You play a gambling game in which you roll a single fair six-sided dice

| August 30, 2017

Question

You play a gambling game in which you roll a single fair six-sided dice and receive $1 if 1 or 2 comes up, you get nothing if 3 or 4 comes up, and lose $1 if 5 or 6 comes up. You start with $10 and will play until either you have $30 or you lose everything. What is the probability you will lose? What is the expected number of plays?

(Xn is the net wealth at time n>=1, you need to find c>0 for which (Xn squared – c(n)) is a Martingale. the apply the optional sampling theorem.)

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