EDIT: Misunderstood the question. Some changes, but the major problem remains.
I've got two dice, one is six-sided (d6) the other is four, six, eight, ten, or twelve sided (d4, d6, d8, d10, or d12). Both get rolled simultaneously. If both roll a 1 that is a Bad Thing. If either rolls their maximum value (6 for the d6, 4, 6, 8, 10, or 12 respectively for the others), that die gets rolled again, and the total is added... unless it maxes out again, in which case a third die is rolled and added... and so on. When all is said and done, unless a Bad Thing is rolled the higher of the two rolls is taken.
I'm trying to work out, for each of d4 through d12, what the probability of each value (Bad Thing, 2, 3, 4, 5, 6, 7,...) is. Specifically, how often does Bad Thing show up, then after that how often do you get X or more. Obviously for each die the answer to 2 is 100%-the amount of times Bad Thing shows up. (Rolling 1 is impossible)
I don't really know how to solve this at all. I could always write a program to do a hundred million trial rolls for each die and see what the answers are, but that seems so.... clumsy.
I've got two dice, one is six-sided (d6) the other is four, six, eight, ten, or twelve sided (d4, d6, d8, d10, or d12). Both get rolled simultaneously. If both roll a 1 that is a Bad Thing. If either rolls their maximum value (6 for the d6, 4, 6, 8, 10, or 12 respectively for the others), that die gets rolled again, and the total is added... unless it maxes out again, in which case a third die is rolled and added... and so on. When all is said and done, unless a Bad Thing is rolled the higher of the two rolls is taken.
I'm trying to work out, for each of d4 through d12, what the probability of each value (Bad Thing, 2, 3, 4, 5, 6, 7,...) is. Specifically, how often does Bad Thing show up, then after that how often do you get X or more. Obviously for each die the answer to 2 is 100%-the amount of times Bad Thing shows up. (Rolling 1 is impossible)
I don't really know how to solve this at all. I could always write a program to do a hundred million trial rolls for each die and see what the answers are, but that seems so.... clumsy.
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