AA vs AA vs KK with KK winning

I was in ten-handed HE game last nite with AA. Capped preflop 3 or 4 ways (I forget). And the Flop comes

K Trash Trash (2-suited). EP bets, I raise, One caller behind me, EP re-raises, I call, player behind me calls. With two players besides me I am really starting to fear KK now. So I check call down to the river. Well, showdown comes and I have AA, the raiser has KK, and the player behind me also has AA. I wanted to figure out the probability of this happening at a ten-handed table, so I wrote a little c-program and ran 1,000,000 hands during lunch. And here is what I came up with.

AA occured 40635 4.06 % ~ 1 out of 24
KK occured 40536 4.05 % ~ 1 out of 24
AA vs AA occurred 138 .0138% ~ 1 out of 7,250
AA vs AA vs KK occurred 8 .0008% ~ 1 out of 125,000

Since 1,000,000 hands probably exceeds my lifetime expectancy of hands, These numbers may be a bit high for life.

I coded the sim rather quickly and was wondering if anyone disputes these. I was a bit suprised by how frequently someone at a table has AA or KK (about 1 out of 1.2 orbits?), so wouldn't be suprised if someone told me I am doing something wrong.

Anyone care to figure out the probability of being one of the two saps holding AA and losing to KK. If only I had known I was drawing dead [img]/forums/images/icons/grin.gif[/img]

Thanks,
-JD