Dice-pool probability calculator

Count successes, rather than add faces

A success is one die showing the threshold or higher. For example, five d10s succeeding on 8, 9 or 10 have a 47.178% chance of at least two successes, averaging 1.5 successes per roll. Rerolling each failed die once raises its individual success chance from 30% to 51%.

What the comparison means

Configure A and B independently. “A wins” means A rolls strictly more successes than B; ties appear separately. The target compares both pools against the same required success count. Zero dice always produce zero successes. The chart plots each exact count; the table also gives the chance of at least that count.

Method and rules

For fair independent dice, p = (sides − threshold + 1) / sides. Success counts follow the binomial distribution described by NIST. A single reroll of misses gives p + (1 − p)p. Rerolling failed ones once gives p + p/sides when a 1 fails. Each reroll replaces that die; it cannot trigger another reroll.

Each die contributes at most one success. Exploding dice, double successes, cancellation, botches and mixed die sizes within one pool are excluded. This is not a complete calculator for any particular RPG. Probabilities are calculated from the distribution, not random trials; displayed values are rounded.

For specific scoring tasks, try the Farkle score calculator or cribbage hand calculator. To explore probability through repeated trials, use the birthday-paradox simulator.