Rangefinders: Which hands should you fold to a 3-bet?

New players to Omaha struggle at the tables because they have weak thought processes. Some weak thought processes are bad questions. And one of these bad questions is, “Which hands should I fold to a 3-bet?”

Experienced Omaha players, if they are feeling patient and kind (or being paid), will ask a series of clarifying questions to better ascertain the context of the situation:

“What position did you open from?”
“What position did your opponent 3-bet from?”
“What are the stack sizes?”
“What are your opponent’s tendencies?”

And so on. Clarifying questions, if carefully crafted, serve to parameterize the context of the situation to enable us to make accurate decisions at the table.

At this point all this talk about contexts seems confusing because we are moving freely between ‘subjective’ and ‘objective’ characterizations of a poker situation and using the same word, ‘context’, to describe them all. I have more to say about ‘objective’ characterization of context but it’s important to be clear that, at present, no computer can tell you what an objective characterization of context is. My personal position, and a major research area for me outside of poker, is that no computer will ever be able to tell you what an objective context is for any situation that is both complex and dynamic. That discussion ventures beyond the confines of this blog post.

Let us return to the subject at hand and introduce some terminology to bring clarity to our analysis. I shall use the term ‘lens’ to refer to a given player’s subjective characterization of a poker situation and retain ‘context’ as an objective characterization of that situation with respect to some trusted authority (on this blog that authority is me!). We will use the term ‘hard factors’ to refer to structural elements of the game which are not dependent upon our opponent’s opinion. Think, “stack sizes, streets left to play, whether the dealer is crooked, whether a meteorite is about to hit the table.”

Your opponent’s lens is an important component to your decision-making in the overwhelming majority of decisions in deep-stacked poker.  As stacks get shorter, the situations become simpler and, for want of a better term, the decisions become more ‘objective’. The reason that ‘math guys’ (really arithmetically-inclined, high-memory, high-patience, low-emotional-volatility guys) like short-stacked poker is that discounting your opponent’s lens makes effective decision-making more computable.

Sharper readers will at this point have recognized the interactionist element intrinsic to this model. If our metric for a given decision is described by the set of factors {Opponent’s lens, hard factors} then it stands to reason that an enlightened opponent will use a metric described by {Our lens, hard factors}. Since each player’s lens changes according to his perception of his opponent’s lens there are a series of interactions which one would expect to converge with both players left with a metric described by {Ideal lens, hard factors}. It is this series of interactions that is being described when members of certain poker circles talk about ‘levelling’.

Fortunately your opponents are neither omniscient nor telepathic and leak a lot of information about their lens from their play style. We shall now continue our analysis of folding pre-flop facing a 3-bet with a discussion of the implications of both hard factors and common lenses upon our decision-making.

We open from the button holding K♥K♦8♥3♥ and a tight opponent 3-bets us from the Big Blind. This hand is right at the top of a wide opening range and, if our opponent were 3-betting the ‘correct’ width, this hand would be an obvious call. However if we know that our opponent only 3-bets a value-oriented 6% width here then our hand is considerably worse, not just in absolute value, but relative to other hands in our range.

Since us holding Kings makes it more likely that our tight opponent holds Aces we see that our hand is heavily dominated pre-flop, as shown in the table below:

The raw Hand vs Range Equity is a coarse-grained ‘hard factor’ (provided we can trust in our estimate of our opponent’s 3-bet range). Despite the similarity in equity, many readers will feel that the J♠7♠6♥4♣ is a more comfortable call here since it is more ‘playable’. If we compare the Hand vs Range Flop Equity Distribution for both hands we see that the unpaired hand has more flops where it passes 40% Equity against our opponent’s 3-bet range whereas the Kings have fewer flops on which they drop below 25% equity:

It is important that you understand the implications of pocket Kings having a large fraction of hands with greater than 25% equity facing the 3-bet. This level of equity is not sufficient to continue facing aggression without the possibility of outplaying your opponent post-flop. The more frequent the C-bet and the larger the sizing, the worse the pre-flop call will fare. If you have ever found yourself frustrated after you make an ‘automatic’ call with Kings against a tight opponent only to stare down the barrel of yet another pot size bet on the flop, then this graph shows you the reason why.

Yet the width of our opponent’s range is not sufficient information for us to assert that we must fold our hand pre-flop. The hand versus range curve only tells us how strong our hand will be across the set of all possible flops. The strong flops for KK are highly visible to us. In fact, the value of pocket Kings facing a 6% 3-bet range drops sharply whenever a King is not present on the flop, as shown in the graphs below:

This observation brings into focus the fact that it is not our opponent’s flop C-bet frequency that matters, it is our opponents flop C-bet frequency on those boards that we hit that matters.

At the two extreme poles of possible flop C-bet frequency (Always/Never) we can evaluate the pre-flop call using the coarse-grained factor (raw flop C-bet frequency) and still make an accurate decision. This is because a predictable opponent leaks high fidelity information about his contextual C-bet frequency from his average C-bet frequency. Put simply, if he always C-bets the flop in 3-bet pots then we know that he always C-bets King-high flops in 3-bet pots; if he never C-bets the flop in 3-bet pots then we know that he never C-bets King-high flops in 3-bet pots. In contrast, knowledge that an opponent C-bets the flop in 3-bet pots 75% of the time is not sufficient for us to make a confident judgement about his C-bet frequency on King-high flops.

Facing a player who will C-bet with a high frequency one might expect J♠7♠6♥4♣ to play better as a call than K♥K♦8♥3♥. Yet before we leap to this (common) conclusion, we need to examine which flops we expect our opponent to attack.

If we know that he will check the flop with a high frequency on boards which do not contain a King then we will have opportunities to move him off of his Aces post-flop. Many tight players will perceive a flop of:

7♣6♦4♥

as threatening and simply check-fold every hand which misses the board. Low [9-high or lower] unpaired flops which contain a made straight only comprise 8% of all flops, so we cannot justify a pre-flop call merely because such boards are profitable. More common are low 0-straight boards such as this:

9♣7♦4♥

Will your opponent check-fold this with AA? Will he check-call one street and check-fold bad turns? Or perhaps he will retain a check-shoving range on the flop? Your answers to these questions will determine the set of post-flop actions that you should take if you decide to call. And it is those post-flop actions that will determine whether your pre-flop call is a profitable play against this opponent.

Of course if this specific opponent will pot all such flops then your K♥K♦8♥3♥ will not be able to continue past the flop. At that point all that remains for a post-flop strategy is set-mining against your opponent’s range. Fortunately set-mining is not as bad a play here as it would be if we had opened from early or middle position. The advantage of holding Kings in this situation compared with an earlier seat is that our opponent is more likely to pay us off on a King-high flop since our perceived range from the Button is not heavily weighted to hit such flops.

Conversely the J♠7♠6♥4♣ would very much prefer an opponent who gave free cards on the King-high flops whilst potting on the lower flops. So it is our opponent’s lens- how he perceives the set of future boards- that dominates our consideration of the value of a pre-flop call. We see that the pre-flop decision should not be made in isolation, but with a view to the post-flop play entailed by that call.

Implementing the post-flop play entailed by pre-flop assumptions is a key area that I work on with private clients who want to move from mid-stakes to high-stakes PLO. If you peel your weak Kings pre-flop because you believe you can move your tight opponent off of a low board then you should NOT allow your opponent a cheap showdown on a runout of:

9♣7♦4♥4♣3♥

A cheap showdown on the very same board would be the correct goal against an opponent with a wider 3-bet range.

Our discussion today has emphasised the value of understanding the lens through which our opponent looks at the game and adjusting our decisions accordingly. It has also made clear the need to execute a post-flop strategy that is consistent with your pre-flop assessment in order for your pre-flop play to be accurate. In deep-stacked Omaha, accurate pre-flop strategy is never independent from post-flop strategy.

The fact that lens considerations are critical does not mean that we cannot make any preparations away from the table. I have done detailed research which identifies how hands change category depending on the context of the situation and I teach this work in my interactive Omaha strategy courses. You can learn more about my courses, which top high stakes players study to help them beat players learning from mainstream sources, here.

Welcome back to the many long-time readers of this blog, and I extend a warm greeting to any new readers. You can ask follow-up questions, good or bad, in the comments below.

Good luck at the tables.