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Old 08-24-2017, 10:25 AM   #9
Anthony
 
Join Date: Feb 2005
Location: Berkeley, CA
Default Re: Minor dice rolling/ probability question

Another way of looking at this: this is a finite state machine with 4 terminating conditions and 6 states. This means the mean number of dice rolled is 1.5, so the average will be (average ignoring rerolls) * 1.5, or since there are 6 values and the average is division by 6, it's just (sum ignoring rerolls) / 4 (and in a more general case, it's (sum ignoring rerolls) / (total terminating conditions).

The sum ignoring rerolls is 0 + 2 + 3 + 4 + 5 + 5 = 19. 19/4 = 4.75.
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