scores by variant
20,000 games per variant, played by the site's own greedy computer player. A thinking human beats it, so treat these as a floor: if you land above the 90th percentile you are playing well.
| Variant | Average | Median | Bottom 10 % | Top 10 % | Bonus | Yatzy |
|---|---|---|---|---|---|---|
| Yatzy | 186.8 | 182 | 136 | 245 | 23.3 % | 32.9 % |
| Forced Yatzy | 144.2 | 151 | 89 | 192 | 59.6 % | 4.6 % |
| Maxi Yatzy | 302.7 | 287 | 221 | 397 | 11.6 % | 32.3 % |
| American 13-category | 215.0 | 206 | 158 | 272 | 11.3 % | 30.6 % |
Exact probabilities use dynamic programming over all dice combinations with optimal keeps for that one box. Score averages come from 20 000 simulated games per variant, played by the site's own computer player with a fixed seed, so they are reproducible. Rules