Re: odds of opponent holding pocket Aces given you holdpocket Kings
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It's 1 in 40.833.
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Sounds about right. If I were lazy, and didn't want to do the math, I'd run about 5 million random hands and find check the number of times any of my opponents got dealt AA.
I expect that I'd see AA in an opponent about 122752 times in a six handed game, with individual frequency ranging from 22,443 times to 24,778.
This would yield AA showing up about 1 in 40.7325 times. Now, this 1 in 40.7325 would be a touch low because I wouldn't have taken into account those times where 2 players have AA. But overall, I would expect this to be consistent with your calculated answer.
Of course, I would NEVER be so lazy as to run the simulation, but if I WERE so lazy, I think I'd see something like this.
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