“The nervous system and the automatic machine are fundamentally alike in that they are devices, which make decisions on the basis of decisions they made in the past.”
Norbert Wiener, originator of cybernetics

When we think of habits what first come to mind are physical actions: brushing our teeth, writing in our journal, going to the gym… or perhaps eating a bag of Cheetos, checking email, mindlessly surfing the internet(!) Yet we all have a far wider set of mental habits- thought patterns which we revert to either under conditions of stress or simply as our daily default mental states. In fact our physical habits are themselves grounded in these habits of thinking.

It should come as no surprise then, that in a game where we make thousands of decisions an hour, we soon develop patterns of thinking that help us automate decision-making. These patterns of thinking manifest themselves in patterns of our play at the table. They become our poker habits.

One of the greatest gifts of poker is that it rewards sincere introspection. To make any progress in your game you must first become aware of the reasoning behind your decisions. This is often an uncomfortable process, since chains of reasoning which once seemed secure are found to have weak links. A ‘standard’ betting line appears, upon closer inspection, as simply a bad habit.

In this article we are going to take a closer look at two common causes of bad poker habits: naive empiricism and positive inference bias. I’m going to use a Pot-Limit Omaha hand as an example, but keep in mind that the fallacies that I describe are evident away from the poker table too.

Below we investigate the value gained by one of the most common post-flop defenses to a pre-flop 3bet: Check-shoving over a C-bet on a duochrome flop.

The Setup

The cut-off opens to 2.5bb and we 3-bet to pot from the Button. The blinds fold, the Cut-off calls and we go heads-up to a flop of 19.5bb. The flop is:

Q 7 3

We C-bet 9bb and our opponent check-raises to pot (46.5bb). What problems, if any, does this present for our range?

He is effectively risking 91bb to win a pot of 27.5bb, since with 44.5bb after check-raising, he would need only 22% equity against our shoving range to call off his stack. A quick calculation shows that we need 41% equity against his check-shoving range to commit our stack on the flop. We depart here from our usual mode of calculation to explore specific hand class match-ups, for reasons which will become apparent shortly.

BTEquity CO
AAhh80-20AKQ9!h
AAhh35-65QQJ9
AAhh85-15KKhh
AAhh73-279875:hh
AA!hh41-589875:hh
AQT8:Ahh80-209875:hh
AQQ568-329875:hh

 

When I examined a sample 9% BTvCO 3bet width I found that 27% of hands matched the following strong range:

{QQ,77,33,Q7,Q3,Ahh,KK:hh,Q:hh,AA:hh,AAQ}

Against this range, AKQ9!h has only 30% equity, which means the Button must fold 63% of the time before check-jamming becomes profitable for the Cut-off. From here it’s only a short calculation (0.27/0.37) to demonstrate that the Button can C-bet as frequently as 73% of the time before him bet/calling as tight as the range above is exploitable. If a 73% C-bet frequency sounds low to you, note that 11% of the Button range is some weak flush draw, which can comfortably check back the flop.

Thus in a few paragraphs we have already sketched out a robust flop strategy for 84% of the Button’s range. To protect against our flop C-bet bluffs, the Cut-off must continue with an absolute minimum of 69% of his flop range. If he cannot profitably check-shove a hand as strong as AKQ9!hh, he certainly cannot check-shove anything weaker. The 9875:hh hand fares scarcely better than the AKQ9!h, with 34% equity against the described bet/calling range. Folding out a few overpairs is not going to compensate for stacking off with poor equity almost 40% of the time.

Having established that the Cut-off cannot play push/fold with his entire range we need to ask if there is any advantage to be gained in check-shoving at all? It’s true that the nut flush draw will be profitable, as will sets or two pairs, but a check-raising range composed only of these hands hardly gives our opponent any difficult decisions.

I contend that, save against the most simple opponents, there is no advantage to be gained by retaining a check-shoving range. Rather, check-shoving here is both easy to play against and grossly distorts your check-calling range, rendering it indefensible on later streets.

If the reader agrees with my assessment, how then is it that the flawed check-shove is so ubiquitous in the present games?

The Perils of Naive Empiricism

Check-shoving the flop often results in winning the pot (since our opponent is forced to either fold or go to showdown and allow us to realize our equity) and so gets chalked up as a positive result in our hedonic calculus. Any line which increases the frequency with which we win the pot feels more appealing, especially to the naive empiricist.

Naive empiricists are ‘results oriented’: they attribute too much weight to the outcome when evaluating the merit of a decision. When they make a play and it pays off, they record it in their minds and are more likely to make that same play in the future, in spite of other factors which have contributed to the success of the play. When they make a play and it fails again they record: without a conscious effort to acknowledge variance they are likely to avoid that play in the future.

The general population is typically either unwilling or unable to think probabilistically. It’s hard to accept that when you don’t get the result you want the decision, given the knowledge you had at that time, was still correct. It’s even harder to countenance the fact that your ‘wins’ may have been due more to luck than judgement.

As a poker player you have the privilege, not only to learn how to think probabilistically, but to profit from it

1! Yet I haven’t brought you here, dear reader, simply to caution you against naive empiricism. The more subtle fallacy exhibited in the hand above is the bias against negative inference.

The Bias against Negative Inference

The real weakness of many ‘standard’ lines is not that they are inherently unprofitable with the hand concerned. It is that by taking the immediately profitable, ‘easy to play’ approach we preclude the possibility of lines that are more profitable for our range, albeit unfamiliar. We have a natural bias towards positive inference: in this situation when we check-raise all in with the nut flush draw we either win the pot on the flop or get the money in on a coin-flip. Both of these outcomes are directly observable events.

In contrast, when we start including stronger hands in our check-calling range we will often get to showdown without the money getting all-in on the flop. These directly observable outcomes will be less profitable than when we get to check-shove the flop and so it will appear that the flop check-call line is inferior. What we do not observe in the moment are all those times that weaker parts of our range get to showdown (or are able to bluff the river) because our opponent is not able to barrel the turn/river as frequently on account of our strengthened check-call range. The value of the ‘negative inference’ is harder to estimate since we receive most of the profit from the strong hand when we don’t hold it!

Fortunately at the poker table, the person who bears the cost of consistent irrational decision making is the one who makes the poor decision. Sadly away from the table the world is not so just. In fact, it’s easy to find examples where the consequences of decisions taken by people who disregard negative inference impose costs on innocent third parties.

Consider the man who buys a house on a flood plain for a bargain in an ‘enlightened’ democratic society. Built into that low price is the expectation that, sooner or later, the house will be flooded. It would thus be appropriate for the man to hold a small celebration at the end of each year on which the the house was not flooded. However, in most cases,  no such celebration will occur…

Nay2 instead, the year the house does flood he will call out in anguish and demand that the government assist him with rebuilding or replacing his home. The government will promptly oblige by confiscating money from those who live elsewhere and giving it to the flood ‘victims’, in effect penalizing the former for having made a prudent decision not to buy houses on the flood plain. This is but one example of the way that modern democratic governments work to subsidize strategies that would otherwise be rendered obsolete3.

Due to a number of requests from regular readers I am re-opening my successful seminar series “Defending the Big Blind against a Button open”.

The series costs €745 per person and will cover the following topics:

Constructing Calling Ranges and general flop principles in a single-raised pot
Constructing 3-betting Ranges and general flop principles as the 3-bettor
A Case Study in a single-raised pot
A Case Study in a 3-bet pot
Defending turn/river transitions in a single-raised pot

This is a one-off opportunity to see material that I don’t usually make available so CONTACT ME NOW to reserve your place on the course!

QUESTION(S) OF THE DAY: Can you describe another poker habit you have? Do you think that habit helps or hinders your game? Please let me know in the comments.

Show 3 footnotes

  1. I have a far more upbeat response to the question of the ‘post-poker future’ of a poker player than most. The value of the skill-set of probabilistic thinking is greatly underestimated by those who employ it daily.
  2. The biblical ‘No’ was too enticing to resist here. This sermon is after all, ‘The wise man built his house upon a rock’ retold!
  3. There will be more posts on this. For now, feel free to message me if this concept is of particular interest to you.