# Dice Probability Dungeons and Dragons

Mathematics Asked by bangini on December 3, 2020

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

?

The answer is $$frac 1 {20} cdot left(frac 1 {10}right)^4 = frac 1 {200000}$$.

However, since you mentioned D&D....

Let me tell you that information theory also tells us that the more unexpected something is, the more knowledge you get for receiving it.

Dice rolls are a type of divination that go beyond the pure realm of math-based probabilities. I've estimated that a dice roll, with flat faces, on a hard surface will give you about 130 bits of information on each roll. This huge number is enough to get data from almost every atom of the universe (science estimates this to be not much more than 1082).

Answered by Marcos on December 3, 2020

Rare events happen all the time. If you imagine all the games of D&D ever played and think of the dice roll sequences that you would want to ask here about you can see that some of them would happen sometimes.

Your confusion comes from asking after you know it happened to you.

Winning the lottery is a very rare event. But someone wins. They think they are special (well, they are lucky).

More discussion here:

Probability of two people from two different countries meeting in a different country and meeting each other

Answered by Ethan Bolker on December 3, 2020

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

Answered by Bram28 on December 3, 2020