@@ -4,13 +4,13 @@
To apply decision theory to the question of whether or not to play, you calculate the expected payoffs of both the alternatives. The expected payoff of playing the game is equal to the payoffs of the possibilities multiplied by the probability of the outcome. There are 3 possible outcomes of playing the game:
* draw a black card (probability = 0.5, payoff = 0, expected payoff = 0.5 x 0 = $0.00)
* draw a heart (probability = 0.25, payoff = 10, expected payoff = 0.25 x 10 = $2.50)
-* draw a diamond (probability = .25, payoff = 20, expected payoff = .25 x 10
= $5.00)
+* draw a diamond (probability = .25, payoff = 20, expected payoff = .25 x 20
= $5.00)
-The expected payoff of the game is the sum of the calculations above, minus the cost of the game, i.e. ($.00 + $2.50 + $5.00 - $5
.00 = $2.50)
+The expected payoff of the game is the sum of the calculations above, minus the cost of the game, i.e. ($.00 + $2.50 + $5.00 - $10
.00 = $-
2.50). Therefore you can expect to lose $2.50 if you play the game.
-Now compare that to
the expected payoff of not playing the game ($, no risk, no reward), and the expected payoff playing the game ($2.50) is higher, therefore you should play the game (assuming, of course, that
you want to maximize your
expected payoff)
.
+Now compare the expected payoff of not playing the game ($, no risk, no reward), and the expected payoff playing the game ($-
2.50). If
you want to maximize expected payoff you should __not__ play the game
.
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See other InterestingMemes.
