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
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Compute the expected “payback” percentage of the machine. In other words, for each coin played, what is the expected coin return?
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Compute the probability that playing the slot machine once will result in a win.
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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.