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asdf1234
10-07-2003, 03:22 PM
Gambling game, a man is paid \$3 if he draws a J or Q, \$5 if he draws K or A from ordinary deck. Any other card and he loses. How much should he pay to play if the game is fair? The only reason I ask is that I think a book has the answer wrong.

Copernicus
10-07-2003, 03:27 PM
\$1.23

asdf1234
10-07-2003, 03:45 PM
Okay, that's what I thought, the book had \$1.78, forgetting to take into account that you pay when you win I think.

BruceZ
10-07-2003, 04:15 PM
\$1.78 is what he should pay if he gets his money back when he wins, in addition to the money he wins.

EV = 8/52 * 5 + 8/52 * 3 - 36/52 * x = 0

x = 1.78

If he doesn't get his money back, then he should only pay \$1.23.

EV = 8/52 *(5-x) + 8/52 * (3-x) - 36/52 * x = 0

x = 1.23

Copernicus
10-07-2003, 04:22 PM
the problem is posed as you are "paid 3 and paid 5" not you "win 3 and win 5", so unless the problem is worded poorly \$1.23 is a better answer than \$1.78.

Its like the old ploy of saying they are giving you 3 for 1, instead of 3 to 1 odds. In the latter the 3 is in addition to your stake, in the former it includes it.

asdf1234
10-07-2003, 04:37 PM
The book specifically says he is paid \$3 or \$5 if he wins, so according to the wording of the question, the answer needs to be \$1.23. If they actually meant he WINS (i.e. profits) \$3 or \$5, then they worded it very very very poorly. I'll probably have to give credit for either answer.

Copernicus
10-07-2003, 05:23 PM
Give them credit for either answer, or challenge them and require two different answers along with the circumstances that make each one correct.

Bozeman
10-07-2003, 06:36 PM
I think it is only a semantic issue. "paid" could be the amount won, or the amount won + amount returned.

Still, it would be nice if the phrasing were not ambiguous.