$f^{*}=p-\frac {q}{b} $where: - *f* * is the fraction of the current bankroll to wager - *p* is the probability of a win - *q* is the probability of a loss - *b* is the proportion of the bet gained with a win >In a 1738 article, [Daniel Bernoulli](https://en.wikipedia.org/wiki/Daniel_Bernoulli "Daniel Bernoulli") suggested that, when one has a choice of bets or investments, one should choose that with the highest [geometric mean](https://en.wikipedia.org/wiki/Geometric_mean "Geometric mean") of outcomes. This is mathematically equivalent to the Kelly criterion, although the motivation is entirely different (Bernoulli wanted to resolve the [St. Petersburg paradox](https://en.wikipedia.org/wiki/St._Petersburg_paradox "St. Petersburg paradox")). > >An [English-language](https://en.wikipedia.org/wiki/English_(language) "English (language)") translation of the Bernoulli article was not published until 1954,[12](https://en.wikipedia.org/wiki/Kelly_criterion#cite_note-Bernoulli_translation-12) but the work was well known among mathematicians and economists. # Optimal betting example > In a study, each participant was given $25 and asked to place even-money bets on a coin that would land heads 60% of the time. Participants had 30 minutes to play, so could place about 300 bets, and the prizes were capped at $250. But the behavior of the test subjects was far from optimal: > > Remarkably, 28% of the participants went bust, and the average payout was just $91. Only 21% of the participants reached the maximum. 18 of the 61 participants bet everything on one toss, while two-thirds gambled on tails at some stage in the experiment.[9](https://en.m.wikipedia.org/wiki/Kelly_criterion#cite_note-9)[10](https://en.m.wikipedia.org/wiki/Kelly_criterion#cite_note-10) # Resources - [Practical implementation of the Kelly criterion-Web](https://www.frontiersin.org/articles/10.3389/fams.2020.577050/full) - [Kelly Criterion for multivariate portfolios](https://1drv.ms/b/s!AkzI3OIfusjvgvtygjsw2TYofihXCA?e=UUF7qC) **Case Studies:** - [[CHG Issue 117 The Game of Life]] Explore Further: [Wikipedia](https://en.wikipedia.org/wiki/Kelly_criterion) | [Moontower Resources](https://moontowerquant.com/kelly-criterion-resources) Tags: #portfolio-management Your support for Cedars Hill Group is greatly appreciated <form action="https://www.paypal.com/donate" method="post" target="_top"> <input type="hidden" name="hosted_button_id" value="74PGN8ZXHQVHS" /> <input type="image" src="https://www.paypalobjects.com/en_US/i/btn/btn_donate_LG.gif" border="0" name="submit" title="PayPal - The safer, easier way to pay online!" alt="Donate with PayPal button" /> <img alt="" border="0" src="https://www.paypal.com/en_US/i/scr/pixel.gif" width="1" height="1" /> </form>