Tuesday, November 5, 2013

A Better Model Means Better Results

If you try to put someone on an exact hand, such as ace king, you might call with 44 and determine that you have a better than 50% chance of winning. You may run into a higher pocket pair and convince yourself you were "unlucky" or "made a bad read". In reality it wasn't that you made a bad read it is that you had a "bad model". An improved model would look at the probability that you are up against 2 unpaired cards and assign a 52% chance of winning, and the probability that you are up against a pocket pair and assign a 20% chance of winning.

Yet an even more accurate model would use poker software like "pokerstove" (I am not sure it is still around) or slice equity calculator. This would approximate the exact odds vs "his range". You could improve upon it with knowledge of pot odds and other variables.

But this is still a limiting model. Afterall, you are not up against a specific "range", but a range of possibilities of all cards. A very small percentage of the time that opponent is dealt a particular card he could play it. Plus, you don't know if he favors suited connectors or suited aces and kings, if he prefers broadway cards or weak aces, and exactly what hand range he is playing. You might venture to guess that he will never fold acesor kings given a particular action and given that way he acted he will have aces or kings every time. Well then, there is a 100% chance that Aces and Kings is in that hand range.  But there may be only a 50% chance that A5s is in that range. In reality the range should be reflected as such. While the opponent may never fold AK he might be more likely to call with it, so the fact that he has raised may reduce the chances of him holding AK. Every hand should be weighted and reflected accordingly to represent a more accurate model.

This model is still flawed, the fact that 7 other people folded increases the probability of an ace being in the deck and thus dealt to your opponent, while LOWER cards like your remaining two 2's are more likely to be folded. If he has an ace king vs your 22, given the action it actually becomes a slight underdog anyways. Trying to model this accurately though is painstakingly difficult as you have to make some sort of probabilistic calculation of what hands each opponent will fold in given position and then run the probability that opponent will fold an ace, king, queen, jack, ten, and so on for all cards, and given that, reflect the variable change and expectation of the next guy having a hand. Although the person on the button may have a 1/221 chance of being dealt aces, when he does the action is much more likely to be folded around to him. Thus, given several folds, the effective odds of him having aces are more like 1/133 than 1/221 because of conditional odds. And while your AK may be stronger, what about AJ which while much stronger against low pairs, is more likely to be facing AK than against 1 or 2 "random" opponents after 6 or 7 folds, especially given that opponent has represented a 3bet hand.

If you can learn to more accurately simulate poker hands and account for subtle variables like this you will be much better off than not doing this. The more accurate your model or mental model and assumptions and the more you adapt to that model, the better off you will be.

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