Yahtzee Small Straight odds
That makes Small Straight the 2nd highest-scoring category of 13 on the sheet, if you spend a whole turn chasing it and nothing else. It pays a fixed 30 when you get it, so the expected score is just that times the completion chance.
What the rerolls buy you
A turn is three rolls: the first, then two rerolls of any dice you don’t keep. Chasing Small Straight from the first roll alone is worth 4.63; using the full turn is worth 18.46.
| Rolls available | Expected score | Chance of hitting it |
|---|---|---|
| First roll only | 4.63 | 15.43% |
| First roll + 1 reroll | 12.35 | 41.18% |
| Full turn (2 rerolls) | 18.46 | 61.54% |
Each row assumes you reroll optimally for this category alone, and nothing else. The two rerolls multiply the first-roll figure by 4.0×.
Every score you can end up with
Expected score is an average, and averages hide the shape. Small Straight only ever ends one of two ways: you get it, or you don’t. You end the turn with nothing 38.46% of the time.
Exact probability of each final score, playing the whole turn for Small Straight. 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 7 genuinely different positions for Small Straight — 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 |
|---|---|---|
| 15.43% | 30.00 | |
| 10.03% | 24.07 | |
| 7.33% | 19.75 | |
| worst tier | 13.17% | 12.35 |
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.