Exercise 13.12

Deciding to put our knowledge of probability to good use, we encounter a slot machine with three independently turning reels, each producing one of the four symbols bar, bell, lemon, or cherry with equal probability. The slot machine has the following payout scheme for a bet of 1 coin (where “?” denotes that we don’t care what comes up for that wheel):

bar/bar/bar pays 21 coins

bell/bell/bell pays 16 coins

lemon/lemon/lemon pays 5 coins

cherry/cherry/cherry pays 3 coins

cherry/cherry/? pays 2 coins

cherry/?/? pays 1 coin

1. Compute the expected “payback” percentage of the machine. In other words, for each coin played, what is the expected coin return?

2. Compute the probability that playing the slot machine once will result in a win.

3. Estimate the mean and median number of plays you can expect to make until you go broke, if you start with 8 coins. You can run a simulation to estimate this, rather than trying to compute an exact answer.