4betting AK should be default

This is in response to another thread. I spent a while doing the math and saved it in a word file. I've shown it to other people I discuss poker with but it hasn't been posted elsewhere yet.

JuniorJunior mentioned he crammed AK, and I thought it was standard. That doesn't seem to be the consensus of the people who posted though. You all should strongly consider reading this.
Although warning, it is a bit tl;dr. but it's good material on preflop play.



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 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 lets multiple. 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.

This is going to hurt my head.
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.

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 andlose 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+, like stated.
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 range that calling with AK is superior to raising or folding it. 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 isn’t all in is often a huge mistake.

The last thing is to realize that I made conservative estimates for pushing. In all likelyhood it's even more profitable than I noted.

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.

I wish I could give an in depth reply, but wow tl;dr. You clearly put in the research though.

great post...lots of good info in there! Now you just have to add how to have the balls to shove AK every time

Wow. That post was craziness. I'm not one to usually give advice, but this post made me realize how inexperienced internet players are to the game of real world poker. I agree that generally ak should be 4 bet, but not for the same reasons mentioned. One would 4 bet mainly because of fold equity and deception. You must remember that poker is a game of people. If people acted like the bots you described, then, your strategy would certainly be optimal. However, people act randomly and even irrationally at times. To say that someone would fold tt 60% of the time to a 4 bet would be an unfounded estimation based on incomplete evidence. Whether the situation in question is a cash game or tournament also affects the outcome. In a $100 nl game this is probably not such a bad idea. In a bigger game, you don't want to just 4 bet or shove without good reason. In a tournament, one misstep with ak and you're out. The true strength of ak is using its value combined with putting pressure on your opponents. The only hand ak is a huge dog to is aa. The only reason you wouldn't really want to shove preflop is because most people like to go in with aa or kk. If you are up against someone who just won't fold, 4 betting would just be a waste of money. You won't hit the flop enough to turn a profit. You might be thinking why not just shove when you do hit to maximize your profits. Many people take a lot of flops because of situations like these and just because they seem loose preflop, that doesn't mean they're going to double you up on the flop. When you play tougher opposition, you're usually not even going to get the opportunity to 4 bet because they won't raise you until they take a flop. But this is a conversation for a different thread.

Eh I registered just to respond to this post and then now find myself having all that much to say, sorry new to forums here but long time lurker to the main site.

OP's math, analysis and advice is solid considering for the 100NL games online.
I agree with diz though. In tournaments a 4 bet AK shove will obviously be a bad play in many situations. OP was not referring to tournaments though, was it? specific reference was made to playing 100NL

Originally Posted by diz

Wow. That post was craziness. I'm not one to usually give advice, but this post made me realize how inexperienced internet players are to the game of real world poker. I agree that generally ak should be 4 bet, but not for the same reasons mentioned. One would 4 bet mainly because of fold equity and deception. You must remember that poker is a game of people. If people acted like the bots you described, then, your strategy would certainly be optimal. However, people act randomly and even irrationally at times. To say that someone would fold tt 60% of the time to a 4 bet would be an unfounded estimation based on incomplete evidence. Whether the situation in question is a cash game or tournament also affects the outcome. In a $100 nl game this is probably not such a bad idea. In a bigger game, you don't want to just 4 bet or shove without good reason. In a tournament, one misstep with ak and you're out. The true strength of ak is using its value combined with putting pressure on your opponents. The only hand ak is a huge dog to is aa. The only reason you wouldn't really want to shove preflop is because most people like to go in with aa or kk. If you are up against someone who just won't fold, 4 betting would just be a waste of money. You won't hit the flop enough to turn a profit. You might be thinking why not just shove when you do hit to maximize your profits. Many people take a lot of flops because of situations like these and just because they seem loose preflop, that doesn't mean they're going to double you up on the flop. When you play tougher opposition, you're usually not even going to get the opportunity to 4 bet because they won't raise you until they take a flop. But this is a conversation for a different thread.

Obv you have to adjust to your opponents. But finding opponent's who won't fold to a 4bet have extremely exploitable leaks.

Frankly, I find your logic terrible. I'll address each thing seperately.

"I agree that generally ak should be 4 bet, but not for the same reasons mentioned. One would 4 bet mainly because of fold equity and deception.
You must remember that poker is a game of people. If people acted like the bots you described, then, your strategy would certainly be optimal. However, people act randomly and even irrationally at times. To say that someone would fold tt 60% of the time to a 4 bet would be an unfounded estimation based on incomplete evidence."

4betting AK for deception and FE. This is obviously true. And it's clearly shown in my post. Nearly ALL the value from AK comes from folding out hands with equity against you. However this only works because you also 4bet hands that they could not profitably call against. Say you 4bet QQ-AA, and AK.

If they have JJ, they should be folding vs this range. They are losing money otherwise. The same is true with QQ and AK.
However, you are gaining when you have AK and 4betting because you are making a hand that is actually a small favorite over you fold.

When I said you can expect that, that is based on my estimation from playing poker. Different opponents will react differently. I didn't say you should 4bet AK EVERYTIME. I said it should be default. You need a reason NOT to 4bet AK, than a reason to 4bet it.

" Whether the situation in question is a cash game or tournament also affects the outcome. In a $100 nl game this is probably not such a bad idea. In a tournament, one misstep with ak and you're out."

My post specfically mentioned this is a cash game and hence the rake calculations. Regardless quite often you should be 4betting AK in tournaments. Many players will be willing to 3bet you with worse hands like AQ, AJs, and even attempt to resteal with marginal holdings like J9s, predicting and often correctly, that you will fold most of your range. But rather than calling and giving them a chance to out draw you, you can push and they will often fold. Coinflipping is a part of tournaments, and just calling with AK often gives your opponents a huge edge in low and medium stack scenarios. The fact is you can't just let go of strong holdings because someone 3bet you even in tournaments. It doesn't matter if your tournament is over if you lose a coinflip with AK, letting someone run you over guarantees it.

"The true strength of ak is using its value combined with putting pressure on your opponents. The only hand ak is a huge dog to is aa. The only reason you wouldn't really want to shove preflop is because most people like to go in with aa or kk."

This is exacltly why you 4bet shove. Sometimes you have a better hand, sometimes they flip, but they don't know which.


"In a bigger game, you don't want to just 4 bet or shove without good reason. If you are up against someone who just won't fold, 4 betting would just be a waste of money. You won't hit the flop enough to turn a profit."

This makes me laugh. Sorry, but it seems to me you're the inexperienced one. Obviously you don't want to 4bet without a good reason. Your good reason, is you hold one of the top 4 holdings in the game, and you have good equity even vs a 3betting range. Your reason for 4betting includes several factors.
1. You have the possibility of folding out a hand that could profitably call if they knew your cards.
2. You regain iniative, and therefore put pressure on your opponent.
3. It makes your hand range harder to read.
4. It doesn't allow your opponent to draw out on your hand or catch a good flop without making them pay more. It also makes your play easier, since you don't have to see if you catch and then play. More often than not, you won't connect the flop.

Obviously if they won't fold TT, 4betting AK is wrong. On the other hand, how can you be SO certain of that? If they don't fold TT, they get KILLED when you have KK. So instead of not 4betting AK, why don't you shove it, so they think they are justified in calling with TT and lose all their money when you have AA. Also I specifically mentioned we had 100bb stacks and that you 4bet SHOVED preflop, so their is no postflop play.

"You might be thinking why not just shove when you do hit to maximize your profits."

Shoving to "maximize your profits when you hit" is just stupidity. I could shove 72o preflop to "maximize my profits when I hit", but that doesn't mean it's profitable.

"Many people take a lot of flops because of situations like these and just because they seem loose preflop, that doesn't mean they're going to double you up on the flop."

Sorry, sounds like to me you just described terrible players. Even if you didn't 4bet shove preflop, and only made it say 35bb, you just made them commit 1/3 of their stack preflop with a marginal holding, not knowing where they are. More often than not they will not catch a good flop, and you will continuation bet all in. They will miss often enough to instantly make it a profitable play. If they call with only pockets they still get crushed, as they have to fold the 1/4 time and A or K falls, and they get stacked everytime you have AA and it doesn't.

But they don't even have that option, because they can't take a flop without paying their entire stack to see it.

"When you play tougher opposition, you're usually not even going to get the opportunity to 4 bet because they won't raise you until they take a flop."

This was the best. If you're opponent's aren't 3betting you, they aren't very tough. They are letting you run them over preflop. So they won't raise me till they see a flop. OK.

They raise their marginal holding, and I 3bet the flop. Now what?
They raise I call, now what?

It's not like I'm just gonna fold my hand because they raised me. That's called being exploitable and it's rather stupid to assume they always hit when you get raised.

Tough players 3bet preflop for a variety of reasons, not just for value. But you talk like they are only 3betting super premiums. Ok, great. Then they are nits and easily crushable.

Sorry, but it sounds like you play low limit live games to me. 5/10 live isn't a tough game.

5/10 online is a tough game.

Feel free to respond, I'm definitely open to discussing this further.

A 5/10 nl game with 100 bb. Some guy in the front raises to $50. You raise him to $200 from the back. He reraises you to $500. Are you just going to shove the rest of your money in? He probably isn't going to fold at this point and he probably is at least a slight favorite. In real life, the dream situation of pair over pair doesn't occur very often especially with big pairs. Most people realize this and you're not going to get many of them to fold aa-1010 preflop. The situation you described when you bet the flop, get raised, and then call. You said "now what." Thats exactly the point. Are you also going to call the raise with just air? Are you going to move in with a blank flop too? You must be fearless if you're going to make moves with $700 behind and nothing but ace high when your opponent shows strength.

Originally Posted by diz

A 5/10 nl game with 100 bb. Some guy in the front raises to $50. You raise him to $200 from the back. He reraises you to $500. Are you just going to shove the rest of your money in? He probably isn't going to fold at this point and he probably is at least a slight favorite. In real life, the dream situation of pair over pair doesn't occur very often especially with big pairs. Most people realize this and you're not going to get many of them to fold aa-1010 preflop. The situation you described when you bet the flop, get raised, and then call. You said "now what." Thats exactly the point. Are you also going to call the raise with just air? Are you going to move in with a blank flop too? You must be fearless if you're going to make moves with $700 behind and nothing but ace high when your opponent shows strength.

You left out a lot of information, position, table image, full ring vs 6max, live vs online. Either way your example is when you 3bet and they 4bet. 5 betting is different because at this point their hand range is far more narrow. 5 Betting was not discussed.

Regardless, let's say they call preflop, and then raise your cbet. Ok so they are showing strength, in the face of your strength? Either they are bluffing a decent % of hte time, meaning you can bluff back, or they are only riasing with a decent hand which makes them easy to hand read. If you call their raise, what does that mean? Are you playing back with AK or do you have QQ? They don't know your hand either.

And they flat call you preflop. An Ace falls, you fold most of your range. Yet quite often they actually miss the flop. So now you play a guessing game, and you have to be very accurate at pegging their tendecies to figure them out. If they can peg you just as well, you're sunk, because you are playing a more passive game than they are.

good post, need to read this one a couple of times