A Free Browser Yahtzee Opponent Plays for the Best Average Until Round 11, Then Switches to Playing to Beat You

The page opens with a flat claim: “The computer does not guess.” It lists every distinct outcome of each remaining roll and works backward through the game with dynamic programming. Its table of reachable scorecard states is precomputed and exact, per the game’s own rules text. Through round 11, the opponent picks the box that maximizes its expected final total.

Then the plan changes. For the last two rounds the page says the computer switches to a mode called Match-W. Instead of chasing the best average, it maximizes the probability of winning plus half the probability of a tie. It still enumerates every dice outcome on its own turn, and the page says every roll is enumerated exactly, 7,776 outcomes, which is six faces on five dice.

The wrinkle is who it thinks you are. The page says the late-game mode assumes you play the exact expected-score policy. So the computer isn’t solving a general game against a stranger. It solves a game against a version of you who always picks the average-maximizing move, then plays whatever beats that version.

That is the useful distinction hiding in a dice game. The move with the best average isn’t automatically the move that wins the match. Chasing average is right when your only goal is a high score. When you are behind with two rounds left, a risky play with a worse average and a fatter tail can give better odds of passing someone.

Published optima show how much room the averages leave. Tom Verhoeff’s trivia page says the expected final score of the Optimal Solitaire Yahtzee Player is “254.5896…,” with a standard deviation of “59.6117…” and a median of 248. The browser page quotes its own early-play target as 254.14. It doesn’t say why its figure sits a bit under Verhoeff’s, and I haven’t tried to guess. What matters is the standard deviation: a spread near 60 points around a 254 average means a lot of games land far from the middle, which is exactly where “win” and “best average” part ways.

The game also sells itself as a teacher. The page has a “Coach exact probabilities” section and a Coach on Rules button, though it doesn’t explain how the coach works beyond that. The turn rules are the usual ones: roll to start your turn, click a die to hold it, three rolls a turn, and bank a result in one open box at any point.

One caution runs through the page. The claims come from its own instructions, and nobody who audited the solver is cited. The page doesn’t name its maker either. Verhoeff’s numbers are for the solitaire game, played alone with no opponent, so they set the bar for averages and say nothing about the Match-W mode.

Expect more small browser games to ship an endgame mode like this one, because the idea travels: any game with a final score and a known opponent policy can swap its objective near the end. In a dice game that means the rival you’re up against stops being a calculator and turns into a competitor.

Loaded dice would be cheating. This is just math.