I did a simulation (100000 hands) of 9 players being dealt random rands and 3.9% of the time at least one opponent will have AA given that one opponent has been dealt KK.

So, the chance that you will be up against AA exactly 7 times in 30 trials is like 1 in 8900.

The chance that you will be up against AA at least 7 times in 30 trials is like 1 in 7900.

I hypothesize that God hates you at 2 to 1.
Someone can check my math on this.