Kelly Criterion / Bankroll Management

[pokrat]

Hi,

my first post here from germany [img]/images/graemlins/smile.gif[/img], the last days i've tried to understand the kelly criterion...what do you think of this? I've found a good article:

www.jimgeary.com/poker/letters/KELLY.HTM

pokrat

[pzhon]

The Kelly Criterion has been discussed quite a bit on these forums.

Google site:twoplustwo.com Kelly Criterion

It can be used to offer consistent bankroll guidelines across variants of poker. Many people prefer to use a fractional Kelly system, with a bankroll c times the bankroll recommended by the pure Kelly Criterion. Common values of c range from 2-4 for individuals.

[uDevil]

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It can be used to offer consistent bankroll guidelines across variants of poker. Many people prefer to use a fractional Kelly system, with a bankroll c times the bankroll recommended by the pure Kelly Criterion. Common values of c range from 2-4 for individuals.

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Hi pzhon,

If applied to investing in the stock market, is the range of c for a typical investor very different from this?

[pzhon]

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Many people prefer to use a fractional Kelly system, with a bankroll c times the bankroll recommended by the pure Kelly Criterion. Common values of c range from 2-4 for individuals.

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If applied to investing in the stock market, is the range of c for a typical investor very different from this?

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Typical individual investors may be far from using a rational strategy, and may not understand the tradeoffs between risk and reward, and the idea of diversifying to obtain the same return at a lower risk.

Some institutional investors use c=6 (personal communication). The atypical Berkshire Hathaway is much more aggressive; one source estimated that they use c=1.25. A wide range should be expected, as some funds focus on growth while others emphasize security.

[uDevil]

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Many people prefer to use a fractional Kelly system, with a bankroll c times the bankroll recommended by the pure Kelly Criterion. Common values of c range from 2-4 for individuals.

[/ QUOTE ]

If applied to investing in the stock market, is the range of c for a typical investor very different from this?

[/ QUOTE ]
Typical individual investors may be far from using a rational strategy, and may not understand the tradeoffs between risk and reward, and the idea of diversifying to obtain the same return at a lower risk.

Some institutional investors use c=6 (personal communication). The atypical Berkshire Hathaway is much more aggressive; one source estimated that they use c=1.25. A wide range should be expected, as some funds focus on growth while others emphasize security.

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That is very helpful. Thanks.

[DrVanNostrin]

From someone who doesn't know much about the subject it seems as though c values should be less than 1. The KC assumes you cannot replenish your roll. If you can reload you should be more aggressive by lowering your c value. Is it just uncertainty in expected value and variance that force investors to use such large c values?

[pzhon]

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From someone who doesn't know much about the subject it seems as though c values should be less than 1.

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The pure Kelly Criterion corresponds to c=1, and the probability that you will ever be reduced to p*initial bankroll by following the Kelly Criterion is p. This is already considered too aggressive by most advantage gamblers. If you use a lower value of c, you will experience much worse swings.

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The KC assumes you cannot replenish your roll.

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The definition of bankroll assumes you cannot replenish your bankroll. It was not a special assumption made by Kelly.

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If you can reload you should be more aggressive by lowering your c value.


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If your bankroll is larger than your balance, you may wish to accept gambles that would appear extremely reckless to someone whose bankroll equals your balance. If your bankroll is not your balance, you may not be able to determine a reasonable strategy based on your balance alone, and there may be no fixed value of c that makes sense for your balance.

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Is it just uncertainty in expected value and variance that force investors to use such large c values?

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Even if there were no uncertainty about the expected value and variance of the gambling opportunities, the value of c should still depend upon personal risk tolerance.

Some of the properties of the Kelly Criterion use the assumption that you can rescale your wagers. This is not the case in poker. In general, you expect that higher stakes games will be tougher. There are also limits on how low the stakes can get. These factors both argue for using a greater value of c than the value corresponding to your utility function.

[BillC]

The c=6 is the "optimal f" suggested by R. Vince (amazon him and see our paper on bjmath.com).
As in poker, a lot of the time investors don't know their edge and variance with much accuracy, so they make guesses and go by the seat of their pants. Marc I. derived a formula for estimating c (giving confidence interval for c -- it is quite complicated) from historical data. This formula could be used for poker too. I will try to dig it out sometime and write it up.
Another comment: It is absurd to use a bankroll that can be replenished. You have to include future contributions to your bankroll. Include the net present value of all future inflows minus expenses and taxes.

[Esection]

I'm reading a really great book about the history of the kelly criterion, kelly, and its subsequent use in gambling and wallstreet.

check it out. a definitely awesome read.

Fortune's Formula by William Poundstone:

http://www.amazon.com/Fortunes-Formula-S...7544851?ie=UTF8