April 3, 2010 – 10:41 am | 7 Comments

I’ve compiled a short (just 7-pages) e-book, an introduction to the mathematics of poker. It’s basically covers how to calculate your expected value in a certain spot – starting with explaining what EV is, all …

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Home » Hand Analysis

Folding AQ offsuit Preflop

Submitted by on March 7, 2010 – 8:30 pm5 Comments

[update: After some discussions on the forum, I realized I was missing something, and so I’ve taken a closer look at the hand. You can read the new analysis here.]

I was playing in a live cash game a few days ago, and was put in what i felt was a difficult decision pre-flop. So I thought I’d do some simple analysis to see if I made the right play.

Here’s how the hand went. It’s a 10-man game, $0.50/$1 blinds. I’m in the small blind, with AQ offsuit. There are a whole bunch of limpers, and I raise to $5.50, in an attempt to narrow the field, figuring some of the limpers are weak and would fold.

Firstly, was this raise right? There were about at least 4 limpers. And even against 4 more random hands, AQ is only about 30% favorite, and I didn’t want that risk. I wanted to narrow it down, and that was why I made the raise. My equity increases exponentially the more players fold, and it gives me more information.

The big blind, a moderate-tight player, who does bluff at times, but not very often, re-raises to $21. UTG, who has been quite tight passive so far, calls, and the rest all fold to me. After some consideration, I folded. I was basically thinking that, I’m either against a lower pocket pair, where I’m in a coin toss, a hand similar to mine, or a higher pocket pair, where I’m crused. So I figured I was either 50-50 or crushed, and so I folded. But was this the right decision?

Let’s take a look at it. Right now, the pot is about $48.50. I’m left with $15.50 to call.

That means that for me to call, I need to have an equity x of

EV > 0
x * (15.50+48.50) – 15.50 > 0
x * (64) > 15.50
x > 15.50/64 = 24.22%

What kind of ranges would I have a 24% equity against? If I put both players on a range 99+, KQ+, that gives me an equity of about 23%. At 23.2%, a case can be made for calling, because of the implied odds of the flop (if I hit an A against KK, for example, I’m bound to win a bit more). So even if both players are on 99+, KQ+, I think I can call here and see a flop.

Obviously, however, the two players would have slightly different ranges. I would think the big blind is on a range like 77+, AT+, QJ+, and the UTG player on a stronger range of 99+, AQ+. Even then, I still have 24.25% equity. Again, that’s not counting the implied odds, the odds of the big blind bluffing, etc.

So, it seems like the fold was a mistake, based on the numbers. What do you think? Would you have folded?


  • Mac says:

    This is standard for 6 max. Why would you think about it for 2 seconds in a 10 max game..?

    When i'm 20 tabling 6max 10nl, I never once was all in with aq or even 3bet unless it was aq suited and in position vs a raise from c/o or button.

    And I would fold all day long. A guy who bluffs alot is also going to float a lot which means you can never bet unless you hit and hope to god he doesn't have you crushed. You have no “implied” odds if he bluffs because he 3bet. You would be better off calling but when you raise and he re raises, he might crush you but I don't know about live poker to much..

  • Derrick Kwa says:

    I don't play 6 mas, so I don't quite know.

    I don't think he's bluffing completely here, I just feel like the game's a bit loose. Generally it feels like live games are looser than online (at least the ones I play). I'm thinking “implied odds” as in, if I hit an A, and he has KK, he's likely to call a bet. I could be wrong, but that's how I feel – that I can probably get at least one more bet in.

    A more detailed look at why I think calling seems like an ok option can be found in the update. But yeah, I don't know. Intuitively, I feel like I should be folding (which is why I folded), but the math I've done seems to show otherwise. So either I'm making faulty assumptions (wrong ranges, etc), or my intuition is wrong, or I'm missing something? I don't quite know.

  • longpost4low$ says:

    50 cent 1 dollar blinds…lol

  • JH1 says:

    Raising limpers: Raising is correct but you don’t state the correct reason. Narrowing the field is not a reason to put money in the pot. Think about limping ranges – suited connectors, random broadways, other random hands Qx and lower. AQ is way ahead of those hands and they will limp/call with those so raising AQ is for value first – anything else (information, isolation etc etc) is simply a by-product.

    After getting limp/reraised, you’re not really looking at equity correctly here in my opinion. You have 24% equity against those ranges if you get to see all 5 cards (hot/cold equity). If you call, you only get to see 3 cards on the flop and most likely have to pay more to see more cards, and therefore your EV calculation does not represent the true cost of realizing that equity.

    Quick example: If you hold a flush draw on the flop vs a made hand you have 36% equity. If the pot is $2 and you have to call $1 you are getting 2:1 and according to your EV calc you have to call. But you are only 20% (4:1) to improve on the next card and most likely have to pay more to see the river. This is obviously where implied odds come into play but I hope you see my point wrt the EV calc vs realizing hot/cold equity in isolation.

    And in your hand, you don’t really have a lot of implied odds against the range that you assessed. If the flop is Axx or Qxx and the money goes in, you’re probably crushed by AK,QQ+ because 99-JJ (and QQ/KK on Axx, AK on Qxx) are not stacking off. Therefore you are attempting to draw to a one pair reverse implied odds hand, not an implied odds hand.

    So if you think you’ve assessed those ranges correctly, you could just shove preflop to add some fold equity to the equation if BB’s range is really that wide for a 3bet out of position. If you shove and he only calls with JJ+,AK, and UTG folds, you have about 30% equity:

    x = required fold equity to breakeven, assuming 100bb stacks
    breakeven = pot * FE% + (1-FE%)(%win * profit – %lose * loss)

    0 = 48.5x + (1-x)(0.30 * 127.5 – 0.70 * 94.5)
    0 = 48.5x + (1-x)(-27.9)
    0 = 48.5x – 27.9 + 27.9x
    x = 0.36 or 36% fold equity

    77+,AT+,QJ+ is 12% of all hands. If we can get him to fold 36% of that range (4.3% of all hands) we have a profitable play. 77-TT, QJ, KJ might fold to a shove and those make up the required fold equity. If he folds any more of the hands in that range you profit.

    If this is not an accurate range and he is actually tighter, you should just fold preflop because of the equity realization problem, the out of position problem, the reverse implied odds problem, along with decreased preflop fold equity.

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