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Math Problem

Veloso sent this to me today.

You're in hell, and you're playing a gambling game where P is your odds of winning each wager. (Each wager pays even money, and you can only wager one unit at a time.) You have unlimited credit, so can play forever. You decide you'll quit playing if you ever become even one unit ahead Otherwise you're forced to play forever. What are the odds of being able to stop?

I eventually got the answer, but I had to rely on some guess work. Veloso actually proved it rigorously. I wish I were better trained in mathematics. Also I am not sure why you have to be in hell for the problem to work.

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( 3 comments — Leave a comment )
(Anonymous)
Jun. 15th, 2007 10:32 pm (UTC)
re: Math problem
As a guess, I'd say it is certain that you will eventually stop. I base this on my understanding that in an infinite series of coin flips, one is certain to somewhere find an arbitrarily large run of heads. This principle seems to imply that at some point, no matter how far behind you may have gotten, you will eventually get ahead.

The game must be played in Hell because it may be played for vast amounts of time, possibly longer than a human lifetime- and there's no gambling in Heaven. It's a sin, you know. -Geekboy
grieve
Jun. 16th, 2007 09:04 pm (UTC)
Re: Math problem
It is not certain. There is just a non-zero chance (unless P itself it 0), that you can stop. Keep in mind if you can have a large run of wins you can also have a large run of losses. :)
grieve
Jun. 16th, 2007 09:05 pm (UTC)
Re: Math problem
Oh and I love your explanation for why it has to be in hell. Now I know.
( 3 comments — Leave a comment )

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