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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

?

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    $\begingroup$ $\frac {1}{20}\frac {1}{100}\frac{1}{100} = \frac {1}{200,000}$ 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.” $\endgroup$
    – Doug M
    Commented Sep 7, 2017 at 0:21
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    $\begingroup$ DIE! The singular of dice is DIE! Gah!!!!! :P $\endgroup$
    – Xander Henderson
    Commented Sep 7, 2017 at 0:22
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    $\begingroup$ 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. $\endgroup$ Commented Sep 7, 2017 at 0:30
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    $\begingroup$ 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. $\endgroup$
    – Xander Henderson
    Commented Sep 7, 2017 at 3:16
  • $\begingroup$ Thanks everybody! You opened up my eyes to something I didn't know, the the lottery paradox. $\endgroup$
    – bangini
    Commented Sep 7, 2017 at 4:48

3 Answers 3

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

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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

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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).

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