Revision as of 03:33, 9 June 2024 by Bot (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> In Monte Carlo roulette (see Example), under option (c), there are six states (<math>S</math>, <math>W</math>, <math>L</math>, <math>E</math>, <math>P_1</math>, and <math>P_2</math>). The reader is referred to Fi...")
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Jun 09'24
Exercise
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In Monte Carlo roulette (see
Example), under option (c), there are six states ([math]S[/math], [math]W[/math], [math]L[/math], [math]E[/math], [math]P_1[/math], and [math]P_2[/math]). The reader is referred to Figure \ref{fig 6.1.5}, which contains a tree for this option. Form a Markov chain for this option, and use the program AbsorbingChain to find the probabilities that you win, lose, or break even for a 1 franc bet on red. Using these probabilities, find the expected winnings for this bet. For a more general discussion of Markov chains applied to roulette, see the article of H. Sagan referred to in Example.