Here and elsewhere, I have seen it said numerous times that you don't want to play AA against multiple opponents. Does anyone have any math on that? I have looked and haven't found anything yet.

Generally, it looks like AA has 77% equity vs. 1 (assuming they are playing a PP) and ~50-54% v. 3 opponents (assuming all 3 are playing PPs and SCs, the worst case scenario). So with that said, might it be true that a very large raise which either takes down blinds + limps or gets one caller (and puts you on a very small range) might be lower EV than if you make a decent sized raise and get three callers where you've got 50% equity in a larger pot?

That's not a statement . . . it's just a question. I'm not advocating limping AA or anything and I definitely see the rationale for pushing a larger raise with KK. I just wonder if there are concrete numbers out there to back up the common wisdom. I'd really love to see some math on this if anyone has a reference.

Mike Caro posted graphs of this years ago, and obv there may be something more up to date. AA over a large sample is most profitable when played with up to 2 other random hands. With this said, I opt to play my aces straightforward 99% of the time to isolate and force other players to make a mistake. The sad reality is so many people completely disregard you of having AA when you rr because they would try to get sneaky and suck you in if they had it.

I feel it is better to play against one opponent because while you have 50% equity vs multiple, you can get too attatched and may feel required to call down at least 2 streets or go all the way when you will only win 50% of the time. many times you lose bigger pots with AA than you win, so 50% equity is not too favorable.

The micro forum did some research and unless there are 8 players in the hand with you with a reasonable range, you always have + equity each time a player calls. If you have AA, you should be doing everything possible to get people to call you pf.

Lots of people confuse equity with winning %. It is far better to have a 30% chance to win $1,000,000 than a 100% chance of winning $1.

yeah having a 8 way pot with AA is only +ev IF you get it all in pre OR you have the sickest soulread on the planet against EVERY single person in the hand.... so pretty much -ev and i'll take it against 1-2 all day every day

against 1-2 opponents, they might think you just cbet all flops and call with marginal holdings
against multiple opponents, they will realize your hand is at around tptk or better when you cbet, which means most of the time they will play their hand in a way that will extract the most from you and not the other way around

of course this depends on alot of the players in your casinos
if there's tons of fish then ignore what i said
but in my area, fish are rare, weaker players are common but most common are postflop nits/preflop station

with 5-6 ppl in pot when you have aa, they will almost never give you action postflop unless they have you beat or have crazy combo draws
or unless they are super fish/weaker players

i usually play with extreme caution against half the table with aa
with 1-2 other players, it's easy to go to valuetown

You are mistaking EV. All EV says is that a certain amount of time you should win the hand not that you are going to. If you are heads up (~80% equity) you obviously have a better chance to win the hand compared to if you are 9 handed (~30%). But the thing is when you are 9 handed you will win a bigger pot which makes up for the equity you lose. Long term thinking says you should want 9 players in the pot with you... Short term thinkers want reduced variance and an easier decision. If you aren't begging for callers when you raise AA then you might want to rethink your game.

If you raise to 5BB PF with AA, and get called by 4 players, your equity against 4 random hands is ~55%. So you have "made" ~11BB.

However, you haven't really made anything, all you've done is enter a siutation...

Now you have to play a pot of 25BB with 95BB behind, against 4 players. In this situation, unless you flop an ace, it will be very easy to over-value AA, and get stuck putting BB's into a pot where your equity might only be 10%, and therefore immensely -EV.

For these reasons, I'd rather play AA no more than 3-handed. When 3-handed or less, ranges are more easy to determine. However, against 4+ players, you will frequently need more than one pair to ship the pot. And more often than not, it will be close to impossible to determine how far behind/ahead you are.

Seeing a flop 8+ handed with AA, I don't see how a player can continue unless they flop an ace.

Of course, it would be great to go AI PF with AA against 4+ players.

Perhaps the better solution is to stop over-valuing AA post flop. However in this situation on a board of 952, it is more likely 9x, TT+ is going to stick it in crushed by AA with an SPR of under 4.

There is a BIG difference between a 9 handed game and:

1) Everyone has $100 and everyone is all in preflop and you have AA.

2) Everyone has $1000 and everyone is in preflop for $10 and you have AA.

In the first example if you win more than 20% (11% but I will round way up) then you will win money over 100 or 500 hands.

In the second example you may tend to lose money over 100 or 500 hands by over valuing AA or folding winning hands.

A tip of the hat to CMAR.

The common them in here is, "Oh hai I haz AA I cant fold" and "I only want to see it 2-3 way to the flop because its easier to play."


I think OP asked for numbers, and the numbers say that the most +EV play with AA at a full ring table is to have each and everyone one of the players in the pot with you pre flop. Would it be easier to play? Absolutely not. Is it more profitable though? Absolutely. I will look up a most I made a while back and repost what I posted there.

edit: I guess the time machine dont go back that far. Not sure if I'll be able to find it...I'll try the hard way.

Only if everyone is all in preflop, otherwise I disagree.

Do you agree with my example two I gave?

Your example is from a ten year old book by Sklansky or someone similar to him. I don't think Harrington would advocate this (playing against everyone in the game).

From a profit maximizing perspective:


100 Hands- you have AA and are against random hands.

Ex 1: You have AA against 1 opponent with a random hand ran 100 times at $100 per hand.

Against 1 opponent we are 85% to win and 15% to lose. That is $8,500 we will win and $1,500 we will lose for a net profit of $7,000.

Ex 2: You have AA against 9 opponents with a random hand ran 100 times at $100 per hand.

Against 9 opponents we are 30% to win and 70% to lose. We will win $27,000and lose $7,000 for a net profit of $20,000.

If you believe in math the proof is in the pudding. However, if you dont agree with the above then you should probably never post anything math related again.

Also, if the above ever happened (you had 9 people call your raise) I can almost guarantee more than half of the hands are going to be random ATC, although it probably never will happen, but thats not the point. The point is mathematically speaking the most profitable sitaution is to get more callers than less (noticed I didnt say easiest).

Actually, the info is from a 2009 book Poker Winners are Different by Schoonmaker.

In the second example you give a great big deep stack (I am assuming you used 1/2 according to raise size)... I dont even think thats relevant because play changes and ranges become narrower. In fact I dont know how relevant getting 9 callers to a raise is. If we use average 1/2 stack sizes (~$120) then ranges are wider. All I am saying is that the more players in the pot, the less our EV will be but our profits will be bigger to compensate for the difference. Its long term, not short term this hand right now.

I was thinking I should have clarified my point by saying "know where you are" rather than "over-valuing".

But then I realized that I did clarify that point later in my post...
So I assume I would get trolled either way...

Really this is a trivial matter, and I came here to help OP.

Here is the simple solution...

Of course we would like to go AI PF with AA and have the entire table call. Players who don't agree or understand this lack a proper understanding of EV.

Very early on, players learn why they should raise PF with AA. Among other things, we raise for value and protection.

By raising and getting called PF with AA, where are entering a +EV situation. More accurately, this should be described as potential EV. Because by getting called with AA PF, you haven't actually won anything yet. Unless we play all three subsequent streets optimally and correctly, we lose value. And to play optimally, we need to be able to deduce our villains' ranges.

In order for us to win the most by realizing the potential EV created by the PF raise with AA, to extract value from our villains, and to extract the most value from the callers' range, we have to do four things:

1. Ship the Pot
2. Not stack off when behind.
3. Not lose value when ahead.
4. Select perfect bet-sizes.

In order to maximize value and minimize loses the optimal game plan is to design a scenario where we maximize the likelihood of achieving all four of the above objectives.

If we are selecting a PF bet size that will attract 7 callers, we will be stuck post flop, being unable to extract max value, because we can not say with confidence where we stand against 7 wide ranges.

On the other hand, if we select a larger bet-size that only attracts 2 callers, we can make an effective assessment of where our one-pair hand stands in relation to 2 PF calling ranges.

Keep in mind that if 7 players see a flop, the last caller PF can call with close to ATC. This is what I mean by "say with confidence where we stand against 7 wide ranges."

In any case, the matter is trivial...

1. If everyone goes AI PF, and you wake up with AA, then you should call.

2. More realistically, raise PF with aces for value and protection. Based on the style of the limpers, blinds, and players behind you, try to select the largest bet size that will entice two players to call. Sometime this will be 5BB. Sometimes this will be 20BB.

In typical 2+2 style, it was clear that OP was asking about the second issue above, not the first. But most posters took the time to ignore that and point out the obvious anyway.

Why would I want to raise AA pre flop for protection? I think the underlying issue here is that you feel entitled to win with AA or at the very least give it the very best possible chance to win that hand right then. It cracks me up when people get too much action with AA they say they cant play it anymore because of the action. When everyone folds to their raise they get mad because no one called. So I guess the magic number is 1 or 2? If we are betting for protection I guess we should be happy that everyone fold because nothings more safe than that?

We are interested in playing three streets of poker which is completely different than "running it".

Here is why...

By raising and getting called PF with AA, where are entering a +EV situation. More accurately, this should be described as potential EV. Because by getting called with AA PF, you haven't actually won anything yet. Unless we play all three subsequent streets optimally and correctly, we lose value. And to play optimally, we need to be able to deduce our villains' ranges.

In order for us to win the most by realizing the potential EV created by the PF raise with AA, to extract value from our villains, and to extract the most value from the callers' range, we have to do four things:

1. Ship the Pot
2. Not stack off when behind.
3. Not lose value when ahead.
4. Select perfect bet-sizes.

In order to maximize value and minimize loses the optimal game plan is to design a scenario where we maximize the likelihood of achieving all four of the above objectives.

If we are selecting a PF bet size that will attract 7 callers, we will be stuck post flop, being unable to extract max value, because we can not say with confidence where we stand against 7 wide ranges.

On the other hand, if we select a larger bet-size that only attracts 2 callers, we can make an effective assessment of where our one-pair hand stands in relation to 2 PF calling ranges.

Keep in mind that if 7 players see a flop, the last caller PF can call with close to ATC. This is what I mean by "say with confidence where we stand against 7 wide ranges."

No I don't. I clearly did not say that. You are using a straw-man argument. Here is what I said,

In order to maximize value and minimize loses the optimal game plan is to design a scenario where we maximize the likelihood of achieving all four of the above objectives.

This is also a straw-man argument. I did not say you should be happy that everyone folds to your PF raise.

What I am reading, and call it a straw man argument if you want, is that everyone is more comfortable playing AA HU or two handed.

I raise with AA OTB and get two callers. Check to me, I bet and I get c/r'd by a laggish player. Whats my play?

I raise with AA OTB and get 7 callers. Check to me, I bet and I get c/r'd by a laggish player. Whats my play?

The point of those questions is not to analyze a specific hand, but rather in both pots you can figure ranges and/or hands by the action that is presented to you. You can still come up with conclusions no matter how many people are in the pot.

And btw id rather be c/r'd by the second guy rather than the first. The second option is an easier choice while the first presents a harder decision and allows you to make worse decisions.

Well obviously we will call, raise, or folding depending on the exact board, history, behavior, ect.

But normally, this is an easy decision. Very simple range calculation, based on history, image, board texture, ect.

This is far more difficult. We have to worry about 5 players besides ourselves and the LAG. How often do we get into a pissing contest with the LAG only to have one of the other 5 players wake up slow playing a monster.

Or do we just fold because the LAG is "good" and is betting into 6 players, so he "must have it"? When in fact we might be WA of his draw?

I notice hero c-bet...Another interesting question (which demonstrates my point in my previous posts), on what boards can a c-bet be justified with AA facing 6 PF callers. Have you looked at the percent of the time AA will be ahead OTF against 6 callers for various flops?

Saying that is completely different that saying...

Your examples illustrate another point I was trying to make...

You are not guaranteed your PF equity because we play three streets of poker, we don't "run it".

In both of your examples you raised PF with AA. You made a +EV decision. By raising PF with AA, you created a pot where you where most likely to be ahead OTF. But now, here we are OTF and we have to play poker...

You are not guaranteed your PF equity because we play three streets of poker, we don't "run it".

So, I thought I would take a stab at comparing one scenario where we make a raise that invites callers and one where we make a bigger raise to isolate just one caller. In both cases, I assumed stacks of 100BB. Interested in comments on the numbers & assumptions . . .

Scenario 1: Raise 10BB and get 4 callers (pot ~ 50BB)
- Hero bets 30BB: 75% all V’s fold & Hero wins 40BB
- 25% one V raises all in [pot = 170]
- Assume Hero always calls and 20% of time we get a set
- V range: 5% bluff, 10% TPTK, 25% Two Pair, 50% Set, 10% FD/OESD [I’ll ignore made flushes/straights to keep this simple]
- Hero is 38.5% to win; -11.5EV
- 25% x -11.5BB = ~-4BB; 75% x 40BB = 30BB, overall expectation for Scenario 1 is 26BB


Scenario 2: Hero makes a “big hand” raise … let’s say 20BB
- Assume this gets 1 caller 50% and all folds 50%
- W/ 1 caller assume 80% win rate
- Wins avg 35BB (half you get a fold on the flop; half you also get a 30BB call on flop and V folds on turn)
- Losses avg 50BB (bet 30BB on flop, V goes all in , Hero folds)
- W/ 1 caller EV = 18BB
- W/ all folds, Hero wins avg 5BB
- Overall Scenario 2 expectation is 11.5BB

He asked for math. Not one mention of the bet size pre flop (lustys came in as I wrote this), as compared to the size of the pot on the flop? It has to be 3x or 4x or all in? wtf?

How bout this, I am going to assume everyone has 100 at the beginning of the hand, blinds are 1 and 2. We are under the gun, and thinking of a bet size with AA at a 10 handed table of uber calling stations... what is the math? I think that $6 is wrong, and I think $100 wrong. The point is, if we add the EV from every call (meaning the fraction of that call we win in the long run) together, there is a point where it does not matter if we sometimes end up in a bad spot. Sooooo, we move the bet size until our opposition has a lose lose decision, right? Lets use poker stove to do math!

So with these 'calling stations' Ill put a conservative range on them, assuming they call a lot of raises. (I am not removing the 3bet hands, but we could, and repeat this)22+,A2s+,KTs+,QJs,JTs,T9s,98s, 87s,76s,65s,54s,43s,32s,ATo+,KQo,QJo,JTo,T9o,98o
[this range is all pairs, all suited connecters, all suited aces, and a few other hands that sukers like]

If 6 other players (with this range) call, our equity is: 36%
-that means if we bet $10, we get 36% of 10x7, making $25 of value for the $10, but we have $90 behind in a bad situation.
-if bet 20 and get 6 callers, we have 36% of 20x7, that's $50 of value, for a $20 investment. Leaving $80 behind.
-betting 30, (still assuming 6 callers) is 36% of 30x7, making $75 of value with only $70 behind. So its not as good as all in yet, but it is starting to not matter. I'm stopping at 30 because I think to bet 40 utg is getting silly.

Now, same range, but 5 callers. (less words, more math) Equity=42.4%
-bet 10: 42% of 10x6 = $25.20 value for the wager of $10. $90 behind.
-bet 20: 42% of 20x6 = $50.40 value for the wager of $20. $80 behind.
-bet 30: 42% of 30x6 = $75.60 value for the wager of $30. $70 behind.

Same range, 4 callers. Equity=50%
-bet 10: 50% of 10x5 = $25 value for a wager of $10. $90 behind.
-bet 20: 50% of 20x5 = $50 value for a wager of $20. $80 behind.
-bet 30: 50% of 30x5 = $75 value for a wager of $30. $70 behind.

Same range, 3 callers. Equity=59%
-bet 10: 59% of 10x4 = $23.50 value for a $10 bet. $90 behind.
-bet 20: 59% of 20x4 = $47 value for a $20 bet. $80 behind.
-bet 30: 59% of 30x4 = $70.50 value for a $30 bet. $70 behind.

Same range, (realize it may change depending on the # of callers, but remember, these were ALL calling stations) 2 callers. Equity=69.9%
-bet 10: 70% of 10x3 = $21 value for a $10 bet. $90 behind.
-bet 20: 70% of 20x3 = $42 value for a $20 bet. $80 behind.
-bet 30: 70% of 30x3 = $63 value for a $30 bet. $70 behind.

Same range, 1 caller. Equity=83.2%
-bet 10: 83% of 10x2 = $16.60 value for your $10 wager. $90 behind.
-bet 20: 83% of 20x2 = $33.20 value for your $20 wager. $80 behind.
-bet 30: 83% of 30x2 = $49.80 value for your $30 wager. $70 behind.

I know there are a lot of assumptions in this example, but it is to make a point, that there is a 'more correct' amount to bet, based on certain considerations. And its not purely "of course you want them all to call", and its not "make sure to protect it!". Go for max EV. Really, what this means that if you bet more good things happen. Either you get a better situation post flop, or the suckers hand you their ass pre. Either way, bet more if you can. My favorite one from these charts is bet 30 and get called 4 ways, but maybe I am missing something.

anyway, there's some math for ya.