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Calling Pre-Flop All-In with KK or AK

Kevin Gong

March 22nd, 2007

In this analysis, I'll examine when you should call with KK or AK in Texas Hold'em when your opponent shows great strength by making the third raise all-in pre-flop. I'll only examine cash games, not tournaments, so it's strictly a math problem. Also keep in mind that your opponent is making the third raise, not just a second raise. So this narrows his possible range of hands down quite a bit. For example, while many players may re-raise with AK, they will be hesitant to put the third raise in with it.

First off, obviously the answer depends on two things -- what your estimation is of what your opponent holds, and what pot odds you are being offered for your call. We'll examine several different scenarios. We'll begin with the analysis for KK.

KK vs. AA

First, suppose your opponent accidentally flips over his cards and shows you AA. You fold, right? Not if you're getting the right pot odds. There are 4 cases:

  • Case 1: you have the same two suits. Then the AA is a 82.6% favorite, and you should only call if you are getting 4.76 : 1 pot odds or better.
  • Case 2: you share one suit. Then the AA is a 81.9% favorite, and you should only call if you are getting 4.54 : 1 pot odds or better.
  • Case 3: you share no suits. Then the AA is a 81.3% favorite, and you should only call if you are getting 4.33 : 1 pot odds or better.
  • Case 4: you don't know the suits. Then the AA is a 81.9% favorite, and you should only call if you are getting 4.54 : 1 pot odds or better.

KK vs. AA or KK

Let's say your opponent isn't so tight and will make the same play with KK. How much does that change your odds?

  • 6 hands: your opponent has AA and you are the underdog 81.9% of the time (81.946031) to be precise
  • 1 hand: your opponent has KK and you are even money (50%)

Your opponent's weighted winning chances are 77.4%, so you need 3.42 : 1 pot odds to call.

KK vs. AA, KK, or AK

Let's take it a step further and say your opponent will also make the play with AK.

  • 6 hands: your opponent has AA and you are the underdog 81.9% of the time (81.946031) to be precise
  • 1 hand: your opponent has KK and you are even money (50%)
  • 8 hands: your opponent has AK and you are 68.9% to win (68.88378174% to be precise)

Your opponent's weighted winning chances are 52.7%, so you need 1.11 : 1 pot odds to call. So you'll call almost anything.

KK vs. AA, KK, QQ, or AK

Again, let's take it a step further and say your opponent will also make the play with QQ.

  • 6 hands: your opponent has AA and you are the underdog 81.9% of the time (81.946031) to be precise
  • 1 hand: your opponent has KK and you are even money (50%)
  • 8 hands: your opponent has AK and you are 68.9% to win
  • 6 hands: your opponent has QQ and you are 82.4% to win (82.39489016% to be precise)

Your opponent's weighted winning chances are 42.68%, so of course you call no matter what the pot odds.

KK vs. Average opponent

Let's try to do something a little more complicated. Let's say you don't know anything about your opponent. You'll have to treat him as average. What's average? For the purposes of this analysis, let's say that:

  • 95% of opponents will re-re-raise all-in with AA (the others will just call)
  • 70% of opponents will re-re-raise all-in with KK
  • 35% of opponents will re-re-raise all-in with AK
  • 20% of opponents will re-re-raise all-in with QQ

For the purposes of this calculation, we'll ignore other hands. In real life, of course, there are players (albeit few) who will re-re-raise you all-in with hands like 66 or QJs. Hopefully that percentage of players is small enough to make it negligible for this calculation. And if you disagree with any of the percentages above, feel free to substitute your own values for the rest of this analysis.

To complete the analysis, we can simply multiply the number of hands by the percentage of opponents who will raise with those hands. So we have:

  • 6 * 0.95 hands: your opponent has AA and you are the underdog 81.9% of the time (81.946031) to be precise
  • 1 * 0.70 hand: your opponent has KK and you are even money (50%)
  • 8 * 0.35 hands: your opponent has AK and you are 68.9% to win
  • 6 * 0.20 hands: your opponent has QQ and you are 82.4% to win (82.39489016% to be precise)

Your opponent's weighted winning chances are 58.69%, so you need 1.42 : 1 odds to call. Let's take an example. With $200 stacks and a $2 big blind, your opponent raises to $6. You re-raise to $20. Your opponent re-re-raises to $200. Then there's $223 in the pot and you have to call $180. That's giving you 1.24 : 1 pot odds, so you should probably fold. But let's say he only had $100 in his stack to start. Then there would be $123 in the pot and you'd need to call $80. Then you'd be getting 1.54 : 1 odds and you should probably call. Summary:

Opponent Required pot odds to call with KK
AA 4.54 : 1
AA or KK 3.42 : 1
AA, KK, or AK 1.11 : 1
AA, KK, QQ or AK always call
"average" oppponent 1.42 : 1

Now let's analyze what happens when you're holding AKs.

AKs vs. AA

AKs will win 12.1% (actually 12.1404844) of the time against AA, so you'll need 7.24 : 1 odds to call.

AKs vs. AA or KK

AKs will win 34.1% (actually 34.106385315) of the time against KK. The chances you are against AA is the same as KK, so your weighted odds of winning are 23.12343486%, requiring pot odds of 3.32 : 1.

AKs vs. AA, KK, or AK

  • 3 hands: your opponent has AKs and you are even money (50.0%)
  • 6 hands: your opponent has AKo and you are 52.4921392463% to win
  • 3 hands: your opponent has AA and you are 12.1404844% to win
  • 3 hands: your opponent has KK and you are 34.106385315% to win

Your weighted winning chances are 40.2462296415%, so you need 1.48 : 1 pot odds to call.

KK vs. AA, KK, QQ, or AK

Again, let's take it a step further and say your opponent will also make the play with QQ.

  • 3 hands: your opponent has AKs and you are even money (50.0%)
  • 6 hands: your opponent has AKo and you are 52.4921392463% to win
  • 3 hands: your opponent has AA and you are 12.1404844% to win
  • 3 hands: your opponent has KK and you are 34.106385315% to win
  • 6 hands: your opponent has QQ and you are 46.04851125% to win

Your weighted winning chances are 41.9040243868%, so you need 1.39 : 1 pot odds to call.

AKs vs. Average opponent

  • 3 * 0.95 hands: your opponent has AA
  • 3 * 0.70 hand: your opponent has KK
  • 3 * 0.35 hands: your opponent has AKs
  • 6 * 0.35 hands: your opponent has AKo
  • 6 * 0.20 hands: your opponent has QQ

Your weighted winning chances are 34.8618812493%, so you need 1.87 : 1 pot odds to call. Summary:

Opponent Required pot odds to call with AKs
AA 7.24 : 1
AA or KK 3.32 : 1
AA, KK, or AK 1.48 : 1
AA, KK, QQ or AK 1.39 : 1
"average" oppponent 1.87 : 1

As you would expect, AKs plays quite a bit weaker than KK, except specifically if you are playing against someone who will always (and only) re-re-raise all-in with AA or KK. In this case, AKs plays a little better, simply because if you have AKs it is equally likely that your opponent has AA or KK; if you have KK, it is much more likely that he has AA.

I leave it as an exercise to the reader to perform this analysis on AKo and (though I wouldn't suggest calling with them) weaker hands.

 

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