22 Oct '10 18:165 edits

The local chess club is having a draw to raise some cash for a new chess set.

There are 50 cards contained inside a hat. One of the cards has "You're Winner!" marked on it. If you pick the winning card, you get half the money put into the pot so far.

It costs 10 bux to pick a card out of the hat and the pot already has 10 bux in it to start with. You can choose to pick a card anytime you want and you don't have to pay your 10 bux until you actually pick the card out.

So, if someone goes first, pays their 10 bux and picks the winning card, then no one else is out money because obviously they haven't paid. However, obviously there is only a 1 in 50 chance that the person picks the card on the first try.

The question is:

Is there an optimum time that you should pay your 10 bux to pick out a card that will maximize your expected winnings? Ie should you pick after maybe the 5th card is picked, the 10, 25th??

Or does it make no difference at all?

You can only pick once.

There are 50 cards contained inside a hat. One of the cards has "You're Winner!" marked on it. If you pick the winning card, you get half the money put into the pot so far.

It costs 10 bux to pick a card out of the hat and the pot already has 10 bux in it to start with. You can choose to pick a card anytime you want and you don't have to pay your 10 bux until you actually pick the card out.

So, if someone goes first, pays their 10 bux and picks the winning card, then no one else is out money because obviously they haven't paid. However, obviously there is only a 1 in 50 chance that the person picks the card on the first try.

The question is:

Is there an optimum time that you should pay your 10 bux to pick out a card that will maximize your expected winnings? Ie should you pick after maybe the 5th card is picked, the 10, 25th??

Or does it make no difference at all?

You can only pick once.