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 Sneaky Joe's Craps (Posted on 2004-04-17)
Sneaky Joe has just invited you as a VIP to his new casino. You know this is probably an attempt steal your money, for he always find ways to swindle people. However, you go anyway.

When you get there, he says, "Come over here and join me in a game of craps." You become slightly suspicious, but agree to come anyway. When you go over, he says, "OK, here's how we play craps in this casino, 'cause it's different here than other casinos. You have 3 dice, 2 of them are 12-sided dice and another is a 40-sided die. I will roll the 2 12-sided dice. Then you roll the 40-sided one. If your number is between (y^2-x) and (x^2-y) inclusively, being that x=the number I got from the first roll and y=the number I got on the second, you will win \$10. Otherwise, you will lose \$10."

"Ok," you think, "I'm pretty sure that the odds are against me, especially if it's a game that Joe made himself. But I need \$30, and I only have \$10." So, what's the probability of you winning \$30 (as in \$30 in the black, without any debt, which included the original \$10 paid) from this game?

(NOTE: It can be done WITHOUT trial and error, and it is my request, though you do not have do it, that you solve this without trial and error.)

 No Solution Yet Submitted by Victor Zapana Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(6): Solution | Comment 9 of 11 |
(In reply to re(5): Solution by Charlie)

Charlie wrote: "If Joe tried that on me, I'd be pretty mad at him and his interpretation.  No wonder Victor is suspicious of this sneaky character."

Why do you think he's called "Sneaky Joe" ?

Edited on April 19, 2004, 3:53 am
 Posted by Penny on 2004-04-18 22:10:38

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