Yahtzee Full House odds
That makes Full House the 7th highest-scoring category of 13 on the sheet, if you spend a whole turn chasing it and nothing else. It pays a fixed 25 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 Full House from the first roll alone is worth 0.96; using the full turn is worth 9.07.
| Rolls available | Expected score | Chance of hitting it |
|---|---|---|
| First roll only | 0.96 | 3.86% |
| First roll + 1 reroll | 4.78 | 19.12% |
| Full turn (2 rerolls) | 9.07 | 36.29% |
Each row assumes you reroll optimally for this category alone, and nothing else. The two rerolls multiply the first-roll figure by 9.4×.
Every score you can end up with
Expected score is an average, and averages hide the shape. Full House only ever ends one of two ways: you get it, or you don’t. You end the turn with nothing 63.71% of the time.
Exact probability of each final score, playing the whole turn for Full House. 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 6 genuinely different positions for Full House — 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 |
|---|---|---|
| 3.86% | 25.00 | |
| 23.15% | 13.89 | |
| 17.36% | 7.64 | |
| worst tier | 9.26% | 4.78 |
Top three tiers, then the worst one. The worst tier covers 6 of the 252 distinct opening rolls and lands 9.26% of the time.