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:
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?
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.
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.
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:
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:
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:
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.
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.
Your weighted winning chances are 41.9040243868%, so you need 1.39 : 1
pot odds to call.
AKs vs. Average opponent
Your weighted winning chances are 34.8618812493%, so you need 1.87 : 1
pot odds to call. Summary:
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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