Raising AK in big blind vs 3 limpers

[elindauer]

In this post, I'll be discussing, again, the old question of whether or not to raise AK from the blinds. Since this is a very complicated topic, I'm going to try to limit the discussion in the following ways:

1. You are the big blind facing 3 limpers. the small blind folds.

2. All limpers have exactly the following hand range:
any ace. any suited connector. any pair below TT. any two cards totalling 20 or more.

3. the framework for discussion: we will calculate 4 numbers
- EV of AK in unraised pot when it improves
- EV of AK in raised pot when it improves
- EV of AK in unraised pot when it misses
- EV of AK in raised pot when it misses

4. the EV of our hand when we hit will be determined by calculating the EV of the draws against us, subtracting this from the pot. See this post for an explanation of why I think this is best.


So, for the purposes of this thread, statements like "AK has an equity edge preflop" and "AK makes more money on every call" are simply inadmissable as they are in violation of rule 4. If this is the way you prefer to think about profit, I respectfully request that you choose not to post in this thread.



Now, I'll get us started with some rough calculations of the 4 key numbers. Please reply with suggested improvements for any of these calculations.

- EV of AK in unraised pot when it improves
It's not uncommon to find draws out against AK that will lose money in this situation. I'll say that players calling down with weaker aces have -EV draws and balance out the EV paid out to hands like flush draws. Factor in the occassional flopped set and maybe we have 90% equity in the pot.

EV = 4.95 SB

- EV of AK in raised pot when it improves

In this spot, the draws out against us have all gotten more valuable, so we can't possibly give the whole pot to AK like we did above. Implied odds have gone up some as there is no way we will almost never get away from this hand. More draws can call profitably. I'll take a stab and say the draws suck out 70% of the 8.5 SB pot on average.

EV: 5.95 SB

- EV of AK in unraised pot when it misses

tough one. AK often can't call a bet, but he sometimes finds ways to show his hand down unimproved to win. I'll call it 10% pot equity in this 5.5 SB pot for it's draw.

EV = .55 SB

- EV of AK in raised pot when it misses

The bigger pot makes the draw more valuable. He'll have profitable opportunities to show down unimproved more often, not to mention more opportunities to draw to the overcards. Maybe 15% equity for the draw.

EV: .825 SB



I have made a good faith effort to stab at these numbers. In fact, I don't even know, as I type this, whether they suggest a raise or a check is correct preflop. I expect all of these numbers to become more clearly defined during this thread, but for starters, here are the results:

EV (check) = 1/3 (.55) + 2/3 (4.95) - .5 ~= 3 SB
EV (raise) = 1/3 (.825) + 2/3 (5.95) - 1 ~= 3.25 SB

These numbers are pretty close, clearly the margin of error in my guesses is greater.

Thanks.
Eric


PS. If anyone can calculate the odds of AK improving given the hand ranges described, that would be helpful.

[SeaEagle]

It looks like you're using 5.5 for 3 of the calculations and 8.5 for the other. You probably want to double check this. It also looks like you're subtracting investments/bets of .5 and 1 sbs, how did you figure this?

Those issues aside, I'd ask you to clarify a couple of things:

One, you are estimating that AK wins 20% less when the pot is bigger?

Two, in the other thread you calculated from the final pot (and that was very important to the outcome). It looks to me like here you are not putting in the extra bets that happen after the flop, and simply calculating from the pot at the beginning of the flop. Am I missing something?

[chief444]

Eric,

I've made this comment about 10 times already but we were discussing against VERY loose opponents. These opponents at least call the flop with any piece whether it's correct or not. So you will "gain" more postflop in a smaller pot against these weak draws that call incorrectly but you don't "lose" (so to speak) any in the bigger pot against these opponents since they would have called anyway. This is sort of important to this analysis as there is a better case for checking against better opponents. It's also important relative to your calculations because you're EV doesn't change...at least not nearly as much as your estimating. Not against very loose opponents. People who limp with any ace don't fold the flop unless they have about no equity anyway.

I commend your efforts. I sincerely do.

Matt

[dark_horse]

you guys are bananas.

[SeaEagle]

[ QUOTE ]
I've made this comment about 10 times already but we were discussing against VERY loose opponents.

[/ QUOTE ]
Chief, with all due respect, Eric has worked really hard on this so far. I'd really like to at least get a working model that we can generally agree comes close and then see if we can modify parameters/values for factors such as opponent looseness and what not. Sound like a plan?

[chief444]

I meant no disrespect whatsoever to Eric and I realize how hard he's working on this. But you can't necessarily use the same logic/math/model whatever for loose opponents. Or if you do you have to at least include what I'm mentioning. That was my only point. There's the aspect of what you gain by many more and greater magnitude mistakes made by these opponents missing in the equation and that's probably the biggest benefit to not raising because your EV as a percentage doesn't really change much with a raise against loose opponents. This is pretty important to any argument for limping IMO.

Look at it this way...we're leaving preflop out of the discussion but we all agree there is an obvious equity edge. The only way you're ever going to make a case for limping is by finding ways to make up more postflop than what you gave up preflop. I'm just pointing out where this money really comes from. Your opponents mistakes are magnified. Or what maybe isn't a mistake in a larger pot now is in a smaller pot. But if you're just looking at it from an EV standpoint assuming everyone is playing correctly according to pot odds in any model than the model will simply show that AK should raise preflop because of the EV advantage.

I'm really not trying in any way to be argumentative. I just think this is an extremely important point that's being overlooked is all. And I feel looking at it from a change in EV as a percentage based on pot size just isn't accurate against loose opponents. Again, I'm not trying do criticize anything or anyone. I'm just trying to point out something I feel is important to any serious discussion regarding this.

[SeaEagle]

[ QUOTE ]
I just think this is an extremely important point that's being overlooked is all. And I feel looking at it from a change in EV as a percentage based on pot size just isn't accurate against loose opponents.

[/ QUOTE ]
I generally agree. In my terminology, I don't see how the "round by round" implied odds are figured in, which is what I think I'm asking in my original post. I'd just like Eric to respond with how/if he's accounts for it. And if he's not (or is in a way that folks don't agree with) maybe the formula can be corrected so it does.

[elindauer]

[ QUOTE ]
It looks like you're using 5.5 for 3 of the calculations and 8.5 for the other. You probably want to double check this.

[/ QUOTE ]

I don't see it. Which calculation is off?

[ QUOTE ]
It also looks like you're subtracting investments/bets of .5 and 1 sbs, how did you figure this?

[/ QUOTE ]

Mistake. For some reason I often mix small and big bets in my posts. That would make the final EVs:

check = 2.5 SB
raise = 2.25 SB

or actually favoring a check.


[ QUOTE ]
One, you are estimating that AK wins 20% less when the pot is bigger?

[/ QUOTE ]

Yes, AK improved wins less in the big pot than in the small pot. I would defend this concept, although perhaps not the absolute value, by pointing out that in the big pot, more players will draw, cutting down the win rate. Also, the weak draws that come along are doing so correctly, so instead of adding to your win, they are instead taking some of the pot from you.

[ QUOTE ]
Two... you are not putting in the extra bets that happen after the flop, and simply calculating from the pot at the beginning of the flop. Am I missing something?

[/ QUOTE ]

Yes. I'm factoring future bets into the implied odds / reverse implied odds of the various draws I'm guestimating will be out against you. I concede that so far I haven't been rigorous about estimating the probability of the various draws or their EV, opting instead to just throw out estimates and hope for some help.

-Eric

[elindauer]

Hi Matt,

You are correct that the type of opponent is very important, which is why I chose to specify exactly the starting range for the players. Postflop play also matters, but we can do a fair job of guessing at how these players will play (for example, I agree with you that someone catching an A will almost never fold).

You also claim that your EV doesn't change if they would have called anyways, but I don't think you're correct. In the small pot, the weak draws are -EV, so they add money to the AK's total take. In the big pot, they are +EV, so they take money away from AK. When viewed as a percentage of the pot, there is a big difference in the percentage you capture between the two cases. In the small pot, the weak draws increase your percentage, while in the big pot, they decrease it. I guesstimated the difference at 20%.

edit: remember that the model we are using for calculating the EV of AK is to sum up the EV of the draws and subtract it from the pot. Please stick to this model if you want to continue to debate this point. You are veering toward the street-by-street model which is off limits in this thread.

Good luck.
Eric

[elindauer]

If you want to continue to believe the existing doctrine of how to play poker, please, take the blue pill and get out of my thread. I am offering you the red pill, which you can use to see for yourself just how deep the rabbit hole goes.

-Eric