[r2p]

I ran your approach using PokerStove and came up with the following % win numbers pre-flop:

Your Hand vs 1 Other Random Hand 2 Other Random Hands

Any Broadway 63% 47%
88 69% 56%
99 70% 59%
TT 75% 61%
JJ 77% 63%
QQ 80% 65%
KK 82% 67%
AA 85% 70%

Each case was run about 25M hands and I rounded.