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Roulette puzzle

Posted By: Timothy Chow
Date: Wednesday, 28 April 2010, at 8:40 p.m.

In Response To: Roulette puzzle (Tom Keith)

Tom, you're dead right about the way the graph fluctuates. In the version I originally heard, which I think was Axler's version (though I didn't hear it directly from Axler), there wasn't this business of trying every number 3 times. Instead you were supposed to bet 105 times. But I thought this was a flaw in the puzzle, because why 105? Why not 100? Well, at least in the puzzle as I originally heard it, 100 wouldn't quite give answer E, which is the answer we want (an answer of D would be "boring"). But once you say 105, then you're tipping your hand that something funny is going on. Therefore I came up with the idea of trying every number 3 times, in order to make 108 trials seem "natural." As a bonus, 108 trials means that breaking even is equivalent to winning exactly 3 times, and this helps you feel you're on the right track when you make this observation.

Another adjustment I made to the puzzle was to choose the ranges in responses A to E to psychologically mislead the solver into thinking that the probability is high. I don't remember what Axler's original multiple choices were but again I felt they were not chosen optimally to make a good puzzle.

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