Yahtzee Category Odds

Assuming you reroll purely to maximize one target category over a full turn (initial roll plus two rerolls), here’s the exact expected score — and, for the fixed-score categories, the exact probability of completing it.

The odds of rolling a Yahtzee in a single turn: exactly 4.6029%, if you reroll everything toward it from the first roll. That’s worse than 1-in-20 — which is exactly why it’s worth 50 points.

Expected score per category under optimal single-category rerolling -- not what you’d actually score if forced to pick the best category after the fact, which would be higher.

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