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The expected payoff of the game is the sum of the calculations above, minus the cost of the game, i.e. ($0.00 + $2.50 + $10.00 - $10.00 = $2.50). Therefore you can expect to win $2.50 if you play the game. Notice that the ''expected'' payoff is not among the possible outcomes.
Now compare the expected payoff of not playing the game ($0, no risk, no reward), and the expected payoff playing the game ($2.50). If you want to maximize expected payoff you __should__ play the game.
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+Now suppose you play the game, draw the 5 of clubs and lose your money. Does that mean it was a bad decision to play? No, that is an example of GoodDecisionBadOutcome. Using decision theory doesn't give you any guarentees, but it does optimize your chances. If you consistently make good decisions, over the long run you will experience more good outcomes (unless, of course, you are __really__ unlucky which does happen, but thankfully is also very rare).
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See other InterestingMemes.
