all-in pre-flop KK vs. QQ deal

[Big_Jim]

Here is the simplest example possible:

Say you have set over setted someone on the turn and the pot has $44. So the underset is drawing to one out.

If you run it once:
He'll win 1/44 times, so his EV is $1.

If you run it twice and don't reshuffle the cards:
He'll get half the pot 1/22 times (he can never win the whole pot) so his EV is again $1.

If you run it twice and do reshuffle the cards:
He'll win the whole pot 1/44^2 = 1/1936
Get half 1/44 * 43/44 * 2 = 86/1936
And lose the whole pot 43/44^2 = 1849/1936

so his EV is:
44 * 1/1936 + 22 * 86/1936 = $1

Therefore:
It doesn't matter at all, EV wise.

QED