Profiling Opponents Accurately

In the past couple of issues, I’ve been writing about the common mistakes that many players make when they try to profile their opponents. Most players are too quick to give opponents credit for having rare traits, and they give too much weight to bits of incomplete information.

We can profile opponents accurately if we understand the principles of the mathematical approach to profiling called Bayesian inference.

I wrote about it in depth last issue, but I’ll summarize the ideas quickly. First you start out with a hypothesis. For example, “That player bluffs a lot,” is a hypothesis. Then you assign a prior probability that your hypothesis is correct. With each observation, you adjust that probability up or down. How much you adjust it depends on how certain you are that the observation confirms (or contradicts) your hypothesis.
As you play, I don’t expect you to have a list of probabilities in your head for each opponent. It’s not the specific numbers that are important, it’s the general process. I’ll give you an in-depth example of how I use the principles of Bayesian inference to profile my opponents accurately.

Reraising preflop is a powerful weapon in no-limit hold’em. Whenever you get reraised preflop, you should consider the range of hands your opponent might be reraising with. Most players tend to fall into one of three groups.

First are the ultra-nits. These players tend to reraise with only A-A or K-K. With A-K, Q-Q, and all weaker hands, they are reluctant to reraise.

Next are the tight reraisers. These players tend to reraise with A-A through J-J and A-K. They might also situationally add 10-10 and A-Q to that range.

Finally are the loose reraisers. These players reraise with A-A through 10-10, A-K, and A-Q, but they also reraise situationally with some weaker hands, and they also reraise frequently as a bluff.

These are the three profiles we’ll consider for preflop reraising:

Ultra-nit: A-A and K-K only
Tight: A-A through J-J and A-K; sometimes 10-10 and A-Q
Loose: A-A through 10-10, A-K, and A-Q; frequent bluffs; sometimes weaker hands for value

Given the opportunity, how often does each of these player types reraise?

There are 1,326 total possible hold’em hands, and the ultra-nit raises exactly 12 of them. (A-A and K-K can both be made six different ways using the different suits.) This means that the ultra-nit will reraise roughly 1 percent of the time.

The tight reraiser will reraise 40 of the 1,326 hands, and also sometimes with 22 other hands. This translates to about a 4 percent reraising frequency.

The loose reraiser will reraise with 62 hands. He will reraise situationally with weaker hands, and he will balance his reraising range with bluffs. Add all these up, and a loose reraiser might reraise about 10 percent of the time.

Now our job is to profile a player as an ultra-nit reraiser, a tight reraiser, or a loose reraiser. It’s our first orbit at the table. Two players limp, and we raise from two off the button. The player on the button reraises.

What should we do? Is our opponent an ultra-nit, a tight reraiser, or a loose reraiser? What’s his most likely hand-range?

The simple way to answer the question is to say that loose players reraise the most of the three types, therefore our opponent is most likely to be loose. This is how most poker players implicitly answer these questions, but it’s the wrong approach. The conclusion is wrong because it ignores the relative rareness of the three player types within the player population.

I hear poker players talk all of the time about unknown players. “I’d never played with him before, so I don’t know anything about him.” However, that’s not true. You have a base of information about all of your opponents, even those whom you’ve never seen play a hand.

Say you’re playing $1-$2 at a local card room. An unknown player is in your game. If nothing else, you know that he’s a $1-$2 player. As a general population, $1-$2 players tend to play a certain way that is quite different from how $10-$20 players play. You can use this general knowledge about $1-$2 players to inform your opinion about any particular unknown $1-$2 player.

My experience with $1-$2 players in Las Vegas is that they overwhelmingly tend to be either ultra-nit reraisers or tight reraisers. Loose reraisers are very uncommon at these stakes. A fair guess is that only about 2 percent of the $1-$2 player pool consists of loose reraisers. I arrive at that estimate by thinking about how many sessions I’d have to play with unknown opponents until I encountered a loose reraiser. I would guess that I encounter a loose reraiser in a $1-$2 game of unknowns perhaps once every five or six sessions.

I’d guess that ultra-nits and tight reraisers roughly evenly split the other 98 percent of $1-$2 players. Therefore, before seeing my opponent play a hand, I’d guess that there’s a 49 percent chance he’s an ultra-nit, a 49 percent chance that he’s tight, and a 2 percent chance that he’s loose.

Now, my opponent has reraised at the first opportunity. How should I adjust my probabilities?

For that, we need to use a mathematical tool called Bayes’ Theorem. I’ll just give you the answer, but if you’re curious how I arrived at it, read up on Bayesian inference.

The new probabilities are:

Ultra-nit: 18.5 percent
Tight: 74 percent
Loose: 7.5 percent

By far the most likely profile for my opponent after having seen him reraise once is that he’s a tight reraiser. He likely has a range of A-A through 10-10, A-K, or A-Q. (Since he’s on the button, I give him credit for reraising with the hands on the fringe.)
Seeing a reraise jumped the probability that my opponent is loose from 2 percent to 7.5 percent, but even so, it’s still the least-likely profile. Loose reraisers are uncommon in $1-$2 games, and one reraise isn’t enough evidence to get me to reconsider that general principle.

Say we played a little longer, and this player failed to reraise a few times and then reraised again. Now would we give him credit for being a loose reraiser? No. If you were to run the numbers, a tight reraiser would still be the most-likely profile, though loose reraiser might slip past ultra-nit into second place.

What’s the takeaway? Given just a few observations, it’s almost always more likely that your opponent is a common player type receiving some uncommon cards rather than an uncommon player type getting out of line with trash. It’s easy to get reraised a few times, get frustrated, and overreact. The next time you start to get frustrated, recall this article, and know that the math says that you are most likely up against a run-of-the-mill opponent who happened to catch a few big pairs.

If you study the process of Bayesian inference, you will find that you can estimate much more accurately, both at the poker table and in the rest of your life.

Ed has authored six poker books and sold more than a quarter million copies. Ed’s newest book, Reading Hands At No-Limit Hold’em, will soon be available for purchase at notedpokerauthority.com. Find him on Facebook at facebook.com/edmillerauthor.