Yahtzee Chance odds
That makes Chance the 1st highest-scoring category of 13 on the sheet, if you spend a whole turn chasing it and nothing else.
What the rerolls buy you
A turn is three rolls: the first, then two rerolls of any dice you don’t keep. Chasing Chance from the first roll alone is worth 17.50; using the full turn is worth 23.33.
| Rolls available | Expected score | Chance of scoring |
|---|---|---|
| First roll only | 17.50 | 100.00% |
| First roll + 1 reroll | 21.25 | 100.00% |
| Full turn (2 rerolls) | 23.33 | 100.00% |
Each row assumes you reroll optimally for this category alone, and nothing else. The two rerolls multiply the first-roll figure by 1.3×.
Every score you can end up with
Expected score is an average, and averages hide the shape. Playing a full turn for Chance, the single likeliest result is 24 at 12.29%. There is no way to score zero — every roll scores something.
Exact probability of each final score, playing the whole turn for Chance. The highlighted bar is the likeliest outcome, not the best one.
How much the first roll decides
Once the first roll lands, you are in one of only 21 genuinely different positions for Chance — every roll inside a tier is worth exactly the same, because the optimal reroll treats them identically.
| Example roll | How often | Turn is now worth |
|---|---|---|
| 0.01% | 30.00 | |
| 0.06% | 29.00 | |
| 0.26% | 28.25 | |
| worst tier | 13.17% | 21.25 |
Top three tiers, then the worst one. The worst tier covers 56 of the 252 distinct opening rolls and lands 13.17% of the time.