Paired board

[rivered]

I seem to be leaking serious chips the last couple of days in this situation. Some of it is luck but some is bad play as well. What are the odds of someone else having trips out of curiousity. Let's say there is 5 other people in the hand and it flops 995. I'll also say that 4 of the people could have anything because 2 are on the blind and 2 play every single hand (2/4 party is pretty accurate I'd guess).

[JNash]

If there are 5 opponents and a pair on the board, and you don't have have trips yourself, then the probability that one (or more) of the opponents has made trips with the pair on the board is 38.4%. Odds against trips are 1.6:1

BTW, here's how it varies by number of opponents:
1 opp: Prob 8.4%, odds against 10.9:1
2 opp: Prob 16.5%, odds against 5.1:1
3 opp: Prob 24.1%, odds against 3.1:1
4 opp: Prob 31.5%, odds against 2.2:1
5 opp: Prob 38.4%, odds against 1.6:1

Explanation:

There are 47 unknown cards. There are 2 nines left. The 5 opponents hold a total of 10 cards.

What's the probability Y that none of these ten cards is a nine?
Prob of the first card being a non-nine is 45/47.
Prob of the second card being a non-nine is 44/46, etc.
Prob of tenth card being a non-nine is 36/38.
Therefore Y (Prob that none are a nine) equals product of these ten terms.

Probability that at least one of the ten cards is a nine is 1-Y.