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This graph shows the expected value of different betting fractions. The game in this example is for a coin flip win-or-lose, with the coin weighted to win 60% of the time. The optimal bet, called the Kelly bet, is 20% of the bankroll. Over time, on average, each round will increase the bankroll by
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2.03%. Betting less than 20% will have a lower average return, e.g. betting 10% will provide an average 1.5% increase. Betting over 38% percent will result in losing money over time.
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The following pages on the
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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets.
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