Dice probability

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

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  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
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  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
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  Choice of the best result amongst two different dice (e.g. 1d4 and 1d6)
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  Choice of the best result amongst two different dice (e.g. 1d4 and 1d6)
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  Reach or make better than a value, with the best result amongst two different dice (e.g. 1d4 and 1d6)
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  Reach or make better than a value, with the best result amongst two different dice (e.g. 1d4 and 1d6)
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  same with three dice
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  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)
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  Probabilities to get a number (top) or to have less than a given threshold (bottom) by summing several six-sided dice (nd6)
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  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.
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  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
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  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)
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  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)