# Every Saturday night a man plays poker at his home with the same group of friends. If he provides…

Every Saturday night a man plays poker at his home with the same group of friends. If he provides refreshments for the group (at an expected cost of \$14) on any given Saturday night, the group will begin the following Saturday night in a good mood with probability 7/8 and in a bad mood with probability 1/8. However, if he fails to provide refreshments, the group will begin the following Saturday night in a good mood with probability 1/8 and in a bad mood with probability 7/8, regardless of their mood this Saturday. Furthermore, if the group begins the night in a bad mood and then he fails to provide refreshments, the group will gang up on him so that he incurs expected poker losses of \$75. Under other circumstances, he averages no gain or loss on his poker play. The man wishes to find the policy regarding when to provide refreshments that will minimise his (long-run) expected average cost per week.