This page is about the probability to "gain" with dice; this depends of course on the rules of the game.

Comparison of the probabilities to have a number, between the sum of three dice and the sum of the best three amongst four dice — this is used in some roleplaying games

Probability to have a value summing two six-sided dice chosen amongst n: sum of the two worst dice amongst three or four dice; sum of the two best dice amongst three or four dice; sum of two dice, simply

Choice of the best result amongst two different dice (e.g. 1d4 and 1d6)

Choice of the best result amongst two different dice (e.g. 1d4 and 1d6)

Reach or make better than a value, with the best result amongst two different dice (e.g. 1d4 and 1d6)

Reach or make better than a value, with the best result amongst two different dice (e.g. 1d4 and 1d6)

same with three dice

Comparison of the probabilities to have a given result (top) or to make less than a given threshold (bottom) with a twenty-sided die (1d20), with the sum of two ten-sided dice (2d10) and of three six-sided dice (3d6)

Probabilities to get a number (top) or to have less than a given threshold (bottom) by summing several six-sided dice (nd6)

Probability to exceed a given threshold with the sum of several six-sided dice (nd6). The points linked by a broken lines correspond to a given threshold. The abscissa corresponds to the total number of dice that are thrown.

Probability to have at least one die with a value equal to or exceeding a given threshold amongst n dice thrown — this is used in some roleplaying games

Probability to have a value with an "open ended" d20 (the die is thrown again recursively when and added when the result is 20, or subtracted when the result is 1)

Probability to roll above a given threshold with an "open ended" d20 (the die is thrown again recursively when and added when the result is 20, or subtracted when the result is 1)