17. Consider the game of craps as played in Las Vegas casinos. The basic rules of...

Transcribed Image Text:

17. Consider the game of craps as played in Las Vegas casinos. The basic rules of the game are as follows. One player (the shooter) rolls a pair of dice. If the outcome of that roll is a 2, 3, or 12, the player immediately loses; if it is a 7 or 11, the player wins. In all other cases (4, 5, 6, 8, 9, or 10), the number rolled on the first toss becomes the point, which the shooter must try to duplicate on subsequent rolls. If the player manages to roll the point before a 7 appears, it's a win; otherwise it is a loss. It may take several rolls to determine whether the player wins or loses. After the first roll, only a 7 or the point have any significance until the win or loss is decided. Of course, there are many ways to place bets on various possibilities, but we are concerned here with just the basic rules of the game, played only once. Model the process as a Markov chain with absorbing states for win and lose. Assume the dice are fair in evaluating the probabilities. 17. Consider the game of craps as played in Las Vegas casinos. The basic rules of the game are as follows. One player (the shooter) rolls a pair of dice. If the outcome of that roll is a 2, 3, or 12, the player immediately loses; if it is a 7 or 11, the player wins. In all other cases (4, 5, 6, 8, 9, or 10), the number rolled on the first toss becomes the point, which the shooter must try to duplicate on subsequent rolls. If the player manages to roll the point before a 7 appears, it's a win; otherwise it is a loss. It may take several rolls to determine whether the player wins or loses. After the first roll, only a 7 or the point have any significance until the win or loss is decided. Of course, there are many ways to place bets on various possibilities, but we are concerned here with just the basic rules of the game, played only once. Model the process as a Markov chain with absorbing states for win and lose. Assume the dice are fair in evaluating the probabilities.

Answer rating: 100% (QA)

Question 1 A Markov chain can be used to model the process of playing craps as it is played in Las Vegas casinos The Markov chain will have two absorb... View the full answer