Double or Nothing: Gambler\'s Ruin. We have seen that by betting on \"red\" in A
ID: 3181857 • Letter: D
Question
Double or Nothing: Gambler's Ruin. We have seen that by betting on "red" in American roulette, you have a 18/38 chance of winning, therefore doubling the money you bet. Suppose that you have $5 and you want to bet until either you reach (and stop with) $10 or you go broke. Is placing individual $1 bets on red more, less, or equally likely to reach this goal than just placing a single $5 bet? First, try to give an answer based on intuition, taking into account the casino's advantage. You could also explore the following formula that gives the probability of going from h dollars to N dollars without going broke by making $1 bets on red in American roulette: 1 - (20/18)^h/1 - (20/18)^N Discuss how the strategy for maximizing the chance of reaching a financial target compares to the strategy for maximizing the length of time that your money lasts (for entertainment value).Explanation / Answer
The probability of winning is 18/38 = 0.4737, which is less than 0.5 (0.5 , means we have equal chance of winning or losing). So, as the number of bets, increases, chance of winning beomes lesser. So, as per my intituition, placing individual $1 bets on red less likely to reach the goal by just placing a single $5 bet.
Chance of winning $10, for a single bet of $5 = 18/38 = 0.4737
Chance of winning $10, when starting with $5 and with single bet of $1 = (1-(20/18)^5)/(1-(20/18)^10)
= 0.3713, which is lesser than Chance of winning $10, for a single bet of $5
The strategy for maximizing the chance of reaching a financial target would be to bet with the maximum amount you have, as the probability of winning is less than 0.5.
The strategy for maximizing the length of time that your money lasts would be to bet with the minimun amount the roulette allows. If the minimum bet amount is say, 5 cents, you can bet for that, to maximize the length of time.
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