Modelling Player Behaviour

What should the model of your opponent begin with?

You can assume a model of the general type of player that you see at the stakes you are playing, but I don't think this is necessarily best. Proper play against any given type of 'average player' could expose serious flaws in your actions and cause you to pay a very high price if your model is wrong. If it takes you a long time to adjust, you've lost a lot of value already.

Instead, start with an assumed model such that your optimal play against that model is very difficult to exploit. Another way of thinking about this is to not really model your opponent, but just come up with a system of behavior that is hard to exploit given any opponent, though I think this is a bad way of thinking about things (even if it's the most natural, and how most people are taught how to play). I think coming up with a model of your opponents and phrasing your own behavior always with respect to that model is a better way of framing the problem. Note that I'm intentionally being ambiguous here -- I haven't said whether "a difficult to exploit" model is TAG/LAG/etc. I don't think I have an answer to that.

Another possibility is to come up with a model that elicits distinct behavior from your opponents; this facilitates information discovery. This is less about creating my action/decisions for you and more about inflicting this on your opponents (though the latter tends to breed the former).


What kind of information should influence your model?

Once you have a model, you begin shaping that model based on two very different types of information. Information aggregated over repeated actions that statistically suggest behavioral patterns and information that is simple and complete.

The first type of information can be watching a player raise every hand preflop for 10 hands in a row. This should statistically suggest this player is raising a wide range of hands, even if you have no showdowns to prove it. There is a high degree of uncertainty in this information.

The second type of information occurs when you do have a show down, and you are privy to all the information (well, sometimes just 'more').

In no limit hold'em the first scenario is far more common, and determining which model suggests the statistical pattern you are observing is very important. This is not an easy task though. What is preferable is to have access to the model, and generate the statistics based off a given model, but of course you can't do that. If you see a player with a VPIP of 23%, what does this mean? If they raise preflop 14% of the time, how do you come up with a good model of what their preflop raising hand range is? And though there is generally a tendency for players to raise/call via an ordered list of hands by strength, this does not have to be true. So clearly this type of information by itself is no good.

But discovering the underlying model is hard even when we build our models off these scenarios, since this information is so infrequent and biased (it will show more hands that make it to show down or end up all in, or where all players have completely missed, played passively and just checked it down -- usually out of the blinds). And how do we deal with intentional information, such as a player showing a hand when all other players have folded? Even without the bias, each way a hand is played has far more information than that particular hand -- it demonstrates behaviors that should be applicable to similar situations. Did the player raise a flush draw? Expect to see that again. Did a player check a huge hand on the river? Be careful of river check raises.

Sleep for now, but more thoughts coming...