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• Winning is worthless • Suppose you start with
$1M • EU(gamble)
EU(do_nothing)=+4.9*10
5 • Gambling is raHonal because losing doesn’t hurt 7 Convexity & Gambling
• Convexity: f (αx + (1 − α ) y ) ≤ αf ( x ) + (1 − α ) f ( y )
0 ≤ α ≤ 1
• Suppose x and y are in the convex region of the uHlity funcHon and are possible outcomes of a bet €
• Current cash on hand is x<z<y • Suppose bet has 0 expected change in monetary value: z = αx + (1
α)y • Will the bet be accepted? • UHlity of doing nothing: f(z) • UHlity of accepHng the bet: αf(x)+(1
α)f(y) MulHahribute UHlity FuncHons
• So far, we have deﬁned uHlity over states • As always, there are too many states •...
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This note was uploaded on 02/17/2012 for the course COMPSCI 170 taught by Professor Parr during the Spring '11 term at Duke.
 Spring '11
 Parr
 Artificial Intelligence

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