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. | KELLY CRITERION FINGER EXERCISES | | | | | | | | | | | | |
. | Return distributions from ten coin flips | | | | | | | | | | | | |
. | "Betting 100%" maximizes expected returns. The Kelly criterion of betting 1/4 maximizes log returns-- think of it as maximizing the chance that you will have more money than any alternative strategy... | | | | | | | | | | | | |
. | | | | | | | | Bet All | Bet 1/4 | Pascal's Triangle | Number of Losses | | |
. | | | | | | | | 59049 | 57.6650390625 | 1 | 0 | | 57.6650390625 |
. | | | | | | | | 0 | 28.83251953125 | 10 | 1 | | 288.3251953125 |
. | | | | | | | | 0 | 14.416259765625 | 45 | 2 | | 648.731689453125 |
. | | | | | | | | 0 | 7.2081298828125 | 120 | 3 | | 864.9755859375 |
. | | | | | | | | 0 | 3.60406494140625 | 210 | 4 | | 756.853637695312 |
. | | | | | | | | 0 | 1.80203247070312 | 252 | 5 | | 454.112182617188 |
. | | | | | | | | 0 | 0.90101623535156 | 210 | 6 | | 189.213409423828 |
. | | | | | | | | 0 | 0.45050811767578 | 120 | 7 | | 54.0609741210938 |
. | | | | | | | | 0 | 0.22525405883789 | 45 | 8 | | 10.1364326477051 |
. | | | | | | | | 0 | 0.11262702941895 | 10 | 9 | | 1.12627029418945 |
. | | | | | | | | 0 | 0.056313514709473 | 1 | 10 | | 0.056313514709473 |
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. | | | | | | | | 57.6650390625 | 3.24732102546841 | 1024 | | | 3325.25673007965 |
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