Diminishing Value of AK

lasvegaspokerchick

lasvegaspokerchick

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Last night Happy Donkey got into an interesting confrontation and I wanted to get some feedback on the concept of the diminishing value of AK in a multi-way pot. The action went down as follows:

Happy Donkey came in from early position for a raise ($12), a middle position player pushed for about $45 (he was short stacked) and the button over pushed for a little over $100 (also short stacked.) Now this table had been playing very weak tight so we can assume that both players have some sort of legitimate hand. Happy Donkey over called (he more than had them both covered) with AK off.

Later we discussed the hand and I disagreed with his call. I argued that when you have more than one player moving all in (if you believe that they are pushing with legitimate hands) the value of your AK diminishes with each additional caller. Of course, you could be dominated by AA or KK, but that wasn't my point in this instance. Even if you aren't dominated, I have read that the more people enter a raised pot before you, the worse AK becomes because of the likelihood that others hold aces and kings in their hands.

Anyway, Happy Donkey ended up facing JJ and AQ and lost to JJ. But beyond that, I am hoping to get some insight into what everyone thinks about that concept of AK being less valuable in a multi-way situation. I will use your insights on my blog entry today, so lay it on me.
 
Emperor IX

Emperor IX

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Well AK loses it's value with additional caller because it's NOT a made hand. THe more hands involved in a pot, the higher the likelihood that someone is going to his two pair, or trips, or a straight, etc. I don't have Pokerstove, but if you were to enter AK into a pot with any hand it isn't dominating, each additional hand is going to lower AK's equity.

That's why AA wins small pots and loses big ones. The more opponents you're facing, the better the chances of someone getting more than just a pair (which with AK you aren't even gtd one)
 
P

phatjose

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It's not just AK that becomes devalued, it's every hand. It's not even the prospects of people holding AA or KK, but the fact that you have to dodge that many more cards from the other players. I was in almost the exact same position a couple weeks ago and easily laid down my AKs to a raise/reraise shove.
 
TubaMark316

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Well, he is a Happy Donkey...do you think he cares?

He looks at face cards and goes "NO ONE CAN BEAT ME!!!"

But I agree with you...A-K's value does diminish once more then one person goes all in...I mean, you're gonna need ALOT of help to knock someone out...

Like you said above...he got beat by JJ...well, he should learn when someone else goes all in as well, fold the A-K and wait another round and try to knock someone else out...

Damn donks I tell ya...
 
zachvac

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This is a concept many people don't seem to understand. Of course it's good to isolate with a hand like AA because I want to be able to put opponents on a range of hands. But I would gladly go all-in PF with 9 other players with AA. Someone said the equity of hands goes down with each person enterring the pot. That's false. The equity of AA goes up as each additional player enters the pot.

Let's pretend everyone has 100 chips for simplicity.

From pokerstove: (I'll round)

AA vs. single random hand, 85%
pot equity = 200*.85 = 170

AA in 4-way pot, 64%
pot equity = 400*.64 = 256

AA in 9-way pot, 33.5%
pot equity = 900*.335 = 301.5

Don't know about you, but I'll take the 301.5 chips over the 170 chips on average any day.

Now let's test it for AKo
heads up, 65.5%
pot equity = 200*.655 = 131

4-way pot, 38%
pot equity = 400*.38 = 152

9-way pot, 18%
pot equity = 900*.18 = 162

So especially since this is a ring game, you would rather have AKo vs. a random hand 9-way than 2-way. Of course as mentioned this is a random hand. The hands that would push like that are not random hands. I'm going to be a little bit liberal on the hands they may hold, say TT+, AJs+, KQs, AQo+.

heads up: 51.64%
pot equity = 200*.5164 = 103.28

3-way: 30.814%
pot equity = 300*.30814 = 92.422

4-way: 18%
pot equity = 400*.18 = 72

So yes, if you have AKo and think the others are pushing with legitimate hand, not only does your equity decrease, but your ev becomes negative with a straight up PF all-in. Pot odds may dictate a call anyway, let's look at the example given:

I was thinking of using pokerstove, but it won't give you how often one player will beat another heads up given that the third player has one of the predefined "legit" hands as well. If we consider the side pot ignoring the third hand (meaning if the results come out close we should fold, because we are boosting the value of our hand with every A or K the other person holds.

He has to pay $88 to get in on the pot. He wins the side pot 51.64% of the time, $110 in that pot ($55 from him and bigger stack of the 2).

110*.5164 = 56.804

Main pot is $135 ($45*3), he wins that 30.814% of the time

135*.30814 = 41.5989

Total win = 56.804 + 41.5989 = ~98.4.

He's paying $88 to win an average of $98.40. Good play based on that criteria of hands, not adjusting to the lesser odds of winning the heads up.
 
pedroman7

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Given the hands he was getting the right odds to call, but after the 3RD raise you have to really worry about AA or KK so I say fold. Maybe if you read both players as total maniacs you could call but I say fold. But I think the value of the gos down because of the posiblity of being up agaist AAor KK not the number of players. Maybe if more play come in but just two not too bad.
 
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lasvegaspokerchick

lasvegaspokerchick

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Thanks all for the input and Zach THANKS MUCH for that detailed analysis. That is awesome and just the sort of data I was looking for. I am going to distill that down and get it on the blog later today. Awesome!
 
OzExorcist

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It's not just AK that becomes devalued, it's every hand. It's not even the prospects of people holding AA or KK, but the fact that you have to dodge that many more cards from the other players.

I'd just be re-stating ^ this if I said anything much more.

I've been in similar situations in tournaments where I've laid AK down in a multi-way all-in pot, but that was based on tournament survival rather than cash game profit. The AK definitely decreased in value with the third player in the pot, but I don't think the call was all that bad.
 
Bombjack

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Normally I'd probably go with AKo but it really depends how deep you are. Versus two lower pairs you have 36% equity so should definitely call. If you're against JJ and AQo this goes down to 33%, or less if the AQ is suited so calling has no value. If someone's pushing over the top of an all-in they'll usually be stronger than AQ so your equity in the side-pot will generally be less than 50%, making it a fold. If as zachvac says above (great post btw) your equity vs (TT+, AJs+, KQs, AQo+) 3-way is only 30.8% then it's a clear fold.

Having said that, it performs pretty well multi-way so long as no-one has Aces, so it's a good hand to shove with in tournaments for fold equity. Also, in tournaments people tend to be more desperate and have lower standards for pushing. In a cash game versus a raise and re-raise I wouldn't worry too much about passing it pre-flop.

There's also the consideration that you're rarely going to win a big pot with AK because the best you can realistically hope for is to flop top pair, top kicker. You might win something if an Ace flops and someone else has AQ or AJ, but you can't make a set or an overpair, where it's more likely someone will put money in with a second best hand. If you make your hand (flop an Ace or King), you get less action.
 
aliengenius

aliengenius

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In situations like this you are often facing another big ace and a pair. While you have the ace dominated, he is also taking one of your cards needed to outdraw the pair. I didn't check the math, but if your equity is 30.8% with three in the pot, then obvioulsy it's a fold (>33.33%).

Also, you don't get to "add" your call into the pot, and then make your calculations. The main pot is $102 ($12 + $45 + $45), and the side pot is $55 ($100 shove - $45 that went in the main pot), not $135 and $110 as given in the above analysis.
 
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