[bushindo]

You meet a guy in a pub. After a couple of beers, he offers you a chance to play a game. The game is as follows: at the beginning every game, you pay him X dollars to start. You then would pick a number from 1 to 10. He would roll five 10-sided dice, and pay you 1 dollar for every time that your number comes up. So instance, suppose that you guess the number 3, and the five rolled dice come up with the numbers (1, 9, 3, 3, 10). You would then win 2 dollars.

1) The guy in the pub offers you the chance to play the game if you pay him 0.90 dollar in the beginning. Would you play?

2) What the the maximum dollar amount X that you would pay to play the game?

Edited July 18, 2009 by bushindo

[Guest]

I wouldn't pay more than $0.50 per try.

If you pay more, you might as well buy lottery tickets.

Suppose you chose the number 1.

If I get $1 for every 1 rolled, the expected value from a single die is $0.10.

The expected value of rolling 5 ten sided dice is 5 * 0.10 = $0.50.

Edited July 18, 2009 by Kerrik

[bonanova]

Your number comes up 5, 4, 3, 2, 1 or 0 times, with probabilities 0.00001, 0.00045, 0.0081, 0.0729, 0.32805 and 0.59049, respectively.

You can expect to win 5x0.00001 + 4x0.00045 + 3x0.0081 + 2x0.0729 + 1x0.32805 + 0x0.59049 = 0.50.

Don't pay more than that to play.

This is not a duplicate post, and I don't mean to divert discussion, but, a while ago,

I suggested a which was never fully solved.

When discussion here is finished, you might want to take a look.