Yahtzee Strategy Calculator

How Yahtzee Expected Value Works

When you hold certain dice and reroll others, each rerolled die has 6 equally likely outcomes. For 2 rerolled dice, there are 36 possible outcomes; for 3, there are 216. This calculator evaluates every outcome for all 32 possible hold combinations (2^5), computing the average score you can expect in each of the 13 categories. The recommendation shows which hold gives you the highest expected score overall.

Understanding the Upper Section Bonus

The upper section (Ones through Sixes) awards a 35-point bonus if your total reaches 63 or more. This means averaging 3 of each number per category. When deciding which dice to keep, consider whether scoring in the upper section helps you reach this threshold. Sometimes a slightly lower expected value in the upper section is worth it for the bonus.

The Math Behind Optimal Play

Yahtzee has about 7.5 billion possible game states when you account for dice rolls, categories, and scoring. While fully optimal play requires dynamic programming across all remaining turns, this calculator provides the optimal single-turn strategy — the mathematically best hold for your current roll targeting any specific category. For most recreational play, this single-turn optimization is sufficient to dramatically improve your scores.

Common Strategy Questions

Three of a kind vs. straight: With three matching dice (e.g., 3,3,3,5,6), keeping the triplet usually beats going for a straight. The expected value for Three of a Kind or building toward Four of a Kind / Yahtzee is typically higher than the probability-weighted value of completing a straight.

When to go for Yahtzee: If you already have four matching dice, always go for Yahtzee — you have a 1/6 chance (16.7%) of hitting it for 50 points. Even with three matching, the expected payoff of trying for Yahtzee can be significant.