[Copernicus]

I would normally say you compute it by inputting the hands into some software. However, a rough estimate is pretty easy given the elimination of the straight and sets. AKo is going to win (almost) whenever any A or K hit the board. Yes, it will lose if trips other than A or K land, but thats rare enough to ignore.

There will at least one A or K
(1-40/46*39/45*38/44*37/43*36/42) = 52% of the time. Add to this about 4% because they are suited and you get 56%.

Thus the duplication of the Qs has turned a slight favorite into a slightly bigger dog.