Sat Apr 25 14:25:43 2020 by Ben |

How can I figure out the probabilities of scoring maximum one occurence of any number in exploding dice? Eg. exploding 2D4 rolling a not more than 1x of: "1" or "2" versus exploding 3d4 rolling max. 2x of "1" |

Sun Apr 26 14:42:32 2020 by Torben |

I assume that you explode on a 4. The set of dice value you get from exploding N d4 is written as`N#(accumulate x:=d4 while x=4)` To count the number of 1s and 2s in this, you write `count 3 > N#(accumulate x:=d4 while x=4)` But it is fairly easy to see that this is the same as counting the number of 1s and 2s in a non-exploding d3: `count 3 > N d3` The reason is that N exploding d4s have any number of 4s and exactly N values from 1 to 3, with equal probability. |