Overcards on the flop

[JeffSpicoli]

I'm sure you guys have this at your fingertips. Sorry if it's been asked earlier...

What's the right way to calculate the probability of overcards hitting the flop? That is, if you have TT in the pocket, what's the probability that an overcard (J,Q, K or A) will hit the flop?

Thanks in advance.

J

[uuDevil]

One way:

1-((50-16)/50)*((49-16)/49)*((48-16)/48)=0.694693878

This is the probability of 1 or more overcards.

Edit: this is for the specific case of TT (16 overcards). Note that even if you flop an overcard, you will sometimes also flop a set or better, so you're in good shape more often than this probability indicates.

[MickeyHoldem]

Here's a table for all PP and the probability that an over card will flop.

p = 1 - (50-n choose 3)/(50 choose 3) where n is number over overcards

AA 0
KK 0.225510204
QQ 0.414285714
JJ 0.569591837
TT 0.694693878
99 0.792857143
88 0.867346939
77 0.921428571
66 0.958367347
55 0.981428571
44 0.993877551
33 0.998979592
22 1

[JeffSpicoli]

Thanks, guys. 'preciate it.

J