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xkcd #3015: D&D Combinatorics (xkcd.com)

submitted 6 days ago by [email protected] to c/[email protected]

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Look, you can't complain about this after giving us so many scenarios involving N locked chests and M unlabeled keys.

https://explainxkcd.com/3015/

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[–] [email protected] 82 points 6 days ago* (last edited 6 days ago) (1 children)

For the probability that at least one arrow picked is cursed: 1/2 + 1/2 × 5/9 = 14/18 = 7/9. (The probability that you picked it the first time, plus the probability that you missed it the first time but picked it the second time).

a dice probability calculator tells me probability of 3d6 + 1d4 at least 16 is 2/9. So the DM is correct.

Sidenote: it doesn't matter whether you grab the arrows one at a time or with both hands at the same time. Unless your party is trying to figure out which arms to amputate.

[–] [email protected] 9 points 5 days ago (1 children)

The math is easier if you look for the probability that the arrows are safe. If you do it that way, it's simply 1/2*4/9, or 2/9.

[–] [email protected] 3 points 5 days ago

That is true. Cueball had asked the question in the way I described, but the check was done in the inverse which is easier to do the math on.