Need help with a bar bet

[jdoe]

A guy said with a pool of 50 people he could guess the birthday of at least one person and that he would take even money.

It seems to me that this is a good bet for me as you would be even money on 50 draws from 1 to 365(with replacement). can someone help me with the math.

Thanks

jdoe

[Cerril]

That -seems- like a great bet. It sounds like he's misunderstanding the classic idea that in a pool of around that size it becomes likely for two people to share a birthday. He's still only 1:7.x to guess a birthday on the nose. Even if you could shave it down by likely birthdays (more births in xx month) he's still not going to manage even money.

Unless of course he's shooting an angle and including someone he knows in the pool.

[duker41]

I can't explain the math, but I've heard that you can get the birthday in about 30 or so people, despite the illogic of that.

[RocketManJames]

These are the possibilities:

1) As another poster pointed out, it is a misinterpretation of the Birthday Paradox, where you need 23 or more people to have greater than 50% chance that two share the same birthday.

2) It's a hustle... he says his own birthday, and it's an instant winner.

3) Again, as pointed out by the other guy, he might know someone in the pool.

-RMJ

[bisonbison]

RocketMan sums up the possibilities very well.

I'm inclined towards 2 or 3.