# Value of Understanding Probabilities

Your response to the question is due by Thursday, October 22nd.

Probability theorems tell us that, from the relative frequency of all possible events, a particular outcome will occur some computed percentage of the time.

Gambling on the slot machines takes into account the probability that after X amount of non matching pulls, there is a pull with a big pay out. There are people who sit at slot machines all day waiting for that pay out. There are other people that watch people at slot machines. The watchers wait until the machine is vacated and jump on in hope of cashing in on the probability that the next pull is a win.

To use probability in slot machines, you have to understand the average payout of the casino. When casinos advertise that their slot machines pay out an average of 90 percent, the fine print they don't want you to read says that you lose 10 cents from each dollar you put into the machines in the long term. (In probability terms, this advertisement means that your expected winnings are minus 10 cents on every dollar you spend every time the money goes through the machines.)

Suppose you start with $100 and bet a dollar at a time, for example. After inserting all $100 into the slot, 100 pulls later you'll end up on average with $90, because you lose 10 percent of your money. If you run the $90 back through the machine, you'll end up with 90 percent of it back, which is 0.90 x 90 = $81. If you run that amount through in 81 pulls, you'll have $72.90 afterward (0.90 x 81 = 72.90). If you keep going for 44 rounds, on average, the money will be gone, unless you are lucky! Reference

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