Running 'em three times

[zepmetal]

I understand that typically players choose to run them three times when it is a cointoss-like hand and they want to reduce their variance. It seems that regardsless of the situation (whether you're getting 1:1 odds to win, or 10:1) the long-term outcome will be the same running them three times or not. Is it faulty logic to say something like "but if he gets allin on the flop with a flush draw, if he hits it on the first run, hes now less likely to hit it on the 2nd run, so hes at a disadvantage". On the other hand, when he misses it on the 1st run, he's getting better odds to hit it on the 2nd run and 3rd run, thus compensating. My question is this: is there ever a situation where running them 3 times gives an advantage to one player and therefore a disadvantage to the other?