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If everyone follows this strategy, then I will win if exactly one person draws the short straw and if that one person isn't me. The former has a probability tha

If everyone follows this strategy, then I will win if exactly one person draws the short straw and if that one person isn't me. The former has a probability that rapidly approaches 1/e≈36.8% as n increases Why is "if exactly one person draws the short straw" probabilistic at all? I assume that's what "the former" means?

mjd 2y ago
That is what the former means. It's probabilistic because we assume (or at least hope) everyone is doing as I do, rolling an n-sided die to decide if they will write -10(n-1) instead of writing 10.
cvoss 2y ago
Each person samples a private random variable to decide if they have drawn the short straw. To use a shared sample would violate the no-communication assumption.
- laweijfmvo 2y ago
  Thanks, missed that part.
  - mjd 2y ago
    I've revised the article to make this clearer. Thanks for pointing out the problem.
Tyr42 2y ago
They would be rolling independently. So it's a with replacement, not without replacement draw.
ldjb 2y ago
Suppose there are two students. Each has a 50% chance of drawing the short straw (by picking either 0 or 1). Therefore, there is a 25% chance that neither will draw the short straw, 25% chance that both will draw the short straw, and 50% chance that only one will draw the short straw.
happytoexplain 2y ago
Using the phrase "draw the short straw" is a little confusing here, because there are 0-n short straws in this scenario. He is describing the probability that there is exactly one short straw (which isn't just 1/n+1 because the straws are not all "present" at once... it's just not a perfect analogy).
ineiti 2y ago
Because you're in an exam, and you cannot really draw a straw. So you have to choose a number randomly, and pretend you chose the short straw if it's a 0. And then hope you're the only one. The article also discussed how it'll work if you prepare beforehand and actually can draw a straw. Spoiler: you might want to cheat if you chose the short straw :)

mjd 2y ago

That is what the former means. It's probabilistic because we assume (or at least hope) everyone is doing as I do, rolling an n-sided die to decide if they will write -10(n-1) instead of writing 10.

cvoss 2y ago

Each person samples a private random variable to decide if they have drawn the short straw. To use a shared sample would violate the no-communication assumption.

laweijfmvo 2y ago
Thanks, missed that part.
- mjd 2y ago
  I've revised the article to make this clearer. Thanks for pointing out the problem.

Tyr42 2y ago

They would be rolling independently. So it's a with replacement, not without replacement draw.

ldjb 2y ago

Suppose there are two students. Each has a 50% chance of drawing the short straw (by picking either 0 or 1). Therefore, there is a 25% chance that neither will draw the short straw, 25% chance that both will draw the short straw, and 50% chance that only one will draw the short straw.

happytoexplain 2y ago

Using the phrase "draw the short straw" is a little confusing here, because there are 0-n short straws in this scenario. He is describing the probability that there is exactly one short straw (which isn't just 1/n+1 because the straws are not all "present" at once... it's just not a perfect analogy).

ineiti 2y ago

Because you're in an exam, and you cannot really draw a straw. So you have to choose a number randomly, and pretend you chose the short straw if it's a 0. And then hope you're the only one. The article also discussed how it'll work if you prepare beforehand and actually can draw a straw. Spoiler: you might want to cheat if you chose the short straw :)