## Thursday, February 16, 2012

### The Squeeze Play

The definition of "squeezing" is to 3-bet a raiser after the raise has already been called. The raiser now has to respond to the 3-bet with another player left to act, and we say that he is in a "squeeze" between the 3-bettor and the caller, thus the name.

Below are three examples of squeezing with the raiser in position and out of position:

Example 2.1: Squeezing with the raiser out of position
\$100NL

MP (\$100) raises pot to \$3.5, CO (\$100) calls, button (\$100) 3-bets pot to \$15.50, the blinds fold, and it's MP's turn to act.

Example 2.2: Squeezing with the raiser out of position
\$100NL

CO (\$100) raises pot to \$3.5, button (\$100) calls, SB folds, BB (\$100) 3-bets pot to \$14.50, and it's CO's turn to act.

Example 2.3: Squeezing with the raiser in position
\$100NL

Button (\$100) raises pot to \$3.5, SB (\$100) calls, BB (\$100) 3-bets pot to \$14, and it's button's turn to act.

If the raiser in these examples should choose to defend against the 3-bet by calling, he is setting himself up for difficult postflop scenarios. He will then often have a weak or marginal hand postflop, and he will often have to respond to the 3-bettor's c-bet without closing the betting (when the preflop coldcaller is left to act). All who have played a bit of NL understand intuitively that this is a difficult situation to play well, and many therefore fold a lot to squeezes when they aren't strong enough to 4-bet for value.

As we shall see soon, the mathematics of the situation dictates that the raiser and the cold-caller have to defend a lot against the 3-bet to prevent the 3-bettor from having a profitable bluff with any two cards. Since many players can't (or won't) defend as actively as they should in an optimal strategy, squeezing is generally a very profitable strategy against weak opposition.

We shall approach the theory behind squeezing using the theory for heads-up 3/4/5-betting as a starting point. We let Alice open-raise pot from some position outside of the blinds, and then she is called by a player between her and Bob. Bob now 3-bets (squeezes) pot with a polarized range made up of value hands and 3-bet bluffs with an optimal value/bluff ratio, Note that this optimal ratio will be slightly different from the corresponding heads-up scenario since the presence of the caller changes the pot size and therefore the pot odds for 3/4/5-betting.

Alice defends against the squeeze by 4-betting/folding out of position and 4-betting/flatting/folding in position. When she 4-bets, she will make her 4-bet a bit less than pot-sized (e.g. to 32 bb in example 2.1 instead of 4-betting pot to 46 bb), and she uses an optimal value/bluff ratio. Bob's response to a 4-bet is to 5-bet his value hands all-in, and fold his 3-bet bluffs. Alice's response to an all-in 5-bet is to call with her value hands and fold her 4-bet bluffs.

We'll now construct a model for a squeeze scenario with the raiser out of position, and then estimate optimal strategy pairs for the raiser and the 3-bettor like we did for heads-up 3/4/5-betting in Part 1 and Part 2

We use the following model:
Alice open-raises pot (3.5bb) from EP (UTG or MP)
A player in CO cold-calls
Bob squeezes with an approximately pot-sized 3-bet (14 bb) on the button with an optimal mix of value hands and 3-bet bluffs
Alice defends against the squeeze by 4-betting to 32 bb (a bit less than pot) with an optimal mix of value hands and 4-bet bluffs, and otherwise folding
We'll assume that CO always folds to Alice's 4-bet
Bob defends against Alice's 4-bets by 5-betting his 3-bet value hands all-in, and otherwise folding
Alice defends against Bob's 5-bet by calling all-in with her 4-bet value hands and otherwise folding

This model is similar to the one we used for heads-up 3/4/5-betting with Bob in position. An important difference is that the pot is bigger because of CO's call when it's Bob's turn to act. The optimal strategy pair for Alice and Bob will therefore change relative to the strategy pairs we found for the corresponding heads-up scenario. We'll assume that CO never continues after a 4-bet from Alice, so that his chips are "dead money" when a 3/4/5-bet war arises between Alice and Bob. We can then estimate the optimal strategy pair using the same method we used heads-up.

We use 14 bb for Bob's 3-bet size as an average of his bet sizing from various positions. From the examples above we see that Bob risks 15.5 bb when he squeezes with a pot-sized 3-bet on the button, but only 13 bb (beyond the big blind he has already posted) when he squeezes from the big blind. So we use 14 bb as a representative 3-bet size for all positions.

We also assume that Bob uses the heads-up ranges for 3-bet bluffing ("IP 3-bet air list"), 5-bet bluffing ("IP 5-bet air list") and flatting ("IP flat list") when he chooses his bluffing and flatting hands:

IP 3-bet air list

A9s-A6s
K9s-K6s
Q9s-Q6s
J9s-J6s
T8s-T7s
97s-96s
87s-86s
76s-75s
65s

100 combos

IP 5-bet air list

A5s-A2s

16 combos

IP flat list

22+
ATs+ AJo+
KTs+ KQo
QTs+
JTs
T9s
98s

Without {KK+}: 162 combos
Without {QQ+}: 156 combos
Without {QQ+,AK}: 140 combos
Without {JJ+,AK}: 134 combos

So Bob's candidate hands for 3-bet bluffing are the same as when 3-betting heads-up. But since the pot now is bigger, Bob's optimal distribution of value hands and bluff hands will change relative to the heads-up scenario. Except for this, we're using a model identical to the heads-up scenario.

We start by asking 3 important questions:
How often do Alice and the coldcaller have to defend against the 3-bet squeeze to prevent Bob from profitably 3-bet buffing any two cards?
How is the defense against the squeeze shared between Alice and the coldcaller?
What is the optimal strategy pair for the heads-up 3/4/5-bet war that occurs between Alice and Bob after Alice 4-bets and the coldcaller folds?

Next we'll find the answers to these questions:

2.1 Optimal defense frequency against a 3-bet squeeze

When Alice and Bob were heads-up, Bob 3-bet to 12 bb to win a 3.5 + 0.5 + 1 =5 bb pot. He got effective pot odds 5 : 12, and had to win at least 12/(5 + 12) =70% to have an automatic profit with any two cards. Heads-up Alice had the whole responsibility for defending sufficiently often to prevent this. So Alice had to defend 30% of the time in an optimal strategy (and a bit more in position where she sometimes defends by calling and lets Bob freeroll flops with his 3-bet bluffs).

But when Alice's raise has gotten called by CO, the pot is 3.5 + 3.5 + 0.5 + 1 =8.5 bb when it's Bob's turn to act. His 14 bb 3-bet squeeze then risks 14 bb to win 8.5 bb and the effective pot odds becomes 8.5 : 14. Bob needs to win at least 14/(8.5 + 14) =62% to have a profitable 3-bet squeeze with any two cards, and Alice and the coldcaller need to defend at least 100 - 62 =38% to prevent this.

The next question is how this 38% defense job should be shared between Alice and the coldcaller. This question can not be answered exactly, but we can state some qualitative guidelines:
The coldcaller has signaled a range with few premium hands when he chooses not to 3-bet Alice
Alice must therefore expect that the coldcaller will often fold to the squeeze
So most of the job of defending will fall on Alice

To get further, let's assume that Alice uses her corresponding heads-up defense strategy as a starting point for the squeeze scenario, and then she makes adjustments in the value/bluff ratio to adapt to the new pot size. In other words, she starts with a defense strategy where she defends 30% (only 4-betting and never calling, since she is out of position), and that the cold caller takes care of the rest by defending some percentage x% . The probability of both Alice and the coldcaller folding is then (1-0.30)(1-x), and the probability of at least one of them defending is 1 - (1-0.30)(1-x). This should be 38% in an optimal strategy, and we get:

1 - (1-0.30)(1-x) =0.38
1 - 0.70(1-x) =0.38
0.70(1-x) =0.62
1-x =0.62/0.70
x =1 - 0.62/0.70 =0.11 =11%

So to make the total defense percentage 38%, the coldcaller needs to defend 11% of his range if Alice defends 30% of her range by 4-betting or folding. Furthermore, if the coldcaller defends partly by flatting, he should defend a bit more than 11%, since flatting lets Bob freeroll flops with his 3-bet bluffs instead of having to fold them to a 4-bet. But here we'll focus on Alice's strategy, and simply assume that the coldcaller defends enough. (estou aqui)

We'll see later that Alice ends up defending a bit less than 30% after adjusting her strategy to the new pot size, so CO has to defend a bit more than 11%. But we'll assume that the distribution of the defense responsibility is 30% and 11% before Alice begins adjusting her strategies.

After choosing this starting point for her defense strategy, Alice needs to find the value/bluff ratio for 4-betting that corresponds to the actual pot size. We make a new simplifying assumption and let Alice use the same value range she would have used in the heads-up scenario. Then we only have to adjust the number of 4-bet bluffs to the new optimal ratio, which follows from the new pot size.

We remember that Alice's ~15% EP opening range is:

22+
A9s+ AJo+
KTs+ KQo
QTs+
J9s+
T9s
98s
87s
76s
65s

194 combos
15%

And when working with the corresponding heads-up scenario we found that Alice used the value range {QQ+,AK} when defending her EP opening range optimally out of position against Bob's heads-up 3-bets. So we have simplified our way down to this:
Alice uses the corresponding heads-up strategy as a starting point for her defense against the squeeze, and then she adjusts it to match the new pot size
Alice uses the same value hands she would have used in a heads-up scenario, so that her only adjustment is to change the number of 4-bet bluffs to get to the new optimal ratio (which follows from the new pot size)
Alice assumes the coldcaller will take care of the remaining defense, so that the total defense adds up to 38%

What remains is to estimate how many 4-bet bluffs Alice needs to get to the new optimal value/bluff ratio for her 4-betting range. Heads-up this ratio was 60/40, and next we'll recalculate this ratio as a function of the new pot size.

2.2 Bob's value/bluff-ratio for 3-bet squeezing

Bob knows that Alice and the coldcaller will defend a total of 38% against his squeeze 3-bet (a bit more when the coldcaller defends partly by flatting). When Alice re-squeezes with a 4-bet to 32 bb, she risks 28.5bb more (32 bb minus the original raise to 3.5 bb) to win a 3.5 + 3.5 + 14 + 0.5 + 1 =22.5 bb pot.

Alice then gets effective pot odds 22.5 : 28.5, and she needs to succeed 28.5/(22.5 + 28.5) =56%. So Bob needs to defend against a 4-bet by 5-betting 100- 56 =44% of his 3-betting range to prevent Alice from having a profitable 4-bet with any two cards. Therefore, 44% of Bob's hands need to be value hands. We can round this to the nearest 5% to keep things simple, and we find that the optimal value/bluff ratio for Bob's 3-bet squeezing range is 45/55 (compared to 40/60 for the heads-up scenario).

2.3 Alice's value/bluff ratio for 4-betting

When Alice re-squeezes Bob's 14 bb squeeze by 4-betting to 32 bb, and the coldcaller between them folds, the pot grows to 32 + 3.5 + 14 + 0.5 + 1 =51 bb. When Bob shoves his remaining 86 bb, he's getting effective pot odds 51: 86.

Bob always has some equity when his 5-bet bluffs get called, and we'll make the same assumption we made in Part 1. There we showed that Bob's weakest 5-betting hands (the Axs hands he used as 5-bet bluffs) had about 30% equity when they got called by Alice's value 4-betting hands. So Bob's 5-bet bluffs win back about 30% of a 100 + 3.5 + 100 + 0.5 + 1 =205 bb pot, or 0.30 x 205 =61.5bb. So Bob effectively risks 86 - 61.5 =24.5 with his 5-bet bluffs and not 86 bb.

The effective pot odds for Bob's 5-bet bluffs is then 51 : 24.5, and he needs to win 24.5/(51 + 24.5) =32%. To make Bob's 5-bet bluffs break-even, Alice needs to defend 100 - 32 =68% against Bob's 3-bets, which we round to 70%.

It follows that Alice's 4-betting range needs to contain 70% value hands (compared to 60% in the heads-up scenario). Alice's optimal value/bluff ratio for 4-betting is then 70/30.

2.4 Adjusting to squeeze scenarios in practice

We have now established that Bob should change his value/bluff ratio for 3-betting from 40/60 to 45/55, which means his 3-betting range should be more weighted towards value hands. Alice's value/bluff ratio for 4-betting should change from 60/40 to 70/30, so range also becomes more weighted towards value.

Do these changes make sense intuitively? Yes, since both players should be less willing to fold when the cold caller's dead money has made the pot bigger, giving them a better risk/reward ratio when continuing in the hand. So bluffing becomes less effective, and both players adjust by reducing their bluffing frequency.

We have already done a systematic discussion of Alice's and Bob's 3/4/5-bet strategy pairs in previous articles. In Part 2 and Part 3 we estimated specific ranges for both of them when Alice raises out of position and Bob 3-bets her in position. In Part 4 we did the same for the scenario where Alice has position on Bob after he has 3-bet from the blinds.

So instead of going through these scenarios one more time with the new value/bluff ratios, we'll instead look at an example that illustrates how we can adjust in practice. We'll then use the previously established heads-up optimal strategy pairs as our starting point.

When we're in a potential squeeze situation, there are two different ways to approach it:
We can used precisely defined ranges based on a value range + "IP 3-bet air list" and "OOP 3-bet air list" together with a randomizer. In other words, we're trying to squeeze 3-bet optimally (the topic for this article)
We can realize that we're in a squeeze and squeeze with whatever cards we have, if we think the situation is good for it (but we're rarely squeezing with pure trash hands). We're now playing exploitatively, probably with an unbalanced range (weighted towards an excess of 3-bet bluffs) in selected spots

For example, let's say button open-raises and SB flats. Button folds often against 3-bets, and SB is loose-passive with a wide flatting range, and he also folds often to 3-bets. You have K7s in the big blind. K7s is to weak for flatting, and it's not a member of the 3-bet bluff candidate list ("OOP 3-bet air list") that we use out of position in the blinds.

So if you're using a strictly defined optimal strategy based on lists + a randomizer, you fold. You know that in the long run you'll squeeze an optimal amount (which is pretty aggressive) by sticking to your strategy, and you don't have to add more bluffing hands to get there (and if you do add more bluffing hands, your strategy will become unbalanced, which isn't necessarily what you want).

Another approach is to exploit whatever good squeezing opportunities that come your way, without worrying about moving away from an optimally balanced 3-betting range. If you want to play this way (deviating from optimal strategy whenever you see an opportunity to exploit a profitable scenario), you'll 3-bet K7s and similar hands in the scenario described above. You do this because you expect to make a good profit from picking up the pot preflop against two players who fold too much to 3-bets (and when the loosest player calls, you will have position on him postflop). This is obviously a fine way to play these scenarios.

But if you choose the exploitative approach, be aware that you might have to tighten up your 3-betting if your opponents realize you are 3-betting too loosely and decide to fight back (for example by 4-bet bluffing you more). On the other hand, if you choose an optimal strategy, your opponents' strategy adjustments will have less impact. If you use an optimal value/bluff ratio for 3-betting, they can't exploit you with any change they make. So you don' have to make any changes in your strategy, unless you want to deviate from optimal play in order to exploit your opponents new tendencies.

Below are adjustments (based on optimal heads-up strategy pairs) for Alice and Bob in a squeeze scenario where Alice open-raises 35% on the button, small blind calls, and Bob sits in the big blind. This is a common squeeze spot, and you will profit from training solid default strategies for it (both as the raiser and as the squeezer) so that you both can squeeze and defend against squeezes with strong control preflop.

Example 2.4: Squeezing from the blinds against a button steal-raise

\$100NL

Alice (\$100) raises pot to \$3.5 from the button, small blind (\$100) calls, Bob (\$100) is in the big blind.

Alice uses her default 35% button range defined in Part 2:

22+

A2s+ A7o+

K2s+ K9o+

Q6s+ Q9o+

J7s+ J9o+

T7s+ T9o+

96s+

86s+

75s+

65s

458 combos

35%

Bob's strategy

Let's start with Bob's 3-betting range against Alice. We have assumed that Alice uses the same value range {QQ+,AK} that she would use heads-up on the button against a 3-bet from the blinds. So Bob's response is to use the same value range for squeezing that he would have used heads-up. Then he adds 3-bet bluffs until he has a 45/55 value/bluff ratio for his 3-betting range.

Using the optimal heads-up strategy pair from Part 3 as our starting point, we get:
Bob 3-bets {TT+,AQ+} =62 combos for value from the blinds against a 35% button open-raise, planning to 5-bet all-in against a 4-bet
Bob then needs (55/45) x 62 =76 3-bet bluff combos to get a 45/55 value/bluff ratio. So he 3-bets 76% of "OOP 3-bet air list" as a bluff. We can round this to 75%.

We remember that "OOP 3-bet Air list" is:

OOP 3-bet air list

66-22

A9s-A6s

K9s-K8s

QTs-Q9s

J9s-J8s

97s+

87s

76s

65s

98 combos

Since the list has about 100 combos, we can convert directly between number of combos and percentages to use with a randomizer. So Bob 3-bets {TT+, AQ+} for value, and when he has a hand from "OOP 3-bet air list" he uses the randomizer. He 3-bet bluffs if the randomizer returns a number between 0 and 75, and otherwise he folds. This gives him the optimal 45/55 value/bluff ratio for squeeze 3-bets in a 3-way pot.

Alice's strategy

From Part 3 we remember that Alice's value range after opening her 35% button range and getting 3-bet heads-up was {QQ+,AK} =34 combos. Then she added the 4-bet bluffs {ATo,A9s-A7s} =24 combos to get a heads-up optimal 60/40 ratio between 4-bet value hands and 4-bet bluffs.

We have chosen a model where Alice uses the same value range in squeeze scenarios, but now with a 70/30 value bluff ratio instead of 60/40. So Alice needs 30/70 bluff combos for every value combo, She therefore 4-bet bluffs with (30/70) x 34 =15 combos. For example, we can drop A8s/A7s from the heads-up 4-bet bluffing range and use {ATo,A9s} =16 combos. The value/bluff ratio then becomes 34/16 =68/32 which is close to the 70/30 that we want.

In addition, Alice defends by flatting a wide range in position, also when there is a cold-caller between her and Bob. Heads-up in position we gave Alice the flatting range {JJ-88,AQ-AJ,ATs,KQ-KJ,KTs,QJ,QTs,JTs} =120 combos, and we can use this as a starting point also in a squeeze scenario. We can adjust as needed, for example by calling tighter if the cold-caller is tight and plays well postflop.

2.5 Summary of the theory for squeezing

We used a model to estimate the new optimal value/bluff ratios that arose in a 3-way squeeze scenario. We found that these were 45/55 for Bob's 3-betting and 70/30 for Alice's 4-betting.

Then we looked at an example with Alice on the button, the coldcaller in the small blind and Bob in the big blind to illustrate how we can adjust to these new optimal ratios. We made some simplifications along the way. For example by assuming that Alice uses the same defense frequency (30%) as in a heads-up 3-bet scenario. We also assumed she uses the same value range. Adjusting the ranges to the new value/bluff ratios then simply becomes an adjustment of the number of 3-bet/4-bet bluffs, while the value ranges are the same as in the heads-up scenario.

This method is of course only an approximation, but it captures the essence of the difference between heads-up pots and multiway pots, namely that both the raiser and the 3-bettor should bluff less and 3/4/5-bet more for value. We can make more accurate adjustments, but I recommend you keep things simple and stick with the simple model we have used here when you find yourselves in a squeeze scenario. Use the corresponding heads-up strategy pair for Alice and Bob as a starting point, and tighten up the bluffing ranges somewhat.

The most important points to take with us from this discussion are:
The raiser and the cold-caller have to defend a lot (38%) against the squeeze to prevent the squeezer to have a profitable 3-bet with any two cards
A bigger pot before it's the 3-bettors turn to act means a higher value/bluff ratio for all players involved. A bigger pot means better risk/reward ratios and therefore less folding. The players adjust by bluffing less.

If you understand these things and use the model presented above to design (or at least think about) new value/bluff-ranges for 3/4/5-betting adjusted to the new pot-size, you should feel comfortable playing squeeze scenarios.

We discussed one specific example here to show how these adjustments can be done. Those of you who have trained the 3/4/5-bet strategy pairs for the heads-up scenarios can now work through any squeeze scenarios on your own and implement the necessary adjustments, based on the model used in this article.

Source: http://pt.donkr.com/news/optimal-3-bet4-bet5-bet-strategies-in-nl-holdem-6-max---part-5-723