Profiling Opponents in the Absence of Statistical Convergence Pt. III

In my previous two columns, we noted how we must constantly make playing decisions in poker without the benefit of statistical convergence, either because we simply do not have enough trials with a given opponent for any statistic to approach convergence (for example, we are facing players new to us) or because a given situation occurs so infrequently that a given statistic will essentially never approach convergence (for example, flush board check-raise stats).

At this point, we have three reasonable choices:

1. Default to basic strategy. With little or no information on an opponent, you should default to basic strategy, which involves making the best play – on average – against the universe of opponents.

2. Play the percentage directly. Take the statistic at face value and play the percentage as if it were statistically significant, or – and more to the point…

3. Profile the player. Use the statistic in the context of other statistics, the way the player has played other hands, your history with the opponent, and other profiling factors in order to improve the accuracy of your decision on a case-by-case basis.

We discussed the first option – defaulting to basic strategy – last time. Now let’s discuss the second option.

Playing the Percentage Directly

When deviating from basic strategy to make opponent-specific decisions, one option is to take a statistic at face value.

Let’s say you c-bet on a flush board flop, your opponent check-raises, and has done so once in five previous opportunities to check-raise on flush board flops for a 20 percent flush board flop check-raise percentage. Also, as before, you decide you will three-bet bluff if your opponent’s flush board check-raise percentage is higher than 10 percent.

In this case, you would take the 20 percent flush board check-raise percentage as if it were statistically significant and three-bet bluff the crap out of your opponent. While this particular stat is not yet statistically significant against this particular opponent, if you were to take the universe of all of the times this situation comes up and play the percentages as if (three-bet if your opponent’s flush board check-raise percentage is above 10 percent, and fold if it is below 10 percent), you will likely be making the correct play on average – assuming, of course, that the 10 percent figure you are using as a pivot point to make the decision is correct itself.

Here’s another example.

Example: Four-Betting 6-5 suited in No-Limit Hold’em

It’s a $1-$2 no-limit 6-max game with $200 stacks (100BBs). You are dealt 6-5 suited in the cutoff seat and open with a raise to $7. The button reraises to $22, and both blinds fold.

Let’s say you decide that if your opponent has a three-bet percentage higher than 18 percent, that you will four-bet. According to Small Stakes No-Limit Hold’em by Ed Miller, Sunny Mehta, and Matt Flynn (Dimat Enterprises, 2010), 4-betting all-in against this opponent will yield a profit of $0.60 if your opponent will only call with 10-10 through A-A and AK; meanwhile, four-betting to $56 and folding to a
five-bet shove all-in will yield a $5.40 profit if your opponent will only shove with the same 10-10 plus and A-K range. 1

Now let’s say that over a 50-hand sample with this opponent, he has three-bet four times in 20 opportunities, for a 20 percent three-bet percentage. While the three-bet percentage is nowhere near statistically significant, you would take this opponent’s 20 percent three-bet percentage at face value and four-bet him.

Because of the sample size problem (and a myriad of other factors we’ll discuss in a minute), it is quite possible that four-betting is actually the wrong play against this particular opponent at this particular time. For example, perhaps in a different 50-hand sample this player only three-bets three times in 20 opportunities for a 15 percent three-bet percentage, with the difference plausibly attributable solely to variance. But in the universe of all of the times this play comes up against all of the opponents you will ever play against, four-betting with 6-5 suited against a player with a 20 percent three-bet percentage – whether or not it is statistically significant – will likely prove profitable over the long run, assuming the initial analysis is correct.

1. If your opponent flat calls the small four-bet with T-T and A-K and calls any shove, the result will be the same $0.60 profit as the four-bet shove all-in. Without the ability to see your hole cards (in which case he could fold those times when you outdraw him and he doesn’t have enough equity to justify calling your flop shove), it would be difficult for your opponent to improve on this result with this hand range.

2. That is, that the opponent’s four-bet calling or five-bet shoving range in this spot is in fact T-T and A-K, and that the 18 percent three-bet percentage prescribed by Miller et al. is the correct pivot point for four-betting vs. calling or folding with 6-5 suited against the opponent’s TT and A-K shove/commit range.

Card Player columnist Jeff Hwang is author of Pot-Limit Omaha Poker: The Big Play Strategy and the three-volume Advanced Pot-Limit Omaha series. Jeff is a consultant for the new PokerTracker 4.