(Why) Do I 3bet A2o SB vs BU?

I’d like to address this question just a little bit. I think it’s one of the most common preflop leaks in SH LHE players from low to highstakes. At least I think now, but I haven’t done any calculations whatsoever, so maybe it’s one of my biggest leaks, we’ll see.

So do you 3bet A2o vs a regular BU opener? I sure do. I’ve heard a lot of arguments against it, and very few for it. Let’s see those arguments, so that we could tear them apart and see if they’re wrong or right.

A few of those arguments (if you have any further, let me know, so that we can elaborate on them too):

  • A2o is a dominated hand
  • if we 3bet with A2o, we either win a small pot, or lose a big one with it (I think DeathDonkey said that about ace-rags)
  • A2o will be in the no men’s land on the turn unimproved, we usually have to check/fold or check/crying calldown with it, which sucks
  • (our range won’t be balanced, it will be too A-high heavy – that one I made up, but for me it’s the only reasonable argument against it)

These are all that I could think of, but if you have any, let me know. So let’s get into it:
Against my own BU range:
ProPokerTools Odds Oracle Results (2.05 Professional)

Holdem, Generic syntax

PLAYER_1 $ORBU

PLAYER_2 A2$o

13068304128 trials (exhaustive)
All-in Equity

$ORBU A2$o
Equity % 51,2244% 48,7756%
Wins Hi % 47,7664% 45,3177%
Ties Hi % 6,9159% 6,9159%
Wins Hi Count 6242261895 5922256311
Ties Hi Count 903785922 9037859

Ok, so first off it seems pretty weird that I don’t want to 3bet a hand with 49% equity, but I want to 3bet a hand like T9s that has 46%. (Of course HCEQ is not everything, it’s more close to nothing than everything.)

Doing a quick HCEV calculation (assuming Villain doesn’t cap anything and BB always folds): 0.49*4.5 – 0.51*2.5 = 0.93 SB

So that ~1 SB has to be lost either by not realizing our equity or by RIO and other factors, like BB being involved in the hand.

True Equity calculation:

Let’s take an easy example: we bet the flop, Villain calls, we check the turn planning to check/fold if we don’t have the appropriate equity to continue. The pot odds would be 5.5:1, so we have to have 15.38 equity to continue. Since we usually have to call down here, and can’t continue drawing, we should use more like 5.5:2 = 26,67%. Since we can call/fold sometimes, let’s say 25%. What will our average equity be, when we have either more than 25% equity on the turn, or 0. I made a quick PQL script for it. Now just accept, that our preflop equity if we always check/fold the turn below 25% equity is around 46.3%. That still doesn’t sounds bad, considering we should have around 43-44% equity to 3bet from the SB. Also this script doesn’t take into account, that most of the time we’re also gonna make him fold some equity (or even a better hand), therefore I believe our actual True Equity should be higher, or at least even to our HCEQ. That didn’t change anything, let’s see the RIO stuff.

Reversed Implied Odds:

That’s a yucky one. I’m not certainly sure how to calculate that exactly, but I’d say against a weak range that contains a lot of rubbish hands that won’t make that much valueraising hands, I don’t think there is a RIO of 1 small bet. In my mind that would basically mean that the opponent plays incorrectly (by not bluffing or vraising thin enough), which we can exploit in theory, so a RIO of 1 SB seems extremely high to me. When I did some RIO calculations in the past, I got around .2-.25 BB maximum, I’m not sure if it was exhaustive enough, but I got the feel that it won’t ever be high enough for us to be folding.

About the domination

The hands this hand is dominated by but A6o is not, are hands that most usually split with our hand (or we make them fold by the river):

ProPokerTools Odds Oracle Results (2.05 Professional)

Holdem, Generic syntax

PLAYER_1 A4$o

PLAYER_2 A2$o

184928832 trials (exhaustive)
All-in Equity

A4$o A2$o
Equity % 53,3909% 46,6091%
Wins Hi % 28,4576% 21,6758%
Ties Hi % 49,8667% 49,8667%
Wins Hi Count 52626276 40084728
Ties Hi Count 92217828 92217828

As you can see these hands will split the pot almost 50% of the time. Also in these situations we will have the advantage of initiative and we can barrel them off of these hands quite easily, so I find that argument very invalid. (Also the chance of him having the A and the board to have an A on it is pretty low.)

About balance

Now here comes the tricky part… I think I convinced myself well enough, so that I could say f*ck balance in this spot, but let’s still take a look at it. Let’s assume two different 3betting ranges: one we put together with a friend of mine for these spots, and the other one with all the aces included in it:

Range 1: 22+,A2s+,K7s+,Q8s+,J8s+,T8s+,97s+,87s,76s,A6o+,K9o+,QTo+,JTo,T9o

Range 2: 22+,A2s+,K7s+,Q8s+,J8s+,T8s+,97s+,87s,76s,A2o+,K9o+,QTo+,JTo,T9o

So if we take a look at how the BU openrange shares against these 2 ranges on an A hi dry board (let’s say A83r for the extreme).

ORBU vs Range 1: range asymmetry is on our side with 56.6%

ORBU vs Range 2: range asymmetry is on our side (LDO) with 59% equity.

Now range on range it’s quite a lot of difference that 2.6%, however I believe that our initial range is maybe a bit tight, and with the offsuit aces included, we may include some more suited/connected stuff in there (Q7s, 98o maybe, Q9o, J9o, something like that), and make peace once again. Also I still don’t hate that 59% percent in itself, although seems a bit highish.

So that would conclude why I 3bet A2o BU vs SB, hope I could convince you to do so (although I’m fine if you don’t :P).

Any feedback or comment is appreciated. Cheers.

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5 thoughts on “(Why) Do I 3bet A2o SB vs BU?

  1. I agree with you. I think it is very important to three-bet with A2 or pretty much any ace, any pair, any king-royal, etc. I don’t play much LHE anymore, but in my opinion the most important reason to three-bet is “defining” his hand. i hate playing blind. I mean we are already OOP against the button. Why further handcuff us? Obviously if the button has something we are going to get four-bet. So then we know where we stand. If he smooth calls then we can at least put him on a range or “define” his hand. If an ace flops our hand might be good. If a royal or two flop our hand is not likely good, but at least we know where to proceed from there. We can also define a drawing hand (either our own or his) by having three-bet PF. There are lots of advantages with this move, and I agree with you, very few drawbacks. Obviously there are times and places to smooth call. The more control we have over the button, the more it might be to our advantage NOT to three-bet. NOT to define either his hand or ours. For instance if we know absolutely that he will call down with any raggedy pair to our flopped ace, it might be advantageous to only smooth call knowing our future equity will more than make up for the missed half-bet PF.

    Occasionally I will do the “buy the button” trick, as well. It’s so juvenile and “chicky,” but it works at the lowest limits. You know the old, “I’m not going to look! I check in the dark, I’m too skerred!” I guess as a guy you could just look away or cover your eyes and verbalize a dark check.

    Wow, I could write a whole post on this one! Hope you don’t mind if I use the “press this” and make my own entry :)

    • Hey Felicia,
      absolutely not, on the contrary, I’ll be really glad if you use it.:)

      However I have to disagree with you on some points. I know you have a different background, mostly live poker, so it all can make sense from that point of view. Sadly I have close to 0 experience live, but I think online you have to look at it in a bit different perspective.
      First of all, I think “defining” the opponent’s hand is pretty hard online, given that 95%+ of my opponents don’t have a capping/4betting range HU. It’s been a really standard balancing play for quite some time now, so I don’t expect to get any information out of that.
      Also, if a 2 flops (and no A or another 2), I’m pretty happy with my hand, according to Odds Oracle we have 56% equity vs my own button openraising range. So we’re not that behind if a 2 flops.:)
      The third point is: coldcalling here is definitely not an option for me. Generally against a single openraise I either 3bet or fold always (except on the big blind of course), for balancing as much as clearing the equity behind me. We really don’t want the BB to tag along with random Ax hands or even with some suited connector that has great equity against us. So in that situation the only two options are 3betting or folding in my eyes.

      Thanks for the comment and the ideas, and I’m looking forward reading the post you mentioned.:)

      All the best,
      Madi

      • You are right, almost all of my experience with this type of example is live. I really can’t imagine being an online player first, then venturing out to play live, like you did. I know many millions are online players first. You guys have passed up old-timers like me, I have little doubt. So naturally everything I say is going to be from live experience, doh!

  2. Pingback: Why Do I 3-Bet A2o SB vs Button? | FeliciaLee Poker

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