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PLO Post-flop Strategy

Change your Game Facing a Linear Range

“The snake which cannot cast its skin has to die. As well the minds which are prevented from changing their opinions; they cease to be mind.
Friedrich Nietzsche

The modern PLO games are saturated with players who have a basic understanding of hand value and a strong aversion to complex decisions. A fundamental component of these players’ strategy is a tendency to bet the flop with a Linear Range and not concern themselves with protecting their checking ranges.

This approach enables them to continue comfortably against check-raises, and to barrel frequently on the turn with a strong range. It crushes loose-passive fish, which explains why so many players rise through micro and small stakes playing this way.

Such opponents can be frustrating to play against, since it is not always clear which marginal hands we should continue past the flop. Sometimes we feel like we are playing too fit/fold and at other times we feel that we call the flop only to fold to the inevitable second barrel.

My analysis below will show you how to adjust your continuing ranges facing Auto C-bet and Linear C-bet strategies respectively on a flop texture which slightly favours the aggressor.

Scenario 1: Facing an Auto C-bet

In a 6-max game we call a 26% CO raise from the BB with 65% of starting hands, having excluded a small 3-bet range. We go heads-up to the flop, which comes down as:

K85

On this flop texture the CO has a small Equity advantage against us (56-44) and a minor polarity advantage (around 1.5 times as many sets, strong two pairs and assorted strong top pairs/overpairs).  The CO had a 56-44 Equity advantage against us Pre-flop so this flop is a typical example of the range interaction we can expect when we call from the BB.

Let’s take a closer look at how well we hit the board; shown below is the Hand vs Range Equity curve:

Hand vs Range Equity on K♣8♦5♥ for BB calling a CO open

If our opponent were to Continuation Bet his entire range, we can see from the graph that we would have little trouble finding hands with sufficient equity to continue.

On first analysis, since even a hand like QJT3 has 27% equity against our entire defending range, our opponent has a +EV check back for even the weakest hands in his range. Let’s say that our opponent uses a half-pot sized bet on this flop with his entire range. If we seek to prevent hit from C-betting any 4 cards more profitably than he might check back, we would not even need to continue to the Folding Threshold of 67%.

Yet from the graph it seems we can do substantially better than this if he C-bets his entire range. More than 50% of our hands on the flop exceed 40% equity against his range. The weaker hands are supported by a significant 10% of hands which dominate our opponent’s range with at least 70% equity. At the 67% Folding Threshold we find hands with only 33% equity against our opponent’s range!

Facing this opponent our main challenge is recognizing which weaker hands can profitably continue due to our opponent’s excessive C-betting. 30% of our hands fall between 30 and 40% equity and we want to select the best of these to continue with. Please note that this is an exploitative strategy; our opponent could restrict his flop C-betting range and prevent us from continuing with as many hands profitably as we shall explore later in this analysis.

Below is a table detailing the Equity for a selection of hand types, most of which fall inside the third quartile of our range:

Hand Equity vs 100% C-bet Frequency
AJ84♠ 40.6%
AQ65♠ 36.0%
KQ33♠ 52.7%
TTA6 33.4%
JT8♠6 38.9%
AJJ♠2♠ 39.8%
Q3Q♠2♠ 41.5%
AT96♠ 30.8%
J654♠ 42.9%
KT9♠8♠ 73.9%

The core of our continuing range is every {K,8,pair + gutter,OESD}. It’s also worth noting the steep drop in value from bare QQ to ATT. With underpairs the absolute rank matters as well as supporting side-cards. Check-calling a bare gut-shot to check the turn is a losing play unless our opponent likes to one-and-done. However, our opponent’s range is so wide that most Two pairs have become comfortable value XR. We can support these by check-raising some gut-shot straight draws on the flop.

The lesson from this investigation is that an opponent who C-bets too much of his air on the flop in position is in fact far less threatening than an opponent who restricts his range by checking back some of his weaker hands. Such a strategy is highly visible, a concept which I first introduced in ‘Predictability’, because it is easy to recognize our favourable equity curve against an opponent who automatically C-bets a flop texture.

Scenario 2: Facing a Linear C-bet

Most of the tight opponents you face will use a Linear C-bet construction on this flop texture. For the purposes of this example I shall use this 63% betting range:

{K,8,55,76,(5,TT,JJ,QQ):(96,97,64,74),AA}

I have not built the range strictly according to equity but rather from the perspective of a straightforward tight player. Such players prefer easy decisions and like to build pots whenever they have the potential to make the nuts by the river. Accordingly I have included within the betting range bet those hands which either already hit the board or have potential nut outs. I have assumed that this player is not concerned with protecting his flop check-back range.

Let’s examine how these changes to our opponent’s betting range affect our Hand vs Range Equity curve at the flop decision point:

Hand vs Range Equity on K♣8♦5♥ facing a Linear C-bet

Now only 32% of our range passes the 40% barrier. It is very clear that we do not want to defend every hand up to the 67% Folding Threshold, since hands at the threshold have only 27% Equity against our opponent’s C-bet range. With only 5% of our hands now exceeding 70% Equity we should refrain from check-raising, and allow the top of our range to protect the weaker hands in our check-call range.

Most of the hands we looked at earlier have dropped in Equity significantly:

Hand Equity vs 100% C-bet Frequency Equity vs Linear C-bet
AJ84♠ 40.6% 32.1%
AQ65♠ 36.0% 27.9%
KQ33♠ 52.7% 38.4%
TTA6 33.4% 24.9%
JT8♠6 38.9% 30.2%
AJJ♠2♠ 39.8% 27.6%
Q3Q♠2♠ 41.5% 26.4%
AT96♠ 30.8% 26.0%
J654♠ 42.9% 37.1%
KT9♠8♠ 73.9% 67.2%

It’s worth noting which hands drop the most in value against the linear betting range. The KQ33♠ and underpairs like Q3Q♠2♠ plummet in value because they have high equity against air and our opponent is checking back most of his air. But even bottom pair plus a low gut-shot remains strong enough to continue.

The following hands form the core of our continuing range:
{88,55,K,76,85,(8,5):(97,96,74,64)}

If we only continued with these hands we would be playing 42% of our range, with a 51% Equity Edge against the Linear C-bet range. Whilst we don’t want to continue up to the Folding Threshold, we still want to find some additional hands that can continue profitably. Evaluating the Range vs Range Equity alone is not sufficient to tell us which hands are the best candidates because the differences are marginal; we can see hands at the 45% mark with only 32% Equity and hands at the 60% mark with 28% Equity.

The method I suggest involves taking a closer look at the relative strength of the transitions for each player. Presently, the Equity Breakdown by Turn card for our core continuing range against our opponent’s Linear C-bet range looks like this:

Core range vs Linear C-bet

The favourable transitions for us are those which complete the straights: {9,7,6,4}. Keep this in mind as it will be important in the discussion which follows.

We know that we are going to be continuing some hands which either pair the 8 or the 5, have an interior pair already, or contain a gut-shot. The question is, “Which side-cards are sufficiently valuable to warrant the flop continuation?”

The best way to answer this question is to evaluate the Hand Equity Breakdown by Turn card in the specific context of the Range Equity Breakdown by Turn card. This method yields results which are frequently surprising. For example, look at the comparison between A973♠ (Left/Top) and A643♠ (Right/Bottom) below:

A context-agnostic approach, conditioned by many experiences of drawing to non-nut hands in multiway pots, and by years of hearing, “PLO is a game of the nuts” would prefer the A973♠ to A643♠ because it contains a nut gutter. In fact it is the A643♠ which has more playable continuations and the drop in equity when we spike our gutter does not mitigate this advantage.

The question that you should ask yourself when selecting these marginal hands is, “When I pair my side-cards which additional draws do I pick up?” That would enable you to recognize the advantage of the ‘weaker’ gutter here, since spiking any of the side-cards with the A643♠ brings additional straight draws, whilst spiking the side-cards with A973♠ does not. If you can pick up an additional straight draw when you pair the turn you will improve to a hand with multiple nut or near-nut river transitions.

You should also learn to recognize the range vs range advantage conferred on your pairing transitions. Consider the Equity Breakdown for QJ54♠  (Left/Top) and AQ53♠ (Right/Bottom), show below.

QJ54♠ might seem like a reasonable hand to continue since it can pick up an open-ender on the turn with the Ten, as well as spiking two pair or trips. Yet if we look more closely at the Equity Breakdown we see that the Ten is a very weak transition against a linear C-betting range. Our opponent will hold {Two Pair+} on the Ten transition 50% of the time and so we are usually unable to capitalize on our straight draw.

In contrast, the hand AQ53♠, despite having no transitions which bring an open-ender, is playable when it hits its side-cards.

Notice that the weakness of AQ53♠ on the straight transitions actually works in its favour. Recall that our range is already a favourite on these transitions and so we can expect to get free river cards with a high frequency. The AQ53♠ will have a profitable path through the hand when our opponent does check back, either by improving on the river to a hand with showdown value, or by bluffing the river to balance the many strong hands which we have on such run-outs.

This contextual transitivity of hand strength is what makes PLO such a complex, interesting game. Against linear betting ranges we place less of an emphasis on raw equity, and care instead about the frequency with which we improve to playable hands on transitions which do not heavily favour either player.

How to identify a player using a linear flop betting range


Now that we recognize which adjustments to make to our continuing range when we face an opponent C-betting with a linear range the challenge is to identify such opponents.

A linear flop C-betting range in a situation where a player only has a marginal flop Equity edge necessarily implies a weak flop Check-back range. The principal markers of a weak flop Check-back range are:

  1. High fold to Turn Lead after checking back.
  2. Low Delayed C-bet frequency

These two statistics are critical to most flop decisions when you are defending from the Big Blind and so should be in the main panel of your HUD. As a guideline for you to check your own performance a ‘Fold to Turn Lead’ over 60% is usually a serious problem. You can only fold this often if you are playing in very juicy loose games where you are consistently being paid off whilst playing ABC poker.

QUESTION(S) OF THE WEEK: Which situations do you consistently run into trouble against tight players? Comment below and your question could be the subject of my next article!

For my blog readers I am offering £250 off of the price of my comprehensive course, “Poker Math 2020: Pre-flop Principles” until midnight UK time on Friday 20th October.

Click here to view the Pre-flop Principles Course and reviews from the High Stakes Winners who bought it before you!

By | 2017-10-04T20:15:12+00:00 October 4th, 2017|

Folding Thresholds in 3-bet Pots: A Closer Look at your Opponents’ Strategy

“If you know the enemy and know yourself you need not fear the results of a hundred battles.”
Sun Tzu, The Art of War

Our primary considerations when choosing a line of play in a poker hand are the particular exploitable tendencies of a given opponent. Both ‘math’ and ‘feel’ players alike will agree that if a player folds ‘too much’ on a given street we can bluff him more often. But exactly how much folding is too much?

Away from the table we can do some valuable analytical work to calculate folding thresholds beyond which a player is vulnerable to exploitative bluffing. In so doing we also discover how our own exploitative lines expose us to being exploited ourselves. Thus the calculation of folding thresholds helps us both to more accurately target imbalances in our opponent’s strategy and to recognize when they are adjusting correctly to our strategy.

3bet pots provide a veritable haven of diverse exploitative lines for the observant player. Given their bloated size relative to single-raised or limped pots they also account for a disproportionate amount of the money per hand which you win/lose at PLO. In this article, we consider the mathematics behind bet/calling, bet/folding and other decisions post-flop in 3-bet pots.

My writing in this post is not meant to be an exhaustive examination of 3bet pots so we shall not go into much detail regarding our opponents’ ranges. The purpose of this analysis is to discover the threshold frequencies at which bet/folding the flop leaves a player open to being exploited. A knowledge of these fundamental frequencies will improve our awareness in 3bet situations at the table.
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By | 2017-04-10T13:22:52+00:00 June 4th, 2015|

The Equity Delusion: How much does chasing cost you?

“The future influences the present just as much as the past.”
Friedrich Nietzsche

Take a look at the picture above and ask yourself, “Why are these men running?”

We can’t be sure, but the chances are that they aren’t running from some rabid beast. In fact they likely aren’t running from anything at all. We can infer this from the fact that not only are these gentlemen wearing inappropriate beast-fleeing attire but that the lead character is looking at his watch. All rather mundane, so why, dear reader, have I bothered bringing this to your attention?

For those of you hoping for a surprise beast-chomps-man denouement complete with a graphic YouTube video this blog post will be something of a disappointment. My readers with a poker-focused disposition will have a lot more fun and should read on.

The point is that these gentlemen are roused to action by anticipatory anxiety: the threat of something bad happening in the future. In this case our heroes are presumably at risk of missing a connection or event. We routinely account for future events in our life decisions yet it seems harder to do in poker. Why? (more…)

By | 2017-04-10T13:22:53+00:00 April 20th, 2015|