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Roulette puzzle

Posted By: Tom Keith
Date: Wednesday, 28 April 2010, at 2:37 p.m.

In Response To: Roulette puzzle (Ian Shaw)

Isn't that cute.

There seem to be two things going on. (For simplicity let's assume no rake (P(win)=1/36 instead of 1/38).)

1. As a general principle the number of losses should be more than the number of wins. That's because there is a much bigger up side than down side in this game -- some of the wins will be quite large. So there will have to be more losses if the game is going to break even in the long term.

2. The probability of coming out a loser goes up and down a lot according to the exact number of trials. (See the plot below.) So, while general principle in #1 holds true overall, there are many specific exceptions.

Plot: Probability of coming out a loser according to number of trials

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