Edward O. Thorp

1. The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market (Handbook of Asset and Liability Management, vol. 1, ch. 9, pp. 385–428) — book or paper, 2006
   A copy hosted on gwern.net; the 44-page text was read.

• Size and riskFor long-term compounders the Kelly criterion maximizes the expected logarithm of wealth: bet a fixed fraction of current capital chosen by edge and variance, recomputed as capital changes.
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• Size and riskOverbetting is much more severely penalized than underbetting, so edge estimates should be conservative.
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• Size and risk“Half Kelly” has 3/4 of the growth rate with much less chance of a big loss: the chance of ever losing half the starting capital is 1/2 at full Kelly but only 1/8 at half Kelly.
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• Size and riskDoubling before halving has probability 2/3 at full Kelly and 8/9 at half Kelly.
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• Size and riskWhy fractional Kelly: if the true edge is half the estimated one and you bet 1.5 times the estimated Kelly fraction, the growth rate is negative and you are ruined; even full Kelly then gives a growth rate of zero with wild swings.
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• DisciplinePeople who watch a large downward swing tend to quit or be forced out; he reports most prefer the comfort of half Kelly in exchange for giving up a quarter of the growth.
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• DisciplineConclusion of the paper: long-term compounders should avoid betting more than the Kelly fraction and, since probabilities are uncertain, should limit their investment fraction enough to prevent a significant risk of overbetting.
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Often attributed to this trader, but not found in the sources above. Not listed as his or her rules.

• The fixed “half Kelly” recommendation is a common simplification: the paper shows how the trade-off works and says most people prefer half Kelly or a nearby value, it does not state half Kelly as a rule.

Kelly sizing needs a known edge, and with an edge that is zero or negative the Kelly fraction is zero or negative: bet nothing. This project has not found a profitable strategy, so the criterion gives no position size for any rule on this site.