Calling a preflop raise with KK

[Bozeman]

I was curious about the recent threads advocating a call with a high pair preflop in an effort to decrease the amount you lose when an ace flops. I know that this goes against the conventional wisdom, but I thought the math should be examined.

First, let's say you have KK. Suppose you raise preflop, and are reraised (all others fold). This puts x in the pot if you call now, leaving you with y left (or your opponent with y left, and you with more). I've done the most detailed math with x=y, that is you have enough for a pot sized bet left if you call. Let's assume you never fold preflop.

The mathematical results are included in the followup post, but since it is pretty long, I would like to summarize the most interesting results.

First, if your opponent will fold every hand except AA to another preflop raise (and has a finite chance of having AA), you will do better by calling, but this difference is small (~1%).

Second, if you opponent is as likely to have a PP as to have Ax, you will do better raising than calling essentially regardless of how they play postflop.

If your opponent is twice as likely to have Ax as to have a dominated PP, you can do better by calling, if he will always bet the flop or he will play the Ax very aggressively postflop, but will check/fold the PP if overcards flop (and no set).

If you call, you would much rather face aggressive play postflop, and facing opponents who are aggressive (loose) postflop with Ax is much better for you than aggression with PP's.

The best cases stand to make you ~10% more than raising, but the worst cases can cost you 20%+.

So it is, in my opinion, possible to have a read on your opponent that makes the call the smarter play (note, calculations are using chip EV, so there may be additional situations to do it because of money EV in tournament play). Still, you are not very wrong to always raise here.

Craig

[Bozeman]

First, I calculated approximate EV (flushes can make some difference here, but I tried to estimate proper averages over available configurations) (results are good to at least +- 0.05) for a few possible holdings/styles from which we can see the extremes: (EV is for x=y=1, and O EV point is leaving with y left, as in calling then folding)
Assuming you know your opps. cards:

Against AJ (similar for almost all Ax) which will be played aggressively (you can count on all the money going in on the flop, regardless):
Call: EVA1c=1.36
Raise(call): EVAr=1.1
Raise(fold): EVf=1 for all cases

Against QQ (similar for all non AA, KK pp's) played aggressively
Call: EVC1c=1.57
Raise(call): EVBr=1.46
(he folds is still EVf=1)

Against AJ played weak-tight (he will push in only if he flops A or J)
Call: EVA3c=0.92
Raise(call): EVAr=1.1

Against QQ played WT (will push iff he has an overpair or better on flop)
Call: EVC2c=1.31
Raise(call): EVBr=1.46

However, the chance that he will play such that you can tell whether he has AK or a pocket pair is tiny, so the best case for calling is when you can put him on Ax, and only be wrong some of the time. If you put him on Ax,
you should make:

Against AJ Ag:
EVA1c=1.36
EVAr=1.1
AJ WT:
EVA3c=0.92
EVAr=1.1
Against QQ Ag:
EVB1c=1.14
EVBr=1.46
Against QQ WT:
EVB3c=1.21
EVBr=1.46
Against AA
Call: EVDc=-0.37
Raise: EVDr=-0.44

Ok, so can we apply these to anything closer to real poker?

What kind of opponents could we have?
1) Aggressive, will always bet the flop
2) Aggressive, will put you on AK unless he also has an A and an A flops
3) PP aggressive, will play Ax WT
4) WT, will play very tight, passive
5) Ax aggressive, will play QQ WT
(I have ranked these according to my rough idea of their probability)

A few reasonable sets of hands
a) is playing this way with QQ,JJ,AK,AQ,KK, and AA
b) is playing 99-AA,AK,AQs
I have neglected KK since it is unlikely and even (and it makes the math easier since I then have 36 possible hands for each case).

With the possible caveat that there are a few granite specimens who will fold everything but AA,KK to a preflop rereraise (fairly unlikely, I would say), for whom EVr(granite)=0.79 if they have a or b for their reraise.

For these cases, assuming you play him for an A,
a) EVr=0.98
1a EVc=1.05
2a EVc=1.04
3a EVc=0.80
4a EVc=0.81
5a EVc=1.07

b) EVr=1.09
1b EVc=0.98
2b EVc=1.02
3b EVc=0.86
4b EVc=0.90
5b EVc=1.03

Not as definitive as I'd hoped,
Craig

[Che]

Sorry all this work wasn’t definitive for you, Craig. Thanks for doing it, though, since it makes my life easier! /images/graemlins/laugh.gif

I will push in in this situation every time for the following reasons:

First, I can’t distinguish between opponents who play this way with set a vs. set b, so I consider the averages of the two groups:

EVr=1.035, EV1=1.015, EV2=1.03, EV3=.83, EV4=.855, and EV5=1.05.

I see that calling is only slightly superior against opponent 5 while calling is greatly inferior against both 3 and 4 so I always raise even if I think an opponent is category 5 since the risk of being wrong far outweighs the slight benefit if my read is correct.

When I develop to the point that I can distinguish between set a and set b opponents, I will still always raise against all set b opponents since this strategy dominates.

Against set a, I will divide the world into those that play Ax WT (i.e. opponents 3 and 4) and those that don’t. Raise against the former and call if I’m and more than .75 sure that the opponent is the latter (benefit of correct read is approx. 1/3 of loss due to incorrect read).

Thus, for practical purposes, even far in the future I will continue to raise in virtually all similar situations.

I say *all* situations because my initial reaction was to push in except when on or near the bubble. However, since many aggressive players shift towards WT on/near the bubble, the proportion of players in categories 3 and 4 will increase, and the odds of calling being low (relative) EV will increase correspondingly.

Many will probably disagree so I should qualify this by saying that my willingness to take risks on the bubble is much higher than average. A more risk averse player would obviously trade the higher EV of raising for the higher probability of not being eliminated when the A flops.

[Schmed]

Maybe I misread this but from an EP I would think that not raising KK is a big mistake because you allow A6s to limp in or other hands that when they flop they beat you but would never call your raise.

Now, depending on my read, I may push all in to a reraise but typically I just call and if no A hits I raise all in.

[Copernicus]

I must have missed the referred to threads about calling vs raising, and I'm sure there were some very cogent arguments, but offhand I cant see it even being close. Your analysis may not be definitive for the hands reviewed, but from a 30000 foot level, risking letting multiple hands in cheaply in fear of the 12% of the time that an A is going to flop when there is one A out there is a bad trade. The biggest disaster, of course, is not knocking out a weak A that would have folded to a raise, which could realistically cut that 12% chance to 6% or less.

[Bozeman]

Sorry, I wasn't clear about this, especially in the title.

This is in direct reference to times when you raise and are reraised ( Jay (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=tourn&Number=362289&Forum= tourn&Words=KK%20calling&Match=And&Searchpage=1&Li mit=25&Old=3months&Main=361492&Search=true#Post362 289) argued for calling the reraise against a particular type of opponents and I think he is right if his read is good), and in indirect reference to just calling a raise if no one else is likely to come in.

Obviously, raises that keep QQ in and knock Ax out are great. This analysis is for a fairly rare situation, since almost all the common ones are not even close (so why bother with the math?).

Craig

PS Also note that this is essentially the best size stack (=pot after call) for the call, any smaller and you are pot committed by a call, and bigger stacks should get in more as the (usual) favorite and a raise better defines the opps. hand.