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Probability Of Rolling 18s in Dungeons & Dragons

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#1 Photon Guy

Photon Guy


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Posted 04 April 2020 - 01:00 PM

Im talking old school Dungeons & Dragons where you would roll 3d6 for all six ability scores. I do know in some of the more recent editions they have alternative methods of rolling and generating scores such as rolling four dice and taking the highest three, re-rolling ones, ect. and that with some editions you don't even roll for abilities but rather you start with so many points to distribute among your ability scores and everybody starts with the same number of points, this was done for more game balance. 


Anyway, as I said Im talking about the old fashioned way, when you would roll 3d6 for each ability and generate a random number from 3 to 18. If you can get an ability score anywhere from 3 to 18 that would mean you have one in fifteen chance of getting an 18 in a single ability, now what are the chances of getting 18s for two abilities? What are the chances of getting 18s for all six abilities? Looking for answers from people who have a background in probability.