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#2
12-04-2005, 11:44 PM
 AaronBrown Senior Member Join Date: May 2005 Location: New York Posts: 505
Re: RoR -- What % loss before double?

I'm not sure I understand the situation. I think you're making a series of identical bets. Your expected profit from each one is fixed at 0.1% of your initial bankroll. To make it concrete, you start with \$1,000 and make bets on which you have an expected profit of \$1. You want to know the expected minimum point before you get up to \$2,000.

Obviously this depends on the standard deviation of the individual bets. If that standard deviation is zero, if you just get \$1 each time, then \$1,000 in your certain minimum. If, instead, you're betting \$1,000 for one chance in 1 million of getting \$1,001,000,000, then you've got a 0.999999 chance of hitting zero before going above \$2,000.

Let's say you have 0.55 chance of winning \$10 and 0.45 chance of losing \$10 each time. Your average minimum point is about \$955. 18% of the time you'll never be behind, and 70% of the time, you'll never be below \$950. 89% of the time you'll never be below \$900 and 98% of the time you'll never be below \$800.