Originally Posted by RogueRivered
What's that have to do with it? The question was which would you prefer. Bet sizing is everything. A set of Queens is only 57.66% to win. I can think of many situations where the money in the pot makes that a nobrainer, profitable call, over the long run.


You'll have to explain to me why I am not understanding you. I am not sure you are defending the play with the aces or the queens. But it doesn;t matter The ONLY "nobrainer, profitable call, over the long run" as you put it is the queens. The aces LOSE. Bet sizing doesn't matter to this question.
Originally Posted by RA2000
I would prefer the Queens.
To get a real percentage which pair would win you have to do the randomizing a little more than 11 times....


You are right we need more than 11 played scenarios to get an acurate result. But we can approximate the distribution of an average result easily without even playing out the hand once. Simple outs calculations will give you a close enough approximation to the answer.
The rule of two and four gets a little inaccurate at a point so a common adjustment is to subtract a percentage for every out over 7.
The guy holding the aces needs: An ace or jack, and any diamond but a queen. The turn and river gives two chances at 12 outs. (the jack is a little funny, as it give the aces a straight and the queens two pair with a FH redraw, but thats so remote we can ignore it)
(Outs * #of cards to come * 2%)  1 * (outs7) = %chance
(12 * 2 * 2)  5 = 485 = 42%
Pretty much the same number Poker Stove comes up with.