Official forced-Joker rules · one trillion trials

Score distribution from one trillion games of optimal solitaire Yahtzee

Official forced-Joker rules · Monte Carlo score distribution

games simulation batches

Interactive distribution

Every observed score, from the ordinary to the extraordinary

Full observed range · logarithmic probabilityDrag the frame to pan · click to recenter

Where the games land

The nested bands show the middle half and middle 90% of outcomes. The dashed span is one standard deviation around the mean.

The right tail

Exceptional scores thin out quickly. Hover or focus a threshold to illuminate that region in the main chart.

Score distribution from one trillion games of optimal solitaire Yahtzee An annotated distribution of one trillion optimal solitaire Yahtzee scores, with a detailed central view and logarithmic full-range overview. ONE TRILLION SIMULATED GAMES · 100 BATCHES Score distribution from one trillion games of optimal solitaire Yahtzee Official forced-Joker rules · Monte Carlo score distribution CENTRAL 90% OF GAMES180–388 points SCORE ≥ 30014.33%SCORE ≥ 4003.83%SCORE ≥ 5000.719%SCORE ≥ 6000.090% 0.00%0.27%0.54%0.82%1.09%1.36% MEDIAN 248MEAN 254.59MODE 266 150200250300350400450500 FINAL SCORE PROBABILITY FULL OBSERVED RANGE · LOG PROBABILITY MIN 47MAX 1248 Observed counts · no smoothing · every integer score represented