Craps is a 1player dice game that is played as follows: Roll two 6sided dice; their sum becomes your "initial" roll. If this initial roll is 2, 3, or 12, you lose. If the initial roll is 7 or 11, you win. Otherwise, keep rolling the dice until you reroll you initial number (and win) or until you roll a 7 (and lose).
You're betting that your adversary is going to lose his game of craps, which should be a favorable bet for you. But you receive an anonymous tip that he's secretly loaded one of the dice, so that it will always come up 5. This increases his chances of winning to 2/3.
Having learned of his evil deed, you're going to secretly load his other die so as to minimize his chance of winning. With what probability should you load each of the six faces? And how does that change his probability of winning?
Fix it to be a two entirely, then point out to whoever is organising it that he is obviously using fixed dice, as he always gets 7. Then he has to use regular dice, decreasing his chances more than you can by rigging the other die!

Posted by Dacre
on 20031024 09:56:30 