Opponent Modelling – Calling/Raising a 4-bet
One thing about poker math is that it’s not just about odds. A proper application of math to poker also looks at modelling opponents.
So, today I want to take an initial look at this. Say, you’re dealt a hand like KK. You raise preflop, there are some folds, 1 player re-raises, it folds around back to you, and you 4-bet preflop. For each possible preflop hand, what are the odds that he will call/raise your 4-bet?
Let’s assume that you don’t have much data on the player, and you’re looking at hand strength alone. And also assume that your opponent is a decent player. For certain hands, it’s easy to predict. With AA he’s always at least calling the 4-bet. For a hand like 7-2, there’s practically no chance that he’ll call a 4-bet.
What about in the middle, though? After a discussion with a friend of mine, we concluded that the distribution would look something like this:
Basically, the horizontal axis shows represents the strength of the hand (with the weakest hand on the left, and the strongest on the right). The vertical axis is the probability of calling (or raising) a 4-bet. Essentially, what the graph means is this. There are a number of weak hands, which players are highly unlikely to call with. 7-2, 9-3; these are all hands which are almost certain to be folded. There are also certain hands which are players will almost definitely call with: AA, KK, QQ, etc. That’s why the extreme left and extreme right side are more or less flat.
In the middle, though, are the marginal hands. With these hands, players might sometimes call, depending on the player’s ability, the situation at the table, a number of factors. But essentially, we believe that the marginal hands would have an increase in frequency of calling, based on the strength of the hand. Basically, there is almost no difference between how often a player would call with AA and KK, or how often he’ll fold 7-2 or 9-4. But there will be larger differences between how he plays KQ offsuit, and 99, for example.
So based on that hypothesis, I’ve created a chart to predict a probability of how often a player will not fold (ie call/raise a 4-bet). I used the Chen formula to determine hand strength, and grouped the hands roughly. Based on the hand strength and the groups, I then assigned a probability, with the lowest group distributed over 0 to 5%, the highest group over 95 to 100%, and the middle groups distributed across the remaining range (with a few more subtleties, but that was the general idea. What I got was this.
To be honest, it doesn’t quite match what I want. The problem with the Chen ratings is that the hands tend to be bunched up together. I’ll look into other ways to evaluate hand strength, but so far, this is my initial (and admittedly very crude model). I’m thinking for the next step, I’ll use the WestonPoker PreFlop Odds chart instead of the Chen formula as a basis for hand strength. I think that will give a much smoother curve. I’ll do that and post an update soon.
What do you think, though? How do you think the chart of a 4-bet call/raise would look like? Am I on the right track or what would you have done differently?