(odds) Flopped set vs. over-set

I haven't played poker for a long time, but I've seen a several instances over my ~ 20k hands experience. Let's look at the odds.

Now suppose the flop comes in three different numbers (not paired), card X, Y, Z, and X < Y < Z.

Case ZZ:

If you hold ZZ, what's the chance that you face at least opponent with XX or YY?

Sample calculation:
There are 6 kinds of XX & YY.
Still, there are 1225 combinations of cards left.
For all of your N (let's use 9 here) opponents to miss them:
((1225-12)/1225)^9 = 0.915
Therefore, you have 0.085, or 1 in 12 chance to be lucky.

To summaraize, the chance you hold the over-set:
9 opponents: 1 in 12
7 opponents: 1 in 15
5 opponents: 1 in 21
3 opponents: 1 in 34
1 opponent: 1 in 102

This is also the odds that when you hold XX, and you are beaten by one of the possible over-sets.

p.s. If you recall my previous post about pair vs. over-pair, this is the identical chance as QQ running into KK or AA.

Case YY:

Now what's the chance you are BEATEN when you hold the middle set?
The above odds also apply to situations where you are AHEAD of the bottom set. The chance for 3 people flopping setsis really low, so I don't think you have to worry about it.

9 opponents: 1 in 23
7 opponents: 1 in 30
5 opponents: 1 in 41
3 opponents: 1 in 68
1 opponent: 1 in 204

p.s. If you recall my previous post about pair vs. over-pair, this is the identical chance as KK running into AA.

I am sure you all had experiences of holding AA, raised it to the roof pre-flop, yet some donk called with an under-pair and stole all your chips.

Suppose you have an overpair (AA, KK, doesn't matter). The flop is all under cards of different numbers. (now if there is some overcard it will be another story.)

There are 6 x 3 = 18 hands that would have flopped a set.
9 opponents: 1 in 8.0
7 opponents: 1 in 10
5 opponents: 1 in 14
3 opponents: 1 in 23
1 opponent: 1 in 68

This is identical to the odds that your pocket JJ running into QQ, KK or AA.