April 3, 2010 – 10:41 am | 7 Comments

I’ve compiled a short (just 7-pages) e-book, an introduction to the mathematics of poker. It’s basically covers how to calculate your expected value in a certain spot – starting with explaining what EV is, all …

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## Opponent Modelling – Calling/Raising a 4-bet

Submitted by on February 9, 2010 – 2:20 am2 Comments

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?

• Mac says:

Well if your up against the standard nit who plays say 15/15 at 0.10NL 6max then..

He will almost never call a 4bet with anything but TT and JJ and QQ is either call fold or raise. KK is shove.

But bad players do call with 88 77 even tho the set mining odds are so -ev when up against over pair its funny.

It depends really what limit your playing. At 0.02NL you will only get a 3 or 4bet with AA and KK and maybe sometimes with AK(he will go all in with it)

The higher you go the move people 3 and 4 bet pairs because they understand the value as compared to the weak players who need to see a flop with 88 in order to call a bet.

At 1/2 people 4 bet/shove AK AQ AA KK QQ JJ TT and maybe 99. The reason for it is many people attack the blinds more and 4betting becomes +ev as opposed to the micro.

I don't know exactly how you can put a chart like this because every stake on every site is different.

But it looks good..

• Derrick Kwa says:

Definitely, it's player specific, and any chart I do at the moment would be very crude. I don't deny that.

I think, though, I have to start somewhere. With this chart I'm assuming players like those you mentioned at 1/2. Basically, in a vacuum, a player who knows what he's doing. And I'm thinking that using this as a starting point, you can include information about the situation (player's stats, the pot size, etc), to get a more definitive “value” on the situation.

But yeah, definitely, this is nowhere near a finished product. This is barely a starting point into my exploration of modelling opponents (in a way that's possible for humans), and I had to start somewhere. Hope it was still interesting and/or of some sort of value to you, though.