exercise:9354e9bb93: Difference between revisions
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(Created page with "<div class="d-none"><math> \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}</math></div> Recall that in the ''martingale doubling system'' (see [[guide:4f3a4e96c3#sec 1.1 |Exercise.]]), the player doubles his bet each time he loses. Suppose that you are playing roulette in a ''fair casino'' where the...") |
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Recall that in the ''martingale doubling system'' (see [[exercise:91ef759ec9|Exercise]]), the player doubles his bet each time he loses. Suppose that you are playing roulette in a ''fair casino'' where there are no 0's, and you bet on red each time. You then win with probability 1/2 each time. Assume that you enter the casino with 100 dollars, start with a 1-dollar bet and employ the martingale system. You stop as soon as you have won one bet, or in the unlikely event that black turns up six times in a row so that you are down 63 dollars and cannot make the required 64-dollar bet. Find your expected winnings under this system of play. | |||
his bet each time he loses. Suppose that you are | |||
playing roulette in a ''fair casino'' where there are no 0's, and you bet on red | |||
each time. You then win with probability 1/2 each time. Assume that you enter the casino with | |||
100 dollars, start with a | |||
1-dollar bet and employ the martingale system. You stop as soon as you have won one bet, or in the unlikely event that black turns up six times in a | |||
row so that you are down 63 dollars and cannot make the required 64-dollar bet. Find | |||
your expected winnings under this system of play. | |||
Latest revision as of 17:27, 14 June 2024
Recall that in the martingale doubling system (see Exercise), the player doubles his bet each time he loses. Suppose that you are playing roulette in a fair casino where there are no 0's, and you bet on red each time. You then win with probability 1/2 each time. Assume that you enter the casino with 100 dollars, start with a 1-dollar bet and employ the martingale system. You stop as soon as you have won one bet, or in the unlikely event that black turns up six times in a row so that you are down 63 dollars and cannot make the required 64-dollar bet. Find your expected winnings under this system of play.