Yahtzee Four of a Kind odds
That makes Four of a Kind the 4th lowest-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 Four of a Kind from the first roll alone is worth 0.35; using the full turn is worth 5.61.
| Rolls available | Expected score | Chance of scoring |
|---|---|---|
| First roll only | 0.35 | 2.01% |
| First roll + 1 reroll | 2.42 | 13.23% |
| Full turn (2 rerolls) | 5.61 | 27.74% |
Each row assumes you reroll optimally for this category alone, and nothing else. The two rerolls multiply the first-roll figure by 16.0×.
Every score you can end up with
Expected score is an average, and averages hide the shape. Playing a full turn for Four of a Kind, the single likeliest result is 0 at 72.26%, and you come away with nothing 72.26% of the time.
Exact probability of each final score, playing the whole turn for Four of a Kind. 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 32 genuinely different positions for Four of a Kind — 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 | 0.77% | 2.53 |
Top three tiers, then the worst one. The worst tier covers 1 of the 252 distinct opening rolls and lands 0.77% of the time.