# Dice Probability Dungeons and Dragons

Last night a "orc" rolled a 20 on a 20 sided die. If that happens, we roll TWO 10 sided dice to look at a critical hit chart numbered 01-100 (one 10 sided die is numbered 00-90). I then rolled a 00-0 which is considered "100" so the character suffered death. We always roll god saves (meaning a god will save them if the player then rolls 00-0 with 2-10 sided die). Well, The player the rolled 00-0 with witnesses. I couldn't believe it!

What is the total probability to roll these numbers consecutively, meaning one after the other:

-"20" on a 20 sided die once, then... -"0" on a 10 sided die FOUR TIMES IN A ROW

?

• $\frac {1}{20}\frac {1}{100}\frac{1}{100} = \frac {1}{200,000}$ As Terry Pratchett says “Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten.” – Doug M Sep 7 '17 at 0:21
• DIE! The singular of dice is DIE! Gah!!!!! :P – Xander Henderson Sep 7 '17 at 0:22
• The capitalization in your last line suggests that you think this should NEVER happen. The answers show that it is in fact rare: 1 in 200,000. But there may well have been well over 200,000 D&D dice rolls in the years since the game began, so that "unusual' event does happen to someone. Just not usually to you. The same kind of argument shows that winning the lottery isn't a rare event when viewed from far away. – Ethan Bolker Sep 7 '17 at 0:30
• It is the "lottery paradox," just in a different context. Even rare outcomes become probable after enough trials. It would be strange is no one ever had such a sequence of die rolls. – Xander Henderson Sep 7 '17 at 3:16
• Thanks everybody! You opened up my eyes to something I didn't know, the the lottery paradox. – bangini Sep 7 '17 at 4:48

It's simply $\frac{1}{20}\cdot (\frac{1}{10})^4$, or 5 in a million.