Fármacos

Before we leave the topic of 3-betting, we'll take a closer look at a frequently occuring special case, namely 3-betting with AAxx hands.

PLO From Scratch Page 77 Previously in this article series (see Part 2 and Part 4) we have warned against 3-betting bad AAxx hands. Bad AAxx hands are AAxx with no suits, or with one suit and little else. For example:

3-betting bad AAxx hands is particularly problematic out of position. The reason is acombination of poor average postflop equity + a well-defined hand + putting ourselves in a scenario where we are "forced" to c-bet a lot.

AAxx is the first hand most opponents will put us on when we 3-bet. And if AA is all we have (meaning, if the xx part of our hand is so bad in can almost be ignored), it will be easy to play a wide range of hands profitably against our 3-bet. This effect is magnified by being out of position, since we now have to c-bet a lot of flops. Since there are lots of bad flops for bad hands, this means we're setting ourselves up for having to bet a lot of flops where we have poor equity. And this, in turn, gives our opponents good implied odds.

When we 3-bet bad AAxx, our opponent knows most of what there is to know about our hand, and his position makes it easier for him to put this information to good use postflop. But when we have good AAxx, the information we send Villain will be less useful to him, and he will make more postflop mistakes, even if he has position.

To illustrate the dramatic difference between 3-betting premium and trashy AAxx hands, we will do a model study, using flop equity distributions. The theory we use (flop equity distributions and numerical integration) was discussed thoroughly in Part 3, so reread this article if necessary.

Our model of this 3-betting scenario is:

 Villain raises pot to 3.5 BB on the button with a range made up of top 50% of hands minus all AAxx hands

 We have either (premium) or (trashy) in the big blind, and Villain

knows our hand

 We 3-bet pot to 11 BB, planning to c-bet all flops and call an all-in raise

 Villain calls the 3-bet with his entire range

 We c-bet all flops, and Villain raises all-in on all flops where he has sufficient equity, and otherwise he folds

The question we want to answer is this:

Is it possible for Villain to use his perfect knowledge to make it profitable to raise preflop and then call a 3-bet with a wide range consisting of top 50% of hands (minus all AAxx hands)?

Note that we have removed the AAxx hands from his range to make things simpler. When Villain has AAxx, the hand will end with a preflop all-in confrontation anyway, and most of these pots will be split. Furthermore, we calculate Villain's EV from the moment he puts the first chips into the pot knowing that we have AAxx, and that he will get 3-bet. He then calls our 3-bet under the assumption that we will bet all flops, planning to call a raise.

The pot is 11 + 11 + 0.5 = 22.5 BB on the flop, and there's 89 BB left in the stack for an SPR of 89/22.5 = 4.0 (so we are in the raise-or-fold region). When Villain raises the flop, he is risking 89 BB to win 22.5 + 89 = 111.5 BB. Thus, he is getting effective pot odds 112.5:89 = 1.25:1, and he needs minimum 1/(1.25 + 1) = 0.44 = 44% equity to profitable raise all-in.

So Villain will raise us all-in on his top_x% of flops where he has 44% equity or more, and otherwise he will fold and lose his 11 BB preflop investment. When he raises all-in, his average equity is av_equity, and he will then be all-in in a 200.5 BB pot where he has invested 100 BB total.

We find both top_x and av_equity from flop equity distribution graphs. Villain's average total EV for raising on the buton againstg our known AAxx hand is then:

EV (total)

= (1 - top_x)(-11 BB) + top_x[av_equity(200.5 BB) - 100 BB]

PLO From Scratch Page 78 Below are the flop equity distribution graphs and calculations for Villain's top 50% range against our hands

and . For both hands we have first calculated the total EV from the moment Villain raises.

Then we have also calculated the EV from the moment Villain calls the 3-bet (Villain then risks 7.5 BB preflop and a total of 96.5 BB, since the 3.5 BB raise now belongs to the pot, not to him).

Top 50% vs AAJT (double-suited)

EV (total)

= (1 - 0.23)(-11 BB) + 0.23[0.654(200.5 BB) - 100 BB]

= -1.32 BB

EV (call 3-bet)

= (1 - 0.23)(-7.5 BB) + 0.23[0.654(200.5 BB) - 96.5 BB]

= +2.18 BB

PLO From Scratch Page 79 Top 50% vs AA72 (rainbow)

EV (total)

= (1 - 0.39)(-11 BB) + 0.39[0.681(200.5 BB) - 100 BB]

= +7.54 BB

EV (call 3-bet)

= (1 - 0.39)(-7.5 BB) + 0.39[0.681(200.5 BB) - 96.5 BB]

= +11.04 BB

An interesting conclusion

Our model first tells us that Villain can not profit (overall) by getting involved against our premium . Even with perfect information, perfect flop play, and maximum implied odds he loses -1.32 BB when he chooses to raise against our premium AAxx hand.

But when we 3-bet trashy , Villain actually makes +7.54 when he raises, even if he know we have AAxx, and even if he knows he will get 3-bet every time!

We also see that it is profitable for Villain to call the 3-bet against , even if he loses chips overall against this hand. He loses from the moment he raises preflop, but when he has been 3-bet, he loses less by calling and continuing in the hand, than by folding preflop.

PLO From Scratch Page 80 What can we conclude from these data?

First of all, it's abundantly clear that the value of premium side cards is huge when we build a big preflop pot with AAxx out of position. We have to keep in mind that when we 3-bet AAxx in the real world, AAxx with unknown (and therefore uninteresting) side cards is the first hand Villain will put us on. Giving away this information hurts us badly when the AA part of our hand is the only part worth anything.

In other words: Playing against our 3-bet as if we only had the two AA cards is a small mistake when the two side cards are bad (e.g. 72 offsuit). But it's a big mistake by Villain to ignore our side cards when they are valuable (e.g. double-suited JT).

Furthermore, we see that setting ourselves up for having to c-bet a lot of flops (which we have to do when we 3-bet heads-up out of position) is a problem for bad AAxx. In reality we will of course not stack off on any flop like we did in the model, but out of position we still have to c-bet a lot of flops, including a lot of flops where we have poor equity.

Being "forced" to c-bet flops out of position is less of a problem with premium AAxx, since these hands often hit a piece of the flop, thus often giving us enough equity to profitably bet and get the rest of the stack in. But with bad side cards, we often have poor equity, and as a result we often have to choose between bet-folding or getting the stack in with insufficient equity.

Finally, we observe that the value of perfect information is huge. Villain played a very wide top 50% range against us, and he still managed to make a solid profit against trashy AAxx. The top 50% range includes a lot of rough hands like

(ProPokerTools calculation), but still it was possible to play the range profitable against trashy AAxx with perfect information. Furthermore, we saw that Villain could call the 3-bet profitably both against premium and trashy AAxx, although he lost overall against (but he lost less by calling the 3-bet than by folding)

We therefore conclude:

Habitually 3-betting trashy AAxx hands out of position with 100 BB stacks is not good for you!

Telling Villain that you have AAxx out of position makes it easy for him to play wide range of weak hands profitably against you, even if you 3-bet preflop, and even if he is a substantial underdog preflop

The observant reader will of course see that the problem of having a well defined betting range can be solved by also 3-betting non-AAxx hands. But this does not solve the problem of not finding enough good flops to stack off on when we have AAxx with bad side cards.

Even when we 3-bet a range of hands, Villain will often put us on AAxx anyway (and he ignores the side cards). And when AA with worthless side cards is what we actually have, he will be able to play very well against us postflop.