Poker and Finance Part II is deeply unsatisfying

[Izverg04]

I think the article is full of conceptual misundersandings and dubious statements. My general dislike of the article is two-fold. One, while it is true that the same general rules of risk management apply to finance and gambling, the examples he choses are really poorly thought out. In fact, professional blackjack community is a much better place to go for all the answers on risk management in poker -- they are really the people who "figured this all out a long time ago." Two, the author is trying to prove that complex risk management is essential to a poker player, while in fact it doesn't have much room in poker -- because there is just so much uncertainty about the rate of return that making fine adjustments due to risk is realistically impossible. Ed Miller wrote an article on this somewhere -- perhaps someone can link to it. Really, the only risk-related formula that a poker player should know is the one for RoR vs bankroll, and he'll do fine.

I'll provide a couple of specifics to explain my first point.

First, let's take the vague attempts to apply Sharpe ratio to poker. Sharpe ratio, in its simplest form, is the solution when you maximize the risk-adjusted return of a portfolio that can contain cash and a single security. The solution is that you should choose the security with maximum ReturnRate/StdDev of the security. But it is essential to be able to size your position -- it will be proportional to ReturnRate/StdDev^2. In fact, if you are unable to float the size of your bet, Sharpe ratio doesn't have any meaning really -- it won't be the solution to this new, different maximization problem. And I don't see how you can size the bet to your liking in none of the examples the author gives

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In poker, Sharpe ratio can be used to express the risk-adjusted characteristics of:

* a single play;


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Nope, your choices are highly limited, with every play having a specific EV and StdDev, so risk-adjusted optimization will never give something like a Sharpe ratio.

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* a single player, in a specific game;
* a single player for a specific period of time, or specific number of hands;
* a single player over his entire poker-playing life


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Nope, you can choose the stakes you are playing for, but again you have a very specific functional dependence of EV and StdDev vs stakes, because the opponent skill level changes, so again, when you maximize risk-adjusted return, Sharpe Ratio will not fall out anywhere by miracle. So basically, I feel that "Sharpe ratio" is introduced in the article just because it sounds cool and has to do with risk management.

Another problem I have is with the use of diversification and the example given:

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excellent players know that they can derive additional value from that tightness by mixing in a few otherwise unplayable hands in spots where observant opponents must give them credit for a high-quality Group 1 or Group 2 hand. This is diversification.

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Diversification in portfolio theory is good because when you combine positions that are uncorrelated, you can now bet more without taking on more risk. When positions are anti-correlated, it's even better, you reduce the overall variance profile of your portfolio for the same return. In the example given, I can't see any parallel to portfolio diversification. You are playing an additional hand, simply because it produces more return, not to reduce variance -- in fact playing an additional hand will have to increase variance. So you can call it diversification but just using the same vague word to describe something doesn't make it the same thing. In fact, the only place in poker where I could see a parallel to portfolio diversification is e.g. playing 2 tables of $10/20 instead of 1 table of $20/40, but this choice is rarely applicable -- multitabling habits typically stay the same while going up through the levels.

I had a couple more specifics in mind, but this is already tl/dr.

[infinite_loop]

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Nope, your choices are highly limited, with every play having a specific EV and StdDev, so risk-adjusted optimization will never give something like a Sharpe ratio.


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Why not? You DO have choices. Some choices will produce different EV than others, at different standard deviations.

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Nope, you can choose the stakes you are playing for, but again you have a very specific functional dependence of EV and StdDev vs stakes, because the opponent skill level changes, so again, when you maximize risk-adjusted return, Sharpe Ratio will not fall out anywhere by miracle. So basically, I feel that "Sharpe ratio" is introduced in the article just because it sounds cool and has to do with risk management.

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EV is what ties it together. EV is the product of all these factors you mention. It's almost like you have more of a problem with defining EV over a range of hands than with using the Sharpe Ratio.

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You are playing an additional hand, simply because it produces more return, not to reduce variance -- in fact playing an additional hand will have to increase variance.

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No where in the article does it say expanding the range of hands you play will reduce variance. It simply says you're adding value.

[Izverg04]

Security 1: Bet=bet1, EV/year=0.1*bet1, Std/year=0.15*bet1
Security 2: Bet=bet2, EV/year=0.15*bet2, Std/year=0.4*bet2

You are free to choose bet1 and bet2 as you wish.

Call: Bet=1 BB, EV=0.1 BB, Std=2 BB
Raise: Bet=2 BB, EV=0.12 BB, Std=3 BB

Do you see how optimizing risk-adjusted return is a different problem in the first example than in the second? You will apply absolutely the same technique to the first problem, and will get the Sharpe ratio. You will apply it to the second example, and you will get a different solution -- for one, the solution will have to include what your bankroll is, while Sharpe ratio won't, because your bets will be proportional to the bankroll.

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In the first exmaple, the bet sizes cancel out and you're left with the same type of problem as the second. EV is a product of these bet sizes among other things. You can't separate the bet size from EV.

Bankroll is not at all a factor here. EV is independent.

[flight2q]

Yes, Izverg04, in portfolio management you get total liberty to pick your investment proportions. In poker, you don't. So things are quite different.

There was an article in the magazine by Bill Chin in July 2005. IMO he does a better job of laying out the applications. And he understands that bankroll size makes a difference.