landsburg exercise 18.7
Steve Langlois ( (no email) )
Tue, 27 Apr 99 18:09:51 -0500
In response to Collision's e-mail,
The actual probability is calculated as p(win)/p(lose) normalized so that the
denominator equals one. For the expected value - E(x) = p(win) x amount of
winning - p(lose) x amount of loss. To get the fair odds, select p(win) and
p(lose) in the expected value equation so that E(x) = $0. The 2 examples for
18.7 go:
restaurant: actual odds = .5/.5 or 1 to 1, E(x) = .5($2,000) - .5($1,000) =
$500 - By inspection you can see that using p(win) of 1/3 and p(lose) of 2/3
gives and E(x) of $0. Normalize it to get .5 to 1 for the fair odds.
concert: actual odds = .75/.25 or 3 to 1, E(x) = .75($1) - .25($1) = $0.50 - By
inspection you can see that using p(win) of 1/2 and p(lose) of 1/2 gives and
E(x) of $0. Normalize it to get 1 to 1 for the fair odds.