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What is the probability that six chips can be accumulated

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Reference no: EM132174511

Discrete Optimization (Dynamic Programming)

Problem Desc: Consider a ‘Casino Problem'where you have 3 chips in the beginning. You are allowed to play thegame 6 times. Your goal is to haveaccumulated 6 chips. You can bet any desirednumber of your availablechips and you have 55% probability ofwinning each play.

In the Dynamic Programming modelwith results presented below, the recursion is "forward", i.e., the stages range fromn=1 (first play of the game) to n=6 (final play of the game). The state is the number ofchips accumulated, and the decision is the number of chips to bet at the current play ofthe game.

a. Compute the missing number in the table for stage 1. __________ and explain how did you get that number.

b. What is the probability that six chips can be accumulated at the end ofsix plays of the game? _______%. And show how you got the %

c. How many chips should be bet at the first play of the game? ________(If more than one value is optimal, choose an answer arbitrarily.)

d. If one bets the amount you selected in (c) and the first play of the gameis won, what should be the bet at the second play of the game? _____ If the firstplay of the game is lost, what should be the bet at the second play of the game? Explain briefly

Attachment:- Casino Problem.rar

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The problem is related with Discrete optimization(Dynamic programming). This is casino problem where we have given 3 chips and wants to accumulate 6 chips with 55% probability of winning each play.

Reference no: EM132174511

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