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The Challenge

You bet a series races, where:
• If you win, you get W dollars for each dollar bet
• If you lose, you lose your bet
• For each race, the probability of winning is p and losing
is q = 1 − p
• You bet some fixed percentage “per” of your bankroll B
each race, for you have (1 − per)B if you lose and
(W − 1) per x B + B if you win.

The Solution

The right value of “per” is the Kelly Criteria