Erroneous calculation

About a year and a half ago I became curious about the probability of being the only player at the table who has been dealt a pocket pair to start a hand. While investigating it, I came across a surprisingly elaborate calculation of the solution done by Brian Alspach. Toward the bottom of this page, you see a table that lists the probability that somebody has a pocket pair larger than the one you were dealt. The first line of this table says that if one player has K-K, the probability that another has been given A-A is 0.0439, or about 4.4%.

This is incorrect.

I have now been keeping careful track over three years of playing, and now have sufficient real-world data to say that Mr. Alspach, bright as he is, has it all wrong. K-K will turn out to be up against A-A 99.3% of the time.

But there's more to this. If you have A-A, you would like an opponent to have K-K so that he is willing to put all his money into the pot for you to take (well, you'll take it about 80% of the time, anyway). But this mismatch turns out to be quite rare, with A-A finding its K-K victim only 0.2% of the time, according to my detailed and extensive records.

This is a statistical paradox, the bizarre mathematics of which have not yet been fully worked out. I have it on good authority that some of the top minds at the Institute for Advanced Study in Princeton, New Jersey, are working on this seeming impossible pair of observations.

The full solution, though, is likely beyond even the next generation of supercomputers, lying in the realm of the paranormal.