[WhiteWolf]

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Well there is definetely some double counting.

Any board of QJT and and no pair wins in either situation.
(i.e. If there is a flush or not isn't relevant)

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And probably more commonly, almost all boards with an Ace or King and no Ten wins in either case, flush or no flush. I'm not sure how to figure the odds on this, or if it explains most of the "discrepancy".

It's not that a flush is going to be beaten so many times: it's that there are many boards that AKs will make a flush with, and although AKo will not make a flush, it will still beat TT some other way.