Dice Probability Calculator

Six of thirty-six outcomes, so one in six. It is the most likely total because it has the most combinations — six ways against a single way for two or twelve.

Because there are six ordered ways to make 7 and only one to make 12. The sum of dice is not uniform even though each die individually is.

The distribution approaches a bell curve, which is the central limit theorem appearing in the simplest possible case. With ten dice the extreme totals become vanishingly rare.

The number of dice times (sides + 1) ÷ 2. Two six-sided dice average 7; three average 10.5, which is not itself a possible roll.

Rolling two dice and taking the higher shifts the distribution upward substantially — the expected value of the best of two d20 rolls is 13.825 rather than 10.5.

Well-made casino dice are close, with sharp edges and balanced pips. Cheap moulded dice with hollowed pips are measurably biased, though rarely enough to matter in a game.

One in six with two dice — six doubles out of thirty-six outcomes. It is the same as any single specific total's most likely case, which surprises people.

Rolling two dice and taking the higher or lower. The best of two d20 rolls has an expected value of 13.825 rather than 10.5, which is a substantial shift.

A mechanic where a maximum roll allows another roll to be added. It creates an unbounded distribution with a long tail, which is why the mean rises above the plain expectation.

So that loading or internal modification is visible. Casino dice also have sharp edges and flush pips, both of which reduce bias compared with rounded consumer dice.

It varies enormously by bet, from well under 1% on the pass line with odds to double digits on some proposition bets. The bets with the best odds are the least prominently marked on the table.

Pseudo-random generators are more than adequate for games, and cryptographically secure ones are used where fairness must be provable. The weakness is usually in how a generator is seeded rather than in the algorithm.