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The gambler should stick to making only even money bets. For the first five bets, he should place bets of $10, $19, $37, $73, and $145 if he does not have any wins up to that point. As soon as he wins on any the first five bets, then all the remaining bets are $1.
If he loses all first five bets, then he will have only $16. For the next 4 bets, he should place bets of $12, $25, $51, and $103, if he keeps winning in the last five bets. As soon as he loses on any of those four bets, he will have just enough to bet $1 on each of the remaining bets.
If in the extreme case of losing the first five and winning the next four, he should make his last bet $94 or greater to have a chance of getting at least $301.
His chances of failing are (10/19)^5 * (1 - (9/19)^5) = .039423 = 3.9423%, which makes his chance of success 96.0573% |
