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Old thread, much older question. It's not solvable unless you know if Monty will always show you a goat, or will show you a goat only if you originally chose the car; also does he know where the car is (and if not, what happens if he reveals the car?)
Example: I have a dollar in one fist, choose left or right? Are the odds 1/2-1/2 if I'm waving one fist at you begging you to pick it? (And are you my to grandchild whom I'm trying to give a dollar, or are you some guy in the bar?) Are the odds 1/2-1/2 if you've observed in a sufficiently large number of trials that I always put the dollar in my right hand when I play this game? Are the odds 1/2-1/2 if you can see the dollar coming out of my right hand?
Old thread, I was cleaning out last year's school papers and found this. Agreed the tie-breakers make a big difference. Otherwise it comes down to working backwards and gaining votes by offering someone more than he will get if the vote is no. The solution seems to ascribe a value to not getting thrown overboard beyond not getting any gold. It is solvable, and is not "You will be hanged within the next week, on a day when you don't expect it."
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