> bar/bar/bar pays 20 coins

> bell/bell/bell pays 15 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 10 coins. You can run a simulation to estimate this, rather than trying to compute an exact answer.

Deciding to put probability theory to good use, we encounter a slot
machine with three independent wheels, 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 20 coins

> bell/bell/bell pays 15 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 10 coins. You can run a
simulation to estimate this, rather than trying to compute an
exact answer.