Quads vs Quads

Just witnessed quite a hand on Stars. What are the odds of Quads vs Quads?


was 55 vs JJ

557 flop, runner runner J's

[Skipbidder]

Do both players have to use both hole cards?
Are we also making the assumption that everyone will play all their hands to the river?

lets say: yes both hole cards for #1
and lets say: heads up - played through to the end for #2

[timex]

You will be a pocket pair 1/17 times, your opponent will then get one 72/1225. Now, of the remaining 48 cards, 4 of them must be definite, and one can be any card. There are 48 choose 5 boards, or 1712304, 44 of these boards will contain the double pair, so 38916. So this means that in a headsup game, quads will lose to quads 1/17 * 72/1225 * 1/38916 times. Or about one every 11 million hands. With ten players at the table, it would be about 45 times more likely, or about 4 hands every million.

So, if your ever see a quads vs quads showdown you're playing way to much poker?