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"i wont be alive long enough for the actual results of 2h3h all in on the flop against AA on an AA7 board to converge with the expected results. i will play maybe one hand where that happens in my lifetime."
Yes you will.
The results will be AA win 100% 2h3h wins 0% on an AA7 board no matter how many times this situation arises. Unless you have A7 hearts on the board (which you didn't state) and then AA would lose only if it comes exactly 4h5h.
Even in this situation, the likelihood of AA losing is so small (precisely 1 in 1012.5) that you would have to be really unlucky to experience it in your lifetime, given that this exact situation might arise 2-3 times at most in a poker player's career.
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Face it, there are some spots in a person's poker career that simply won't even out. How many times are you going to play a $135,000 pot with 86h vs ThTc on a Td Ts 7h board and win? It's ok to complain about bad beats sometimes, because some things just don't even out. The 'long run' is often much longer than people realize because of pots like this one that sometimes occur in big cash games and deep in major WSOP/WPT events.
http://www.pokerhand.org/?1711300