Re: 20%??
This post was fraught with logical errors. In fact, your three main reasons for playing 20% of hands are all dead wrong
1.
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I am not a big fan of maths, but let's give an intuitive shot. Let's say the game is ten handed, so 10% of the time I have the best hand preflop. If the pot is always played heads up between the best and the second best hand, and if all the players have the same level, then I should only play those 10% best hands, then I will be a favorite everytime I play. Now if the hand is played between the three best hands (30% of hands dealt), if I play my 15% best hands, I should maximize my EV. And if 40% of hands are played preflop (average in tough games), playing the 20% best should be optimum. But I dont know at all if it makes any sense...
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This little thought-experiment is deeply misguided. The notion that you can guarantee e.v. merely by cutting the “losing” 20% of hands is ridiculous. Imagine for one second that the table contains 10 clones of yourself, and you play perfectly. On average, you play 30% of hands. Do you think one of your clones could actually improve his E.V. by decided to play only 15% of hands? What hands would he be cutting? Well, by the stipulation that you play perfectly, he would be dumping only profitable situations. Thus, the clone who only played 15% of his hands would be the fish! He would be failing to extract equity when it exists! Suddenly everyone at the table would have a + E.V. except for him.
And just to make an obvious point, let’s say that clone actually could make money by playing half as many hands as you. What would the game-theoretical response to that be? Well, the other clones should start playing 7.5%, 3.75%, and so on, until all clones play 0 hands, and you can just go home.
Certainly you can make money in poker by playing fewer hands than your opponents, but not inherently, as you wrongly suggest. You make money by recognizing situations that aren’t profitable and avoiding them - the same situations that your opponents gladly enter.
2.
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Let me give another reason : most NLHE experts advocate playing 15-20 of your hands. I think this percentage is not very game-dependant, it should be an intuitive approximation of a mathematical rule from game theory, considering the optimum number of hands you should play when 10 players are dealt random hands that can roughly be classified. I cant explain why exaclty, but I am quite sure the optimum percentage of hands play dont depend on the game played, but on the structure, the stackes, and the looseness of the games. So I play as many hands in every game of similar structure, whether it is stud, HE, Omaha, Omaha 8 etc.
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This is also just game-theoretically incorrect. The optimum percentage of hands played absolutely depends on the game you are playing -- specifically, it depends on the variance involved in that game, your likelihood of catching up after the flop, and the likelihood of an individual hand ending up the winner against the field. In hold-em, the optimal number of hands that you should play is fairly low because it is hard to “catch up” with the winning hand. The first limitation on how many PLO hands is optimal should be the instant recognition that it should be higher.
If you don’t see the relationship between variance and %age of hands played, imagine a game in which a hand could be no more than a 1% favorite against 80% of hands, but would be a 90% favorite against the other 20%. Blinds are $10 and your stack is $100. You are playing 3-handed and someone raises all-in UTG -- What %age of hands should you be calling with? Clearly you should call with all hands that are in the 80% category, and fold the other 20%. You would make money in this game from times when people call with the 20%, or times when people fold the 80%, or when someone tries to bluff you with the 20%, etc -- but you would be playing a LOT of hands in this game.
3.
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A last reason : I think a good player should always play less hands than the other players at the table. Once again, I am sure game theory could help me understand why, but I havent studied it. Usually, when a friend asks me how many hands he should play preflop, I advise him to play between 20 and 10% less than the oither players, depemding on his level. Since I want to minimize my swings, and I consider myself a poor PLO player, I want to play about 20% less hands than the other players in a tough PLO game.
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I think it is generally the case that a good player will end up playing less hands than average at any table -- even I play a bit less than average. However, it by no means follows that they should “game theoretically.” If, god help me, I’m playing at a rock table where everyone is passing up profitable situations, I would be remiss to pass up even MORE profitable situations myself. In that case, I should definitely be playing MORE hands than everyone else. You should only be playing 10% less than the other players if, by your estimation, the other players are playing 10% too many hands. Again, your fundamental error here is that you seem to think that throwing away perfectly good hands somehow gives you an inherent “game theoretical” edge. As someone who has dabbled in both game theory and logic, I can tell you that your thoughts here run afoul of both.
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