View Full Version : Odds the board pairs?

12-23-2004, 04:22 PM
What are the odds of the board pairing? Any two cards at any point.. I calculated it as 25% but that feels wrong to me..

I'm basically figuring..

First card, 0/52
Second card, 3/51 (3 chances to pair previous)
Third card, 6/50 (3 chances to pair either previous)
Turn, 9/49 (etc..)
River, 12/48

Am I retarded? /images/graemlins/blush.gif

12-23-2004, 04:41 PM
Asuming you don't look at your hole cards the odds of the board exactly pairing once are 13*C(4,2)*48*44*40/6 divided by C(52,5)=42.3% The odds of no matching cards appearing in dummy are (52*48*44*40*36/5!)/C(52,5)=50.7%.

C(X,Y)=X!/(Y!*(X-Y)!) which represents the number of unique combinations of Y items from a pool of size X.

Dave H.
12-23-2004, 05:40 PM
...and the probability that a pair occurs ON THE FLOP...

For each rank, there are (4 choose 2) = 6 possible ways to make a pair. Each of those goes with 48 possible 3rd cards. So it's 13*6*48/(52 choose 3) = .1694

12-25-2004, 11:53 AM
Argh. Speaking of which..

I hold 2 2
Flop : 8 K K
Other guy bets small, all fold but me
Turn : 2
Guy bets, I raise he calls
River : 8

I'm sure you know the rest..