Example



Posted by Steve Heston on July 07, 1997 at 22:08:02: In Reply to: ?Steve posted by Mike Lea on July 07, 1997 at 14:19:49:

Suppose you win one unit with probability .505 and lose one unit with probability .495. If you bet fraction "a" of your bankroll then the expectation of G is

.505*(1+a) + .495*(1-a).

The expected logarithm of G is

.505*ln(1+a) + .495*ln(1-a).

You can easily verify that the expectation of G is maximized by letting a = 1, but the expected logarithm of G is maximized by letting a=.01 (approximately).



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