## June 9, 2016

Event

#### Submission Title

Estimating the Fraction of the Kelly Bet

#### Session Title

Session 3-2-D: The Math of Game Play

#### Location

The Mirage Hotel & Casino, Las Vegas, Nevada

#### Start Date

9-6-2016 10:30 AM

#### End Date

9-6-2016 12:00 PM

#### Disciplines

Statistics and Probability

#### Abstract

It is well known that an advantage gambler maximizes the average geometric growth rate by using Kelly betting. If the advantage is known precisely, then one can to use Full Kelly betting or, more commonly, some fraction of it. Systematic gamblers may have an advantage, but may not know exactly how large it is. This may be the case for e.g. sports bettors, blackjack and poker players and future traders. We show how they can estimate the fraction of full Kelly they have been employing, from their past results. This ongoing process enables them to select future bet sizing scientifically according to their risk tolerance. We use a geometric Brownian motion model to obtain a confidence interval estimator for the fraction of Kelly bet based on historical bankroll data.

#### Keywords

Optimal betting, proportional betting, Kelly betting, confidence intervals

Attachment: PDF containing 28 slides

Title slide: Estimating Kelly Fraction

Audio recording of session is attached as a downloadable MP3 audio file, 59.16 MB. This speaker’s presentation begins at 18:33.

#### Share

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Jun 9th, 10:30 AM Jun 9th, 12:00 PM

Estimating the Fraction of the Kelly Bet

The Mirage Hotel & Casino, Las Vegas, Nevada

It is well known that an advantage gambler maximizes the average geometric growth rate by using Kelly betting. If the advantage is known precisely, then one can to use Full Kelly betting or, more commonly, some fraction of it. Systematic gamblers may have an advantage, but may not know exactly how large it is. This may be the case for e.g. sports bettors, blackjack and poker players and future traders. We show how they can estimate the fraction of full Kelly they have been employing, from their past results. This ongoing process enables them to select future bet sizing scientifically according to their risk tolerance. We use a geometric Brownian motion model to obtain a confidence interval estimator for the fraction of Kelly bet based on historical bankroll data.