When drawing straws, are you more likely to get the short straw if you pick first, or after several people have already picked?
In: Mathematics
It doesn’t matter.
The easiest way to think about this is that everyone who hasn’t already picked a straw has an equal chance of picking the short straw; the straw, after all, doesn’t care who picks it. It’s a straw. Straws are, notoriously, indifferent to people.
So say you’ve got five people deciding. Everyone has a 20% chance of pulling the short straw and ending the game. Person A pulls the straw, and success! Long straw. He’s safe. The game continues.
Now you’ve got a situation where there are four straws available, one of which is short. Everyone else has a 25% chance of pulling the short straw… but remember, there’s already been one round, which means there’s already a certain number of possible outcomes that have been taken off the board. (For example, if Person A pulls the short straw, there *is* no second round.) The odds of the game going to a second round is 80% (that is, the odds that Person A doesn’t pull the short straw). **Your overall odds, then, are 25% of that 80%… or, put another way, 20%.**
You can go down and down and down through the various [probability trees](https://www.mathsisfun.com/data/probability-tree-diagrams.html) of how the game might play itself out, but you’ll find that each person’s odds of picking a straw is 20% in any given round, *if* you don’t know the status of the straws pulled before.
That’s why it’s functionally equivalent to have everyone pull the straws one by one, or to have them pull the straws at the same time. The only difference is in how tense it gets when it’s down to two and you haven’t decided who’s paying for the pizza yet.
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