Range Merging by Joejoe1337

[joejoe1337]

Meh this was something I did for black belt a few months ago, I'm guessing I own intellectual property rights to it or w/e

Bluff-Catchers

Let’s face it, we all play in games with tricky aggressive players. If we could play every day with eight Guy Lalibertés then we’d all jump at the chance, but as it is, our need to provide for the lifestyle we’ve grown accustomed to forces us to play in bigger games with better (and more aggressive) players. The dilemma with facing these players is that they’re constantly going to put us to hard decisions by betting frequently and leaving us scratching our heads as to whether they’ve “actually got it this time” or not.

Many successful high stakes players have adapted to this by ‘bluff catching’: checking and calling or just calling (when in position) an opponent’s river bet when your hand beats all of their bluffing range, and therefore could not make any more money by making positive action yourself.

Here’s an example of a medium stakes heads-up hand in which we have a bluff catching hand on the river:

$5/10 heads-up

Hero (BTN/SB): $2,101.5
Villain (BB): $1,890

Hero is dealt [Js-Jh]

Hero raises to $30
Villain calls

Flop ($60) [Qd-7c-8c]
Villain checks
Hero bets $40
Villain raises to $150
Hero calls

Turn ($360) [2d]
Villain bets $270
Hero calls $270

River ($900) [3s]
Villain bets $990 (all in)
Hero…

Without getting into the correctness of Hero’s play or the outcome of the hand, this is a very basic example: Villain check-raises on a very draw heavy board then continues to fire as a brick arrives on fourth and fifth street. Assuming that our opponent is an aggressive but straightforward and basic player, we can expect him to either have a nut hand (A-Q/K-Q/8-7/8-8/7-7) or a semi-bluffing hand (A-xs/T-9s/7-6s/T-7s, etc) which has missed. Assuming that he is checking all of his marginal hands like Q-J/Q-T/A-8 down, we can therefore give him a ‘polarised’ range on the river. In this spot we can generally calculate our opponent’s likeliness of having a pat, and therefore, bluffing, hand and act accordingly. (In this case, call if you believe Villain will shove all his missed semi-bluffs).

Creating a Scale

In a hand like the one illustrated above, both players obviously have hand ranges, and on the river the strength of your range runs like a scale in decreasing value (from nuts to air). In our example, let’s say [1] is Q-Q for the effective nuts and [20] is all of our hands with no showdown value (7-6 for example). Our opponent will also have a range which while slightly different because of the action he has taken throughout (we can exclude Q-Q and 2-2 at the top and complete air from the bottom), on the river is still something like [1] being 7-7 and [20] being 7-6. In this situation, our opponent has almost certainly (because he is a straightforward player) got either between [1] and [4] or [16] and [20].

Merging Your Range

This, however, is where our problem starts. Unlike Villain in this hand, strong-aggressive players are forever looking for a way to thwart our ways of counteracting their aggressive nature. Thus the range merge was born.

Merging your range is effectively getting extremely thin value from your opponents overplaying bluff catchers by including middling points of your range (that beat most of your opponent’s bluff catchers) when you bet the river. In the above example, it would be Villain betting [1] to [6] of his range all of the time, [7] 90 percent of the time, [8] 80 percent of the time [9], 70 percent of the time and so forth, as well as all of his hands with no showdown value like [16] through to [20].

Why Bother Merging?

Say you’re heads-up on fifth street with a hand you think is good, but you’re playing a tricky opponent who has often gotten the better of you on the river and has maybe check-raised you a few hands ago or called and showed you a better hand. Checking your hand behind with showdown value obviously can’t be terrible here, but by betting a wider volume of your range you make yourself much harder to play against rather than a player who bets only his value and bluff hands.

There are two potential sub products of merging your range. Firstly, opponents will occasionally fold some superior hands that you would have lost to if you’d checked the river. Secondly, you will be called by superior hands in which losses could have been minimised had you checked behind. This creates a noticeable paradox: how can a bet be both for value and a bluff? A lot of players would argue that a bet must either be for value or to fold out a better holding.

An important basic point to remember is that betting the river is only preferable to a check when:

1. Opponent folds out a high enough percentage of hands that beat you.
2. Opponent calls with more than 50 percent of hands that you beat.

Sum of [% opponent folds x pot size - % opponent calls with better x bet size] and [% opponent calls with worse x (bet size + pot size)]

The fact that you can be both called by worse or be folding out better is an irrelevance. The argument that you must bet for value or as a bluff is flawed because poker is, in fact, not a game of perfect information and most winning players base their strategy on deception. Therefore, there is often a point where ranges overlap and a ‘grey area’ is created in which a lot of players are uncertain as to the strength of their hand and whether or not they should value bet.

Many players lose a lot of money in potential value bets because they are clouded by insecurity in their hand’s strength. Range merging is essentially designed to thin your value betting range so heavily that you are constantly putting your opponents to tough decisions on the river, maybe even forcing them to make the wrong decision.

Here’s a Pot Limit Omaha hand I played a few months ago:

Stakes £1/2, Hero has £500, Villain covers
9-handed

Dealt to hero UTG+1 [A-A-6-8o]

1 Fold, Hero Raises to £18, 6 folds, Straddle calls £13

Flop (£39) [Jd-8d-2s]
Villain checks
Hero bets £33
Villain Calls £33

Turn (£105) [4h]
Villain checks
Hero bets £68
Villain calls £68
River (£241) [2h]
Villain checks
Hero bets (£195)

This is a hand in which I attempted to gain a third street of thin value by representing the missed draws in my range and trying to get called by a smart, calculated opponent who is easily capable of calling me here with top pair or a weak overpair. Obviously the top of my range is jacks/eights full, but in this spot I’d bet multiple overpairs (in a descending amount based on their relative strength) because our ranges had started to overlap and he may call me with K-K/Q-Q/A-J/J-8 and, in some cases, even fold 2-x-x-x if he misjudges my river betting range.

When playing a strong, thinking player on the river and you have a hand with marginal strength and both players’ ranges are overlapping, it is usually going to be more correct to bet and merge your range than checking and forfeiting the chance that an opponent makes a mistake.

[Pates]

Great article Joe. Sorry I didn't moderate it sooner! Interesting concept and good to see some HU PLO advice in there. +reppage

[bridgey321]

+rep, nice article.

Very thin value bet in the PLO hand (although I hardly play much) but you explained why very well so nice one. Very dry board I suppose and good river. Did you get called in the end?

This Joe hu went Uni Leicester for a while?

[deaks102]

I really like this article. Good read in my opinion. +1 reppage!