Mike,


You have to be very careful with this kind of question. It's too easy to multiply all the various probabilities together, come up with some enormous number and go "wow, I'm so unlucky".


In the event, you know you have AK and you know there is a King on the flop - seeing is believing, right :-). The odds against two random cards that you can't see being the remaining two Kings are very high. But your opponent's cards are not random. You can narrow her holding down to a range, according to her actions.


Here is an example of how to do this. After whatever reraise you decide that your opponent can only have AA, KK or AK. There are three Aces and two Kings unaccounted for. Your opponent can have Aces 3 ways (if you have the As, then AcAd, AhAd, AcAh), Kings 1 way, and AK 6 ways. It's 9-1 against her having KK now - but 40% of the time you are beaten and the rest you split.


I apologise if you already know this. The point is that in the event it may have seemed unlikely for your opponent to have the other two Kings - but with each reraise it becomes more and more likely that you are beat ! When you have eliminated the impossible, the improbable must be correct (apologies to Conan Doyle fans if I have misquoted that slightly)


Andy.


PS A favourite example of mine is as follows. Someone wrote in to a lottery "expert" in a UK tabloid to ask him what was the probability of this series of events which had actually happened : he walked into a casino at 12 minutes past 12 and placed £12 on number 12 at roulette, which duly obliged. The expert pronounced the odds to be "millions to one".