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Efficient Poker Theory

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By RalphCramden
January 7, 2003

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You can't make money playing poker. It is because all of the players have access to the same information, and the bets have that information factored into them. If you are playing 5 card draw, we all know the probabilities of being dealt certain hands. We all know the probabilities of drawing certain hands from our dealt hands. We all know the probabilities of particular hands we have winning in the game against the number of people we are playing against.

We all know how to make our bets without telegraphing the information about what we have in our hands. Similarly, we all know how to read the information that the other players are telegraphing about their hands, as they attempt to bet "optimally" given the hands that they have. (Example, player A never bets except when he has a full house or better. Everybody will figure that out, so they will fold when player A bets, unless they can beat a full house. But Player A sees everybody folding when he bets, so he knows to change his betting pattern. But now he is betting on wimpy hands, cutting into his winnings. BUT EVERYBODY KNOWS THIS, so they all get efficient, somehow.)

Obviously, (to some of us only, I will grant), the chain of reasoning of "Efficient Poker Theory" starts out wrong and just gets wronger. We can relatively easily learn how to draw cards. We can learn probabilities of certain hands, and probabilities (under simplifying assumptions) of what rank hand it will take to win. Most poker players don't learn all this, but we can. BUT BETTING OPTIMALLY! Can't learn it! Can barely define it! Because it is dynamic. If you always bet on full houses, if other people don't know that, it is a good strategy because you will mostly win with full houses. But once the other people know it, you find the only time people stay in when you have a full house is when they can beat it! So you make no money (because people fold) when they can't beat it, and you lose big money once in a while when they can beat your hand! So you have to change your strategy, what is optimal at one time is non-optimal later as other people exploit different pieces of the information.

And I am thinking draw poker. What about 7 card stud where you successively bet on 3, 4, 5, 6 and 7 cards, and you see 1, 2, 3, & 4 cards of your opponents? All the information is there... but even just tracking the mechanical probabilities of the outcomes at all the intermediate steps is overwhelming. Then to put the effects of telegraphing information about your hands to the other bettors, who then use that information in betting against you?

In case you have not had the pleasure of playing in a real poker game, it isn't even a LITTLE random. Great poker players crush good poker players with astonishing consistency. They are just better at using the information, and dancing around the dynamics of the information as it changes.

Now I ask you, which is, on the face of it, more perfectly a game of chance? Playing poker or investing in stocks?

The answer, remarkably, doesn't matter. Poker is clearly a game of chance, and yet Efficient Poker Theory is obviously wrong in a strong way. You can't prove it is wrong from theory, you can prove it is wrong by going out there and losing \$100s of dollars with great consistency to people who just do it better than you do.

Now if Efficient Poker Theory is wrong, and poker really is a game of chance in a world which is much more finite than business, then how could Efficient Market Theory be right?

Well it COULD be right, maybe there is some other difference between poker and stocks we haven't thought of. But the EVIDENCE is that it is wrong. http://www.tilsonfunds.com/superinvestors.html is a good argument. You can only deflect that argument by claiming the high performance of the superinvestors cited is just the skinny tail of the bell (or other more tail-heavy) curve.

Here is a reasonable test for the Efficient Market Theory. Go out and buy a basket of all the stocks on the Nasdaq that trade for \$1/share or less. Equally weight by value, so you gotta buy 10 shares of the one trading for a dime. Every 3 months (or 6 months, or you choose the interval) go and re-balance: sell the ones who are over \$1/share and re-buy and re-balance your holdings. I have not done this, but I bet this will be a nice mechanical trading strategy that handily under performs the NASDAQ index. (Note: I could be wrong, I haven't done this.)

I think a good test of Efficient Market Theory is can you invent a mechanical investing criterion that UNDERPERFORMS the market. If you can, it means that the market is not efficient, that not all prices reflect values equivalently.

Peace and Full Houses,
Ralph

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