Obviously if two people go to the flop, each with a pair, flopping a set vs quads will only happen when all 3 of the cards that hit the board hit one of their outs. Since they each have 2 outs, there are 4 options for the first card, 3 options for the second card, and 2 options for the 3rd card.
(4/48) * (3/47) * (2/46) = 1 in 4,324.
Now, how often will you have pair vs pair?
Obviously you have a pair 1 time in 17.
The odds that someone else will have a pair ... say it's an 8-handed table. It's not really 8 in 17, but let's use that anyway.
1/4324 * 1/17 * 8/17 = 1 in 156,205.
I 4-table full ring games, and I always figure roughly 200 hands per hour. So quads versus set will happen to me once every 781 hours, give or take. Since half the time I will be the one with quads, I will get stacked like this once every 1,562 hours. I think I can live with that.
If you played live, at say 25 hands per hour, it would happen to you once every 12,496 hours!!! So say you hit Vegas once a month for a 20-hour weekend of play -- it would happen once 52 years!
OK, I can live with having zero chance to escape going broke that often.
