The expected payoff is always the probability of the payoff times the amount of the payoff. Suppose you make an investment for which you believe there is a 90% chance you'll earn $5,000 and a 10% chance you'll earn $20,000. The expected payoff from this investment is:
E = .9 x 5,000 + .1 x 20,000 = 4,500 + 2,000 = 6,500.
It may interest you to note that the expected value of a typical lottery ticket is around 1/2 its price.. which is why lotteries make a profit, just as in casinos the expected payoff from the typical bet is less than the amount of the bet. As you've no doubt heard, "the odds favor the house."

   We will suppose that our game players always try to maximize the expected payoff from any game. (In more advanced courses you will study how this approach might be changed to allow for different attitudes towards risk.) Using these simple ideas let's look at the coin matching game again.

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