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Let's simplify the situation:

  • you have pocket aces (AA)
  • cash game
  • all players but one have folded (heads-up)
  • the remaining player goes all-in.
  • we are pre-flop

Is there a situation where folding makes sense? Specifically, would you fold based on how much you have to call?

If I am correct, 56, 67 and 78 are all roughly 23% against AA. So with AA you are, at least, 77% likely to win (pre-flop). Can you think of a situation where that is not enough to make the call?

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In light of the comments below I think that this question should be re-written to take bankroll issues into consideration as that seems to be what the OP is actually asking about. –  hmmmm Mar 7 '13 at 11:20
    
When SHIT happens ! –  user851 Mar 25 '13 at 11:49
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If you are considering folding AA preflop in a cash game, why are you playing in the first place? –  John Dibling Oct 19 '13 at 16:38
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10 Answers 10

up vote 9 down vote accepted

Theoretically, no. For every dollar you and your opponent add to the pot, you stand to win your dollar back plus some of his, regardless of his hand. However there are a few practical edge-cases worth considering.

Trusting the game

If this is your first time playing in a home game, there are a few ways this could be a mistake. The first is cheating; there is a small, generally negligent chance that the dealer and player you are in against are working together. He could have KK, and the dealer could base-deal a third King. Even without knowing that you won't get an ace as well and still win, this makes the odds of you winning very slim. The second is if you will get paid or robbed before you leave the game. Consider a situation where you've been winning all night in a deep game and now sit with 2000BBs. Some home games let players buy in for the largest stack on the table, and if this player is playing on credit, the home game could give you a long run-around for getting your money. The player who loses to you could also have friends in the area planning on taking this money back.

Your stack is your net worth

You shouldn't be buying in with a stack that you can't lose. If you have $1000 to your name, you shouldn't be playing 5-10. Though it's still possible to win up to this amount. Consider you have $10,000 in your bankroll, and decide to take a very aggressive shot at 5-10 with 1 buy-in. If you lose it, you will move back to 2-5. But then the shot goes very well, and you run your $1000 up to $8000 or so. Most of the time, you should stand up. But let's also pretend it's a very soft table; someone is buying in for $1000 and losing it every hand with no sign of stopping. There may be a situation here that warrants folding AA against a different player; the value in the game so great that you don't want to leave, but you also don't want to take a 20% shot of losing roughly half of your net worth.

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Great Cory, that last part is roughly what I was thinking. –  jeckyll2hide Feb 24 '13 at 17:53
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@gonvaled If that last part was what you were thinking about, then that's a different question and has nothing to do with AA. In that case you fold any hand where the $1000/hand player is not in, since you'll never have a better chance to win other than AA. And it's easy to come up with those type of hypotheticals- you always fold AA against the guy who you happen to know is an assasin who offs people that beat him with AA, etc. Though admittedly Cory's scenario is at least plausible. –  TTT Mar 25 '13 at 3:53
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In a cash game, never fold AA preflop. You're always ahead.

The only time this might be reasonable is in a tournament, and the reasons would relate directly to ICM calculations. Even then, the situations will be rare where folding AA is reasonable.

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No matter the amounts involved? Would you want to risk 1000 times the big blind? 10000 times? 1 million times? Is there a limit? You have not yet won: you are just very much ahead. –  jeckyll2hide Feb 23 '13 at 10:01
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@gonvaled If we're discussing limits regarding how much you're prepared to wager on a hand like this, then that's about bankroll/risk management and nothing to do with making correct decisions based on equity. Totally different question. –  Toby Booth Feb 23 '13 at 15:41
    
Well, my question states clearly: would you fold based on how much you have to call?, so I guess it is a bankroll/risk management question. –  jeckyll2hide Feb 23 '13 at 18:34
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@gonvaled So this isn't a question about equity then? If I have AA and I can afford to bet thousands of bb, or more, on this one hand then i'd do it in a heartbeat! 'Risk of Ruin' will factor into it, but that's relative to your individual preferences regarding going broke. –  Toby Booth Feb 23 '13 at 19:49
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The problem with this angle on the question is that not being willing to risk your stack should stop you from sitting in the game, not change the way you play it. If you aren't comfortable calling 1 million times the big blind, you shouldn't have 1 million times the big blind in front of you. –  Cory Kendall Feb 23 '13 at 21:15
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The only time you can consider folding AA preflop is:

  • You are on the bubble in a tournament, and
  • More than two players are all in, and one of them WILL bust, and
  • Your stack is such that you could bust out if you call, and
  • If you fold, you are guaranteed a place in the money.

ALL of these things MUST be true to make folding AA the right decision. There is no other time, in any game, when folding AA is correct.

Updated Answer

OK, it sounds like you want a "risk management" answer. The correct answer, then, is to risk a percentage of your complete bankroll that corresponds with the Kelly Criterion.

According to the Kelly Criterion, to achieve the maximum long-term gain, you should risk the percentage of your bankroll that corresponds to your edge. That means if you take the worst-case scenario, AA only being ahead about 75/25, you should risk 75% of your bankroll on the hand, but no more.

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Could you clarify how you came to the conclusion on percentage of BR to risk using Kelly. It seems off to me?! –  Toby Booth Mar 7 '13 at 11:49
    
(should get chk but) the math is off slightly: {p(b+1)-1}/b -> {.75(1+1)-1}/.75 = 2/3 –  Cincinnatus Oct 21 '13 at 23:11
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The general formula for the minimum pot size that is worth a call goes like this:

Break-even pot size = Probability of losing / probability of winning * price of call

In the worse case (you opponent is holding 65s), the numbers are:

Break-even pot size = 23 / 77 * aa = 0.3*aa

where aa is the amout of the all-in.

The pot is worth aa + blinds, which must be bigger than 0.3*aa. So in a cash game, the call will always be worth it (bankroll issues apart, but these are supposed to be taken care of when you sit at the table).

ref: PokerGym.com - Break-even pot size

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I just want to point out that the worst case for Aces is when the opponent has 87s, not 65s. That being said, the best case for opponent against AA, however, is 65s. –  TTT Mar 25 '13 at 3:45
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Never fold AA preflop in cash.

I would consider folding AA preflop if I were on or close to making the WSOP Final Table and one or more short-stacks moved all-in against another opponent, however, this would still depend on the types of players.

The reason I would consider folding is because not only is the payout structure top heavy at that point, but placing higher at the final table sometimes provides endorsement deals that provide even more value.

Aside from that, the bottom line is... what other hand are you waiting for the dealer to send you?

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A hand with 100% chances of winning. Like nuts flush. Obviously, not pre-flop, that's why I would consider folding AA (depending on the amounts involved). –  jeckyll2hide Mar 7 '13 at 9:06
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In cash games, I believe there is no such situation (heads'up, preflop).

When it comes to tournaments, sometimes it can make sense. For example:

  • there are 32 people left in the tournament
  • the top 30 people get payed
  • 3 players move all-in preflop and now it's your turn.

This is a rare occurrence but, if it happens, then it's not a mistake to fold pocket Aces. Your chance of winning is less than 50 % and, since the bubble is about to burst, it makes sense.

Another situation:

  • you're on the turn against 2 opponents
  • there are 4 diamonds on the board
  • one of your opponent pushes all-in and the other opponent calls
  • none of your 2 Aces is a diamond
  • there's no chance to make a full house on the river

Then you can pretty much be sure with a high probability that at least 1 of those players has a flush. In this case it's best to fold. Even if the 5th diamond comes on the river (giving you a flush as well), your opponent's flush will probably be better

Another situation:

  • it's super early in a tournament
  • the pot is getting big preflop
  • the flop comes and it has 2 Kings in it
  • one of your opponents bets big (70 - 80 % of the pot) and the other calls

Even if the first one is likely to bluff at it to take it down, the fact that the 2nd one called him pretty much means he has a set of Kings or even better, which means you're behind. So fold your Aces. You don't want to risk your entire tournament life on a coin flip, especially so early and especially when you're this deep (it's early, like I said, so you still have a lot of BBs in your stack).

There are probably more situations like this, but you have to keep in mind the following: even against a single opponent holding random hole cards, pocket Aces has a chance of about 85 % to win. If it's 3 opponents we're talking about, then it's more like 60 %.

Pocket Aces is the best. But it's not unbeatable.

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You never, ever (almost), fold AA in that situation no matter what.

If you're in the bubble you might be out but you're completely ahead, in tournaments the money is at the top not inside the bubble, and you're gonna need those extra chips if you want to get to the final table and win the tournament.

In cash games the only reason to fold wold be the posibility of losing money that you can't afford to lose, but if that's the case you shouldn't be playing at all in the first place.

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The short answer, in a cash game, in the situation you describe, is definitely never fold.

That you would even contemplate a fold in that spot simply proves that the stakes (at that movement at least) are too high for you to play correctly.

In other words - poker is all about finding opportunities in which you have a mathematical advantage, then using your chips to leverage and exploit that advantage.

If you're afraid to do that - risk your chips when you're a 75% favorite - you can't possibly be making correct decisions.

For what it's worth... if you're holding out for situations in which you're odds of winning are greater than 75%, then you're not going to have many chances to play.

For example - if you flop a set, and your opponent only has a flush or open-ended straight draw, you're still around a 75% favorite.

If you flop an Ace-high flush and your opponent has trips - you're only a 65% favorite.

Essentially you're saying that, unless you're sitting on the nuts, you'd fold to an all-in bet. That's clearly sub-optimal. Especially since your opponents will quickly sniff out your fear, and exploit it.

This isn't what you asked, but it's possible that you might fold AA in a tournament (under very specific circumstances.) But, even there - if you're knowingly folding the best hand, it's because you're willing to sacrifice any chance of winning in order to just finish in the money.

And, it sounds like you realize this, but if there are more than three people all-in pre-flop, it's possible that AA is less than 50% to win. (Although you're ALWAY the strong favorite).

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Here is a valid answer:

You have a seat at a mega big tournament. You've taken a week off work to play. You've paid for flight and accommodation for the week.

First day, first hand some joker is all in.

Im going to fold that AA just so my expensive week doesnt end in 1 minute.

There is no argument against this. Ive done it twice.

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You never fold AA preflop in a Cash Game. I rarely ever say never in poker, and almost any advice is dependent on the situation. This is an exception. Preflop in a cash game is one of the rare cases where saying never is OK, because you should never fold AA.

Some answers on this thread try to justify it using bankroll considerations, or speculating that your opponent might be cheating. If your opponent might be cheating, don't play that game. If you are playing outside your bankroll (don't do that), it is still incorrect to fold AA preflop in a cash game.

There are a very very small number of situations where you would fold AA preflop. I have heard elsewhere in this thread that you should consider folding AA close to the bubble. This is wrong. In a standard tournament, you want to win, not min cash. AA is a good hand and will help you get chips, don't be afraid to get it in preflop with the best hand, even if you are near the bubble.

The exception to this is a flat payout structure tournament. If you are in a satellite, or a double or nothing type tournament, where the top X all get paid the same amount, then it is OK to fold AA on the bubble to someone who has you covered. But only do this if you have enough chips to fold to the money, and there are several shorter stacks than you that are about to bust.

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