Reroll-Ones Dice Roller

Rolls a set of dice and automatically rerolls any die that lands on 1 (once each) — a common tabletop house rule that softens the worst rolls without removing randomness entirely.

Sides per die

Number of dice

Seed (optional)

Replays the same rolls. Deterministic, not cryptographic.

Your roll will appear here, with what the reroll is worth.

✓ A 1 survives only by being rolled twice — 2.8% a die, against 16.7% without the reroll
✓ Every other face picks up the share the ones lose, rising to 19.4% each
✓ The face odds add up to one, and the totals are folded together exactly rather than simulated

What this generator does

Rolls dice and automatically rerolls any that come up 1, a common house rule for reducing the sting of the worst possible result. Both the original roll and the reroll are shown, so the rule stays visible rather than silently improving your total — and the page puts a number on what the rule is worth, comparing the exact average with and without it.

How to use this tool

Set the dice sides and count.
Press roll — any 1s are automatically rerolled once and shown alongside the original.

Understanding the controls

Sides per die: The size of each die. The reroll is worth more on a small die than a large one, because a 1 is a bigger share of what you lose.
Number of dice: How many are rolled together. Each is rerolled independently if it lands on a 1, so more dice means more rerolls but the same effect per die.
Seed: Empty for ordinary random rolls. Type anything to replay the same sequence, including which dice were rerolled. Deterministic, not cryptographic.

Common use cases

Tabletop RPG house rules
Damage rolls with a reroll-1s rule
Comparing original vs rerolled outcomes

How this generator works

Each die is rolled, and any that shows a 1 is rolled again once — no further rerolls, however the second roll lands. The exact effect is then computed rather than estimated: the face probabilities after the rule are 1/s² for a 1 and (s+1)/s² for everything else, which add up to one, and those are folded together across the dice by convolution to give the distribution of the total. That is what lets the page say precisely how much the house rule is worth on a given roll — for three six-sided dice it lifts the average from 10.5 to 11.5, a full point.

Randomness and fairness

Every die comes from your browser's cryptographic random source, and a die showing a 1 is rolled once more from the same source. That changes the odds of each face in a way worth stating: a 1 now survives only by being rolled twice, so on a six-sided die it falls from one in six to one in thirty-six, and every other face rises from six thirty-sixths to seven. The averages shown are computed from those exact face odds and folded together across the dice, not sampled. A seed replaces the source with a deterministic generator that repeats the same rolls and the same rerolls for the same seed — deterministic, not cryptographic.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

Rerolling ones raises the average of every die, so it makes outcomes better rather than merely fairer. Apply it consistently to everyone at the table.