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 (http://http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=2954711&page=&view=&s b=5&o=) 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

[SeaEagle]

EV = 4.95 SB = 90% of 5.5
EV: 5.95 SB = 70% of 8.5
EV = .55 SB = 10% of 5.5
EV: .825 SB = 15% of 5.5

The last one should be 1.275

Additionally, depending on when you're measuring the EV, I believe the pots need to be 4.5 & 8.5 or 5.5 & 9.5. And if you're measuring them at 5.5 & 9.5 that assumes that BB has already bet postflop which doesn't make sense to me since he won't always bet when he misses.

[jason_t]

[ QUOTE ]

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

[/ QUOTE ]

Nice reference. I've been following this discussion closely and I am quite interested in it and might start participating now that I'm done with work on my thesis for a few days. Please keep it up and thank you.

[SeaEagle]

[ QUOTE ]
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.

[/ QUOTE ]
Ok. Since the only way I know how to express this is in the traditional EV way, I'm going to do that (against the rules of the thread) and ask you how this is reflected in your formula.

Let's suppose in the raised pot (although I think the odds are probably high enough in the unraised pot to make this same situation a correct play), that AK hits. Postflop 2 players are going to fold outright and one player is going to continue with a decent draw and will end up winning 30% of the time. So the immediate EV of the 8.5 pot for AK is .7 * 8.5 or 5.95.

Now lets assume that both players are going to play pretty well and one bet each will go in on the flop, one big bet each on the turn, and AK will always put a big bet in on the river but Draw will fold half the time he's losing but always put in a bet when he's winning (this infers that both players make mistakes on the river from time to time).

The implied EV is that AK will win 4 extra sbs 70% of the time and lose 5 extra sbs 30% of the time for a net EV of 4 * .7 - 5 * .3 or 2.8 - 1.5 or +1.3 in implied EV. And the actual EVs for the two players are 7.25 and 1.25.

So in this case, which is probably one of the poorer situations for AK when he hits, his actual EV is substantially higher than his immediate EV.

In the other thread, as I understand it, you used the final pot size so you could include the implied EV. This is really important to this situation because the raised pot is going to have a lot more bets go in the pot postflop than the unraised pot is - and that's going to help offset the fact that AK loses more of these pots.

[Jake (The Snake)]

[ QUOTE ]

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

[/ QUOTE ]

The pot size for unraised should be 4.5.

3 limpers + SB + BB

[ 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.

[/ QUOTE ]

I don't see how you are doing this either. You are taking the % you think we will end up winning and multiplying only by the preflop pot size as far as I can tell.

raise to build the pot up if u hit, in small stakes the limpers will all call, all that other mumbo jumbo is silly

[chief444]

Eric,

When I say you're EV as a percentage doesn't change I really just mean you're pot equity as a percentage. But I don't mean on any given street. I agree completely that you're EV itself will change. But I don't think you're percentage changes 20%. I think it changes slightly but you gain more EV postflop. But the percentage for when you catch could be exactly the same and your EV will still be different between a preflop call/check and a preflop raise. And I don't mean your EV on any given street. Just to be clear I'm not disagreeing whatsoever that you gain more value postflop with the smaller pot than you gain postflop with the larger pot. But that can be true even without a win% change. That was all I was saying.

And Eric...I hope you're not taking my comments in this and the other threads negatively because I think it's a topic worth discussing and really do appreciate your efforts and comments.

Matt

[SeaEagle]

[ QUOTE ]
But the percentage for when you catch could be exactly the same and your EV will still be different between a preflop call/check and a preflop raise. And I don't mean your EV on any given street. Just to be clear I'm not disagreeing whatsoever that you gain more value postflop with the smaller pot than you gain postflop with the larger pot.

[/ QUOTE ]
If I give a shot to Eric's approach:
EV for AK when hit in raised pot = Big Pot - (%draw * big pot) + investment
EV for AK when his in unrasied pot = small Pot - (%draw * small pot) + investment

A raised pot flush draw would look something like this:
20sb - (.36*20sb) + 3

An unraised pot flush draw would look something like this:
10sb - (.18*10sb) + 1

I haven't even bothered to do the math on the two situations because I didn't really try to make the actual numbers correct. But I believe this is what Eric is trying to show - in the unraised pot you win a higher % of the time because the flush draw is folding the turn whenever he misses. I'm just not sure he's taking into account that you win bigger pots in the raised hand.

[SeaEagle]

[ QUOTE ]
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.


[/ QUOTE ]
Here's some PS numbers for the hand ranges you give:
PF equity: AK - 31%. Others 23% each.
Ac8d7d equity: AK - 53%. Others 16% each
Ac7d2h equity: AK - 61%. Others 13% each
QcJc7c equity: AK - 29%. Others 24% each
9s7c5d equity: AK - 21%. Others 26% each

I don't think this tells us much, but it gives us some starting points. AK will be win more than 53-61% when he hits because opponents will fold. AK will win less than 29-21% when he misses because he will fold.

[SeaEagle]

[ QUOTE ]
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

[/ QUOTE ]
Oh. And I think your hit %'s are reversed. i.e., shouldn't the first equation be:
EV (check) = 2/3 (.55) + 1/3 (4.95)
since you miss 2/3 of the time?

[chief444]

[ QUOTE ]
in the unraised pot you win a higher % of the time because the flush draw is folding the turn whenever he misses.

[/ QUOTE ]
See, this is where you guys are losing me. A flush draw or any half decent draw whatsoever is folding the turn never whether you raise preflop or not.

[SeaEagle]

[ QUOTE ]
See, this is where you guys are losing me. A flush draw or any half decent draw whatsoever is folding the turn never whether you raise preflop or not.

[/ QUOTE ]

With an unraised pot there's only 3.25BBs in the pot on the turn, so a flush draw is getting just about the right price at 4.25-1. I was showing him folding just to make Eric's point about why the unraised pot makes more EV.

One of the things about his formula is that it makes the "loose players" analysis pretty easy. If we assume that the opponents are really bad and will always play the same way regardless of the pot size then we get:

assumption: Big pot is 24sbs. Small put must then be 24-4 or 20sbs. If AK goes to showdown, the smallest post possible is 18.5, so 24 is probably a decent average.
assumption: AK wins 80% of the time. This isn't really all that important because AK wins the same amount of time in both sitations now.
assumption: postflop investment for AK is always 5.

EV Raise: 24 - (.2*24) - 5
EV Check: 20 - (.2*20) - 5

You can easily see that in the worst case, where pot size never matters to opponents, there is a constant 4 - (.2*4) or 3.2 EV advanage to the raise when AK hits. And using Eric's estimates, AK has about a .8 advantage when he misses.

When we subract out the extra bet the PF raise costs, we get an overall advantage of 1/3 * 3.2 + 2/3 * .8 - 1 or about .6.

So, in the very worst situation that I can think of, it's still solidly profitable to raise PF. If the players play more correctly, it's even better.

[elindauer]

[ QUOTE ]
When I say you're EV as a percentage doesn't change I really just mean you're pot equity as a percentage.

[/ QUOTE ]

I understand what you mean, and I don't think it is correct. For example, let's say you make $10 postflop in both cases. If the pot is $10, you make 100% of the pot. If the pot is $20, you make 50% of the pot. See?

I think a few other people are confusing this as well. The percentages I'm giving are not % won but % of pot captured. These are different and will change based on pot-size, implied odds for the draws, etc.


[ QUOTE ]
And Eric...I hope you're not taking my comments in this and the other threads negatively because I think it's a topic worth discussing and really do appreciate your efforts and comments.

[/ QUOTE ]

That's exactly how I take it, no need to worry. Thanks for the encouragement.

Good luck.
Eric

[elindauer]

[ QUOTE ]
The pot size for unraised should be 4.5.

[/ QUOTE ]

Ah, thanks.

[ QUOTE ]
[ 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.

[/ QUOTE ]

I don't see how you are doing this either. You are taking the % you think we will end up winning and multiplying only by the preflop pot size as far as I can tell.

[/ QUOTE ]

It's not clear because I'm just hand waving at the implied odds and calling it a day, but the key is to understand that the percentage I am giving is not an estimate of the probability the AK will be good, but an estimate of the percentage of the pot this hand will capture.

See the thread in the original post of the method of calculation for more explanation of this. In that thread, AK wins 91% of the time, but captures 98% of the pot. To the extent that just throwing out numbers can be considered doing any math at all, that's exactly what I'm doing here.

Good luck.
Eric

[elindauer]

Thanks SeaEagle, this is very helpful. Some other things that would make this even better:

- when we miss, how often is AK the best hand?
- when we hit, how common are boards similar to the ones you listed?
- when we hit, what kinds of draws are typically against on each of these boards?

I'll try to incorporate these suggestions along with the math errors you pointed out into a new post and put some new best guess estimates of the values of checking and raising.

Thanks,
Eric

[elindauer]

This explanation isn't correct, see my other posts for a better description. AK can win exactly the same % of the time and still capture totally different percentages of the two different pots.

Good luck.
Eric

[SeaEagle]

[ QUOTE ]
when we miss, how often is AK the best hand?

[/ QUOTE ]
Unfortunately, I don't how to narrow this down very well. AK will only win a showdown about 25% of the time but about 24% of the time he'll improve between now and the river. SO that doesn't tell me much.

On the other hand, if I look at from the other side and try to figure out the odds that 3 random hands miss the flop, assuming each hand misses the flop 2/3 of the time all 3 will miss the flop about 30% of the time, so that doesn't help either.

[ QUOTE ]
- when we hit, how common are boards similar to the ones you listed?


[/ QUOTE ]
I put in a bunch of different boards and took the ones that showed the highest and lowest equity sitations for AK, so these are intended to show a plausible range of draw equities.

[ QUOTE ]
when we hit, what kinds of draws are typically against on each of these boards?


[/ QUOTE ] This would be really valuable, but I have no way of even guessing at this one. For instance, the Ac8d7d flop is all over the place with flush, straight, Ax 3-out draws, and 8x/7x 5-out draws.

[elindauer]

Argh... I just lost a huge post. I'll try to sum up:

SeaEagle gives some estimates for AK's pot equity in various flops. Jake the Snake points out that I messed up the odds of improvement. I calculated the following new numbers:

AK unimproved, check pf:

I guess that weaker aces capture .15 SB of the pot with their 30% chance at having nailed their 2nd pair

flush draws capture 3.5 SB (surprise) because they do so well with the implied odds from the AK.

There isn't not often a flush draw out though, I estimate AK captures about 3.7 SB of the 4.5 SB pot.

AK unimproved, raise pf:

weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate. Flush draws are somewhat less profitable as a percentage of the pot, because their implied odds are smaller relative to the pot. All told, I figured AK captures 6 SB of the 8.5 SB pot. That's 71% of the big pot, compared to 83% of the small pot. A tighter range than before, as suggested by chief.

AK improved, check pf:

AK folds often, so his 24% equity is cut down a lot. I estimated 9%

AK improved, raise pf:

AK is not forced to fold as often, capturing maybe 12% of the pot.


Adding it together:

EV (check): (1/3 * .09 + 2/3 * .83) * 4.5 - 1 = 1.75 SB
EV (raise): (1/3 * .12 + 2/3 * .71) * 8.5 - 2 = 2.33 SB


Still favoring raising, but still within the margin of error. I find that estimating the EV of the draws against us when we hit will still have a significant impact on the numbers. Next round of refinement anyone?


Good luck.
Eric

[chief444]

[ QUOTE ]
I think a few other people are confusing this as well. The percentages I'm giving are not % won but % of pot captured.

[/ QUOTE ]
Gotcha.

[SeaEagle]

[ QUOTE ]
EV (check): (1/3 * .09 + 2/3 * .83) * 4.5 - 1 = 1.75 SB
EV (raise): (1/3 * .12 + 2/3 * .71) * 8.5 - 2 = 2.33 SB

[/ QUOTE ]
Your number and my numbers are coming out remarkably close - about .6sbs for the raise.

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.

If you're looking for a number that's bigger than your current margin of error, I don't think you're going to find it. .6 EV on a bet of 1 is a darn good return given how close most poker decisions are.

The alternative would to be to bring your margin of error down and I'm not sure how you do that either. Quite frankly, it looks to me like you're taking wild shots in the dark with your draw estimates and they could be anywhere from "dead on" to "miles off".

[SeaEagle]

[ QUOTE ]
weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate.

[/ QUOTE ]
I'm confused on this. Won't the post-flop action be the same with a weaker A regardless of the size of the pot? If so, when A-x wins, won't it win a larger % of the smaller pot?

[elindauer]

[ QUOTE ]
[ QUOTE ]
weaker aces are more profitable, capturing 8% of the pot instead of 3%, despite winning at exactly the same rate.

[/ QUOTE ]
I'm confused on this. Won't the post-flop action be the same with a weaker A regardless of the size of the pot? If so, when A-x wins, won't it win a larger % of the smaller pot?

[/ QUOTE ]

No. For example, in the other thread I had KQ calling in a 4 SB pot, making .08 SB. If I make the pot bigger, say, 100 SB, and still have him play exactly the same way (ie, folding the turn when missed, raising a J, etc), then he makes:

9% * (100 in pot + 7 from AK) + 91% * -1 = 8.72 SB

which is 8.72% of the big pot. the .08 SB he wins in the small pot represents only 2% of that pot.

He still wins exactly 9% of the time, but he captures a much bigger percentage of the big pot with his weak draw. To put it another way, if the small pot had been only 3SB in that example, KQ would have actually captured a NEGATIVE percentage of the pot by playing that way, which is clearly less than he wins of the big pot. In the small pot it makes almost no difference whether or not the KQ calls, but in the big pot, he is very right to call, and this is reflected in the percentage of the pot owned by the better hand.

-Eric

[elindauer]

I actually think these estimates are better than "wild shots" at the draws, and I had a lot more to say about these guesses in my first attempt at posting. Oh well.

I think you're right that the trend suggests that raising is always going to come out on top in this example. The .6 SB is quite a lot to overcome given the thought we've put into the calculations so far. I still think it would be interesting to refine these numbers a bit as it would provide a guideline for performing a similar analysis on other hands, like KQ or 77. Are these raises in this situation?

Good luck.
Eric

[elindauer]

- It looks like raising is probably better, and perhaps is significantly better, but more work could be done
- Given the current numbers, raising even weaker hands like AQ might be right as well
- Playing AK well when it hits is probably MUCH more important to your bottom line that playing unimproved overcards. Examining lines like check-raising when you hit to try to limit the field should be a high priority.
- Avoiding paying off implied odds to draws has a significant impact on your profits. It's worth the time to profile opponents and recognize those players against whom you can fold one pair to a raise. Incorrectly paying off a player that will not raise a hand you can beat is a sizable error.


Well, that's it for now. If anybody's interested, we could do something similar and talk about KQ and 77 in this spot, seeing if hands that weak are raises. We'd have to fine-tune the draw calculations in this thread which will be difficult, but could be done. Otherwise, as always,

Good luck.
Eric

[Jake (The Snake)]

I find this interesting.

I wonder at what point (opponent hand ranges) make raising -EV.

Based on the hand ranges you gave in the OP, Hero has almost exactly 50% equity, so raising shows a preflop profit of almost exaclty 1 SB. Your numbers show that the end EV is +.58 SB for raising. So postflop, checking is .42 SB more profitable.

[SeaEagle]

[ QUOTE ]
Based on the hand ranges you gave in the OP, Hero has almost exactly 50% equity, so raising shows a preflop profit of almost exaclty 1 SB. Your numbers show that the end EV is +.58 SB for raising.

[/ QUOTE ]
I posted earlier that PS gave AK a 31% EV given these starting hands. How did you get 50%?

At 31% vs 23% for the other 3 hands, the PF raise has an immediate value of .24sbs

[1800GAMBLER]

In my quest of replying to nearly every thread on this forum i can't reply to this one because your writing style is like MicroBobs, i doubt you will give a [censored] though, anyhow, not raising AKo in the BB is criminal, learning why though is good.

[SeaEagle]

Addendum to the last comment. The .24 is just the immediate equity gain, but the raise also has some implied equity gain that will only come when people fold or at showdown. The traditional way of "street by street equity" isn't very good at working through the myriad variations and collecting that implied equity but Eric's method seems to be pretty good at it.

Using a combination of Eric's posts and the post I did comparing the EVs of two hands played exactly the same way post flop, I would say that the total hand equity value of the PF raise is about 1.4sbs but that the small pot does .8sbs better postflop so the total value of the raise is .6.

FWIW, my poker tracker db shows me averaging just over 1.5sbs per hand w/ AKo. Eric's stats show 1.33sbs.

[SeaEagle]

[ QUOTE ]
not raising AKo in the BB is criminal, learning why though is good.


[/ QUOTE ]
As you can see, some of are interested in the reasons behind why raising certain hands is good or not good, and not just willing to take some author's word (who most likely just took some other author's word, who most likely just cribbed from SS1).

Maybe you could save us a lot of effort and just tell us why not raising is criminal. Care to elaborate?

[1800GAMBLER]

[ QUOTE ]
[ QUOTE ]
not raising AKo in the BB is criminal, learning why though is good.


[/ QUOTE ]
As you can see, some of are interested in the reasons behind why raising certain hands is good or not good, and not just willing to take some author's word (who most likely just took some other author's word, who most likely just cribbed from SS1).

Maybe you could save us a lot of effort and just tell us why not raising is criminal. Care to elaborate?

[/ QUOTE ]

Too drunk for long ones but lets take AJo for example; you have a preflop edge with AJo in the BB vs limpers, right now limpers have even worse hands than when books were written, yet if you raise you give the limpers good odds (correct odds) to make their two pair or gutshots or overcard on the flop, thus more seeing the turn (correctly, because of their preflop mistake + blinds), whatever, so this disadvantage overweights the preflop equity you get from raising from the bb. 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 i'm coming off like a dick i'm sorry, it's not intended.

If you want to play around with this more pokerstove is great for this. As per usual the Older Archives are a gold mine, this is been discussed and explained by better players than myself.

[SeaEagle]

[ QUOTE ]
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.

[/ QUOTE ]

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" /images/graemlins/smile.gif

[1800GAMBLER]

[ QUOTE ]
[ QUOTE ]
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.

[/ QUOTE ]

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" /images/graemlins/smile.gif

[/ QUOTE ]

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)]

[ QUOTE ]
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.

[/ QUOTE ]

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]

[ QUOTE ]
Maybe I added too many hands.


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

[SeaEagle]

[ QUOTE ]
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.

[/ QUOTE ]
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.

[ QUOTE ]
Also, where does your 1.4 sb number come from?

[/ QUOTE ]
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.