Ace King is one of the strongest hands in No Limit Hold'Em. The fact is AK is strong enough to justify moving in preflop for your entire stack in most situations. You get a tl;dr warning here. (too long, don't read) This is the longest post I've written so far and by a good margin.
The dreaded Ace King. Dreaded because of how much trouble it gives beginners. In reality, AK is one of the harder hands to play in the game. Much of the time, it is a favorite preflop or very minor dog. But postflop Ace King, rarely makes more than one pair. However, there is sometimes a simple solution to playing Big Slick that makes life easy on you. And luckily, it's often the most profitable play you can make.
Push all in.
Hahaha... That probably needs some explanation.
When you have AK and are facing a reraise preflop, you should often move all in. You are only dominated by AA and KK, flip with QQ-22 and beat all other hands. In fact, you dominate nearly every non-pocketpair that would call a preflop all in. However, as nearly everything in poker, this play is player dependant. Obviously if you are against someone who only reraises AA and KK, you shouldn't make this play. Against someone who reraises a very wide range of hands and commits a lot of money postflop, it could be better to trap.
Regardless quite often it's correct to reraise all in with AK depending on your stack size. If you have 100bb or less it's often profitable. I wrote up a lot of information on it that I'll add at the end.
Let's examine all our options with AK.
Assuming we are at a full 9 handed table and are UTG. Our opponents are not very strong and have stacks ranging for 20bb to 200bb. You cover everyone at the table. First let's examine our options and lay out a plan for each one.
Fold. Not happening. AK is way to good to be folding UTG. If you fold this, what do you play? Folding AK here is a big mistake.
Call. An interesting play that gives you some options when the action comes back around. The danger is that the action might not come back you and you'll play a limped pot with AK multiway. Not really stellar, but assuming you can get away from it postflop, you can probably still turn a profit postflop.
On the other hand, if someone raises, a new set of options arises. You could call and see a flop, you could reraise or you could fold.
Again folding is almost never correct, you should definitely at least call unless they are extremely tight as in they raise more hands that dominate AK than hands that don't.
Calling can put you in a tricky spot. This is partly because if they have an Ace or King it's less likely you'll hit and therefore you'll miss more often. If they don't they aren't likely to give you action unless they can beat top pair. Your best case scenario is for them to have a dominated hand and give you action, but the odds of that are about the same odds as flopping a set, since you have 2 cards to improve both your hands simultaneously. Doesn't look to hot, but you should call occasionally to mix up your game.
Raising is probably the best choice. Now that you limped in and trapped some money in the middle, a reraise gives you a chance to win the pot immediately and fold out some hands that you coinflip with. It also gives you initiative allowing you to take down the pot postflop a large majority of the time, even when you miss. If you get 4bet here, carefully examine your opponent and his actions. If it fits with ONLY AA and KK fold. Otherwise you should probably move all in/call all in if you have less than 100bb.
Now back to our third option, opening the pot for a raise.
Raising first in gives you the chance to win the blinds immediately (never a terrible result, it's always better to win a small pot than lose a big one), get called by hands you beat (and therefore raise for value), fold out pocket pairs occasionally (and you gain because you will miss often), and build a pot if you hit. Aggresive poker is winning poker.
There are 3 results if you raise.
Everyone folds.
1+ people call.
Someone raises, possibly there are callers of either raise.
If someone calls, you should probably continuation bet. However postflop play is beyond the scope of this post.
Someone raises.
This is where it gets interesting. You could call, shove, or reraise less than all in.
The last two options are pretty close to the same for AK. If you reraise less than all in, you're going to be pot committed to call a shove nearly everytime. If they just call, you're probably going to cbet all in on every flop.
Now lets us examine calling vs shoving.
/puts on nerd glasses
Everything beyond this is a copy and paste of a word article I written previously. It's a rather intesive analysis of 4bet shoving AK vs calling a reraise with it.
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This examines the merits of 4 bet shoving AKo preflop, opposed to calling with it. It does not examine whether or not AK should be 4bet for less than 100bb compared to shoving it.
I used a very simple formula of outs x 2% per card on the flop. I couldn’t remember the exact numbers, but it's pretty close to 2% I think.
This is why I 4bet shove AK, feel free to slaughter my argument or point out flaws in my math.
My 3bet range at 100nl was like 77+, AJs+, AQ+, KQs, A2s-A5s sometimes, some suited connectors.
His range probably isn’t that wide, but let’s says it is. (so we can analyze what we do with AK vs different hands) And we can figure out why we 4 bet AK.
Lets say you open to 3.5bb, he makes it 12bb.
It folds back to you. Pot is currently 17bb. Rake is 6bb at 50nl when stacks get in.
This is where it gets interesting. We're going to group the different hands and analyze how AK plays against them.
Group 1 - Dominated hands; AJ, AQ, KQ (and other dominated Aces and Kings)
When you push for 100bb, you WANT a call from these hands. Poker stove says your equity is 68.875% against this range of dominated hands. That means when all the chips go in the middle you get back 69% of the 195 bb pot. (The missing big blinds are the rake. At $100+, I'm going to say they rake $3 since most poker rooms cap at $3) that means when they call you win 135.93bb, or a profit of 36bb. However they usually don’t call when you 4bet push with these hands, so you net a 17 bb profit.
But if you want to play against these hands, why aren't you calling? We raise for value here. We also don't want to miss and suddenly try to figure out whether we are good vs a whiffed AJ, or drawing to 3 outs vs KK or facing a flush draw from T9s. Cramming preflop gives you control of the hand again, and prevents you from making a postflop mistake.
Against Group 1, pushing gets you an expected net of 17bb assuming you are never called.
Group 2 – Pocket Pairs lower than QQ; 22-QQ, and also AK.
When you push for 100bb, you want your opponent to fold. When they fold you win 17bb. On average you will lose 9bb when you are called. That means if they fold 53% of the time this is a +EV play of .01bb. Usually they will fold more than that. If they only reraise TT – QQ, when you 4bet shove, most people will find it extremely difficult to call with TT or JJ. Your raise represents QQ+, AK. Against that range JJ and TT only have 36% equity, and your large overbet shove means that they need to fold as they are now priced out.
Usually they will fold QQ some of the time too. Generally you can expect to get called about these percentages. TT 20%, JJ 50%, QQ 85%. That’s fewer than the 53% (actually its 51.666% repeating) you need to turn a profit, and it gets even better if they raise hands lower than TT.
Against group 2, your expected return is about break even, assuming they call at the exact above ratio, 53%, and never 3bet pocket pairs less than TT.
Group 3 - Suited Connectors
against 76s we have 59% equity. When we push we expect to get back 115bb and risk 96bb. We profit 19bb, which is marginally different from the 17bb we expect to pick up if he folds. (and trust me unless he's terrible, he's folding)
Against group 3 – expected profit of 17bb.
Group 4 - AA and KK.
They aren't folding and our equity here is a terrible 19.636%. If you call it's because you dont want to stack off to these hands. We only get back 38bb putting our play at a -58bb if they have these hands. specifically against KK we have an expected return of 60bb, and against AA we have a return of 15.6bb
Against Group 4 we have an expected loss of 58bb.
While this looks terrible, keep in mind that some catagories are far more likely than others.
Now none of this factors in postflop play. Let's do that now.
If we call, AND plan to c/f a whiffed flop.
Group 1. Dominated hands.
If we connect with our 2 outer and stack them, that's awesome and our best case scenario. The odds of flopping one of the two remaining aces is about 12.5% (same odds as flopping a set, so keep that in mind, since that’s basically what we're aiming to do.)
Generally a TAG will fold if they flop air, and get their cbet when we c/r in a reraised pot. If we call, we should check to them to pick up a cbet when they have air. So we connect with one of our 5 outs about 30% of the time. We will win the 17bb in the pot + a cbet ranging from 10-17bb. We can say 13 for ease of calculation. When they miss, you hit you win 30bb.
So one of 3 things happens.
1) You both hit top pair, and you stack them. You profit 13.5bb (the money you invest that you lose if you don't win) + 100bb (their stack) - 6bb for the rake. That's a net of 107.5bb. It happens 12.5% of the time so let's do some math.
107.5*0.125= 13.5bb when we call for this scenario. That doesn't include the times they outdraw you either.
Results for scenario 1: 13.5bb
2) You connect, they don’t, you win 30bb. This is pretty straight forward. We c/r their bet they fold. We win 30bb. This will happen the other 18.5% of the time we connect. 30*0.185 = 5.55bb
3) We miss, and c/f. We lose 7.5bb. This will happen about 70% of the time. -8.5 * 0.7 = -5.95bb.
Add them up you get 12.9bb for calling against this group.
So when they have a dominated hand, our expect return is 4bb less than if we shove.
group 2. Coinflips. i.e. Pocket pairs
There are 2 sub groups actually. AK and 77-QQ.
We run the same scenarios
vs AK
1) We hit, they hit. When they have AK, we have 4 outs to hit to a CHOP (this obv changes if we have AKs, but I'm going to ignore that for now). This will happen about 24% of the time. When this happens we get back half of 195bb, or 97.5bb for a profit of 1.5bb 24% of the time. 0.36bb profit. Not too hot but at least its profit.
2) We both miss. We fold to his cbet, he wins a pot we could've chopped. -7.5bb* 76% = -5.7bb when we miss.
So when he has AK we have a net loss of 5.34bb. Not too good. Especially considering when we shove and he folds, we win 17bb and when he calls we have a marginal win of 1.5bb
Pocket pairs.
1) We hit, they hit. We lose our stack. We will hit about 36% of the time. To do that, we need to use one of the possible cards on the flop. So they have two cards to spike a set with two outs. It will happen 8% of the time WE hit.
So 0.36*0.08 = 2.88% One in 40 times this will happen. We can expect to lose our entire stack (after all we called to get AI on a flop we hit)
This means we lose 96bb. 96*0.0288 = -2.76bb
2) We hit, they miss. We c/r and while they may stack off QQ on a king high flop, I'm just going to assume, they don't to keep the math simpler. We will win 30bb. This will happen 36% of the time, except for the times they have a set. So 0.36-0.0288 = .3312 33.12% of the time we win 30bb.
30*0.3312 = 9.936bb.
3) You miss. You lose 8.5bb 64% of the time. 8.5*0.64= -5.44bb
When he has a pocket pair under KK you win 1.736bb.
Slightly better than pushing.
There are 9 combos of AK, and 30 combos of 77 – QQ.
The net is
(0.23 * -5.34bb) + ( 0.769 * 1.736bb) = 0.10678bb
Practically 0, much like shoving.
Group 3 - Suited Connectors,
1) You hit, they hit better. It won't happen too often. And sometimes you'll out draw them. The equity calculation for it isn't too different from the pocket pair issue, so I'll just assume it's the same. Sorry my math skills just aren't up to figure this out right now. We can drop this a little bit since when they flop two pair we can draw out much easier.
-2.5bb.
2) We hit, they miss (something they won't call a check raise with. say less than top pair) We win 30bb. This will happen about 36% (less the chance of them flopping better which is covered above) of the time so same the same calculations as pocket pairs here. 9.936bb.
3) This is the same as pocket pairs too. -5.44bb
When he has a suited connector you win 1.99 bb.
(The difference in EV between group 2 and 3 is because AK is not in this catagory)
4)AA and KK.
I'm going to deal with them seperately.
Cowboys (KK)
3 scenarios.
1) You spike the 4th King. This obviously the worst case scenario for you since you will lose your entire stack. If you flop Aces and Kings you will catch on him 8% of the time, but don't count on it. The case king will come out 6% of the time. When it does you lose your stack, so that’s -96bb for you. -96bb * 0.06 = -5.76bb
2) The Ace magnets screw him over again.
You will flop one of your 3 outs about 18% of the time. When you do, you can probably expect him to cbet and you can snap it; 30bb for you. 30*0.18 = 5.4bb
(On a related note, checking behind kings when an ace hits is a good idea. I've read some very interesting theory on that.)
3) You miss. You lose 8.5bb 76% of the time. 8.5*0.76 = -6.46bb
Against kings you have an expected loss of -6.82bb
This is 53bb less than we can expect to lose if we shove.
Pocket Rockets (AA)
1) You hit, you're screwed. When he has AA, you will hit one of your 4 cards and lose your entire stack 24% of the time. -96 * 0.24 = -23.04bb
2) Thank god, you miss. You only lose 8.5bb 76% of the time.
8.5*0.76 = -6.46bb
We lose 29.5bb vs AA.
If we shove, we lose 80.4bb
against the group we have an expected loss of 43.61bb
In TOTAL.
If we call
Group 1) Dominated hands = 12.9 bb
Group 2) AK = -5.34 bb PP < KK = 1.73 bb
Net = 0.10 bb
Group 3) Suited Connectors
76s = 1.99 bb.
Group 4) AA and KK = -43.61bb
If we shove
Group 1) Dominated hands. They almost always fold, and it’s better for us if they call, so we will assume they won’t. 17bb.
Group 2) AK = 1.5bb if he always calls. He won’t ALWAYS call. PP = 0.01 bb if he folds exactly 53% of the time. In reality, fold more than that.
Group 3) Suited Connectors. Better for us if he calls so we’ll assume he won’t. 17bb.
Group 4) AA and KK. We get killed here and have an expect net loss of -58bb.
Compare the groups and think for a bit. Remember than AA and KK is less likely since we have an Ace and a King. In fact the odds of either is cut in half.
OK! So now that is out of the way.
Now the real question at hand, is what is he ACTUALLY 3betting us with. Just what is his range?
If it’s just TT+, and AJ+, there are 18 combinations of TT-QQ, 6 Combinations of AA-KK, and 24 combinations of AJ and AQ, and 9 combinations of AK. There are 57 combinations total.This means…AJ and AQ = 42.1% of the time. AK = 15.7% of the time.TT-QQ = 31.5% of the time.AA-KK = 10.5% of the time.
If we call we win ((0.421*12.9)+(0.157*-5.34)+(0.31*1.73)+(0.105*-43.61) = 0.54977bb
A net gain of 0.55bb
Now for cramming.
To figure the equity of shoving, we should figure how often pocket pairs fold here. I’d say TT folds about 90% of the time, JJ folds 60% of the time and QQ folds 10% of the time. Is that a fair assumption? Together that means they fold 53.3% of the time. How convenient. Now honestly ask yourself if you’re facing this kind of action, how often would you actually call with these hands.
But for now we’ll assume it’s a break even proposition. When it’s up against AK, how often does he fold that? Let’s say he folds 25% of the time. So 17*0.25 + 1.5*0.75= 5.375bb
So onto our calculation. We’ll assume he always folds hands we dominate because that’s our worst case scenario for those hands.If we shove, we win ((0.421*17)+(0.157*5.375)+(0.31*0)+(0.105*-58) = 1.910875
A net gain of 1.91bb.
This shows that for the exact same range, 4 bet shoving with 100bb is over 3x as profitable as calling.The question shouldn’t be do I call or 4 bet, the question is should I 4 bet or shove?However that’s a question for another day.
The tighter his range is the more you should consider folding, BUT not calling. There is no hand range that calling with AK is superior to raising or folding it assuming he is a decent player.
However, given his postflop play, it is possible that calling is superior. However it’s rare to find opponents that stack off with less than top pair, and other leaks that make calling AK superior, such as never cbetting when they miss.
This whole article was done under the assumption you have 100bb stacks (common online) and you are out of position. As stack sizes increase, shoving AK because less profitable. The opposite is also true. This is why folding AK in tournaments preflop to a 3bet that is often a huge mistake.
As a note, I realize in this post I've been a little inconsistent with bet sizes, I said 3.5bb as original raise, yet I mentioned losing 96bb not 96.5bb. Sorry for this, but I'm not up to fixing it for now. The difference is negligible. All of my calculations were based off AKo and AKs combined btw.
See you across the felt.
Bryce
