Your turn
3 rolls
Roll to start your turn. Click a die to hold it.
Coach
exact probabilities
Play the odds
Roll to start your turn. Click a die to hold it.
Solving the dice…
How to play
Ones through Sixes. Score the sum of all dice showing that number. Reach 63 or more across the six upper boxes to earn the 35-point upper bonus.
Upper bonus. 35 points when the upper section totals 63 or more.
Yahtzee bonus. After the Yahtzee box has been scored for 50, every extra five-of-a-kind is worth +100. A five-of-a-kind also counts as a full house (joker rule), and you may bank it in any open box.
You get three rolls each turn. Hold any dice between rolls, then bank the result in one open box. You may stop and bank after any roll.
The computer does not guess. It enumerates every distinct outcome of every remaining roll, solves each turn backwards by dynamic programming, and through round 11 scores into the box that maximises its expected final total. The value of the boxes it has left comes from a precomputed exact table over every reachable scorecard state.
In the final two rounds it switches to Match-W. With both scorecards tracked, it maximises P(win) + 0.5 × P(tie) instead of average score, assuming you finish with the exact expected-score policy. It still enumerates every dice outcome on its own turn exactly.
Early play maximises the exact 254.14 expected score; the endgame protects or chases the match.
Final scores