Playing AK in Limit: A Logical Framework to start from...

[DonkeyKong]

I have been trying to analyze all the math of various starting hands. While this is a useful exercise to understand the game, I clearly feel like I am re-inventing the wheel here.

So can someone who has been thinking along these lines tell me if I am on the right track and critique this mode of thinking. I don't want to be nitpicked with the semantics of various flops -- I just want create a logical place to start from when thinking about AK (and this applies quite closely to AQ as well) especially when you flop nothing.

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So you get AK in early/middle/late position and RAISE…
On average, at low stakes, a few others will call your raise, often including the BB since it only costs him ½ a bet.

Lets make a few assumptions…

1) Others will call with top 11% of hands (this equates to Sklansky Groups 1-4)

Note that 11% vs a raise is FAR looser than Sklansky suggests vs a raise (assuming an early or MP raise). They actually suggest playing here with the top 3% of hands… But since this is small-stakes and most players do not have such tight pre-flop standards, this is my assumption for now (please chime in with a critique of this if you think it is WAY off).

Assumption 2) When others do hold a pair pre-flop, they will only play on with 88 or better vs a raise… (of course they will re-raise with big pairs and call any pair from the BB)

Note that they may indeed call with <88 but given where we are going with this, we will be assuming that your opponent will call you down and that most players will not call down with <88… (They might, they might not.. its debatable but we need to make some assumptions here and the exactness here isn’t crucial to the framework…)

Ok,

When you hold AK, you will flop a pair about 32% of the time (thus not pairing 68% of the time)… and will hit a pair on the turn about 12-13% of the time (6 outs with 47 unseen cards) and so 'not pairing' on the turn 87% of the time…

So if we assume playing vs 1 other player and they called with a Sklansky Group 1-4 hand, it works out that they will be holding unpaired cards about 71% of the time and they will be holding a pair 29% of the time (88-AA / top 11%)

If we combine this math,
% time other starts without a pair and also doesn’t pair on the flop is approximately:
.71 x .68 = ~48%

So roughly speaking, for every player that is in the pot, even if you don’t improve your AK on the flop, you can STILL expect to be ahead in the hand as follows:
Vs 1: 48%
Vs 2: 23%
Vs 3: 11%
Vs 4: 5%
Vs 5: 3%

But you will also flop an A or K another 32% of the time…

So vs 1, you will be ahead a dominant majority of the times whether you pair (32%)... or don't pair as you will still be ahead another 48% of time.

Either way, you should clearly continue to bet after the flop vs 1 other player...

So rather than continue with my complete rough draft of my spreadsheet/analysis, I stop for comments...

thx

DK

[Octopus]

So your question is: Would you ever not bet on the flop heads up out of position with AKo as the pre-flop raiser? Extreme reads aside, I'll go with 'almost never'.

[DonkeyKong]

my real question... why is AK/AQ so +EV for everyone but me?

lol

[Octopus]

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my real question... why is AK/AQ so +EV for everyone but me?

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Sample size.

[Octopus]

Ed Miller:

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Oh, and by the way. NO ONE plays ace-king, suited or offsuit, poorly enough to turn it into a net long-term money loser. No one. The hand is too good.

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