Raising AK in big blind vs 3 limpers

[1800GAMBLER]

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If you somehow knew your preflop equity was 0.1bb you would not raise because of this disadvatange. Yet with AKo your preflop equity is just too large to give up for other reasons.
If you want to play around with this more pokerstove is great for this.

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Interestingly, pokerstove shows AKo's equity edge to be .12bbs in the hand under discussion. Seems kinda close to your folding threshold to be "criminal" [img]/images/graemlins/smile.gif[/img]

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What line up did you put AK against?

[chief444]

Earlier I ran the exact lineup Eric gave for this example and AK had a 10% preflop equity edge against the three limpers. It was like 32% compared to 22% for the others. I didn't mention it only because Eric asked that we not discuss that. I don't think anyone stopped raising AKo yet though.

[Jake (The Snake)]

Yeah I have no idea where I got 50 before.

I did it again and got this:

Text results appended to pokerstove.txt

6,935,716 games 80.837 secs 85,798 games/sec

Board:
Dead:

equity (%) win (%) tie (%)
Hand 1: 37.4787 % 35.47% 02.18% { AdKs }
Hand 2: 20.8450 % 19.47% 01.48% { AQs-A2s, K7s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, 65s, A2o+, K7o+, Q8o+, J9o+ }
Hand 3: 20.8364 % 19.46% 01.48% { AQs-A2s, K7s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, 65s, A2o+, K7o+, Q8o+, J9o+ }
Hand 4: 20.8398 % 19.46% 01.48% { AQs-A2s, K7s+, Q8s+, J8s+, T8s+, 97s+, 87s, 76s, 65s, A2o+, K7o+, Q8o+, J9o+ }


So that makes the preflop advantage almost exactly .5 SB, much closer to what yours was. I'm not sure what the remaining difference between mine and your ranges is. Maybe I added too many hands.

Edit: nm

[Jake (The Snake)]

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I recognize that this is within your margin of error, but I also think it's a pretty decent estimate. The immediate value of his PF raise based on the equity edge I posted above would be about .25 and he has decent implied odds so picking up another .35 somewhere is certainly reasonable.

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Sorry I can't understand this. Are you saying that raising has a postflop advantage of .35? That's what it looks like to me but that doesn't make any sense since checking should have the advantage postflop. Also, where does your 1.4 sb number come from? I need this explained a little more, I'm sure you're right I just don't follow.

[Jake (The Snake)]

A couple things to ask.

1. Why are you subtracting 1 and 2 in the equations? Shouldn't it just be 1 for raising and 0 for checking? This is the preflop investment part right?

2. Is the 1/3 and 2/3 numbers how often you expect AK to be improved or not improved? If so, are you counting the whole board or just the flop? I say this because if it's just the flop, it looks to me like the numbers are backwards because AK is only going to pair on the flop 1/3 of the time. If it's the whole board it should be about 50,50.

[SeaEagle]

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Maybe I added too many hands.


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Yes. Eric posted his hand ranges in the first post of this thread. It's tighter than your ranges.

[SeaEagle]

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Are you saying that raising has a postflop advantage of .35? That's what it looks like to me but that doesn't make any sense since checking should have the advantage postflop.

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If you look at the final profit for a given hand and exactly where that profit was made, you'll see that some happens before the flop and some happens after the flop, even when opponents play correctly. So in the case of AK, if we say the raise makes .6sbs, .24 of that goes into the pot preflop and .36 of that goes into the pot postflop. I can go into more detail on this, but I think it'll only confuse this particular thread - because Eric's approach doesn't worry about where the money goes in and just figures out how much you make across the entire hand.

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Also, where does your 1.4 sb number come from?

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In my post that said "what if your opponents play the same regardless of the pot size", I estimated 16sbs will go into the pot postflop and that AK will end up winning the pot 80% of the time. Using the part of Eric's formula that says how much the draws collect of the pot:
postflop EV is (OriginalPot+PostflopBetting) * DrawWinRate
So for the unraised pot: (4+20)*.2 or 4.8
and for the raised pot: (8+20)*.2 or 5.6

So the draws collect .8 more in the larger pot.

I really wished I hadn't posted the original .24 immediate equity number, because it's based on looking at the problem from a whole different viewpoint than this thread is intended for and, as is often the case, mixing apples and oranges just makes everyone confused. If it helps, I'll try to explain it this way:

When you raise PF, you force 3 more sbs into the pot. If everyone were all in, you would win often enough to collect, on average, .24 of the 3sbs. But everyone isn't all in, and everytime someone folds you earn another little bit of the 3sbs that went into the pot.

If you wanted, you could walk through each betting round and estimate who would likely fold and subsequently figure out how much of the 3sbs you'd collect at that point (this is the traditional way of figuring EV).

Personally, I think there are times when Eric's approach is really sweet and other times when it's not so effective. Figuring implied EV is one of those places where it really shines. He says, in effect, "I don't care when people fold. I just know that the draws are going to take x% of the pot and from that I can figure out how much of the 3sbs is left over for the PF raiser." His approach estimates that the raise earns, in total, about .6sbs. His approach also estimates that another factor (draws are more profitable in a bigger pot) is costing the raised pot .8sbs. So it's fair to say that the raise is going to collect a total of 1.4 of the 3sbs as people fold out and that's going to more than compensate for better price draws are getting.