Poker Digest Vol. 2, No. 4, February 12 - 25, 1999
I walked into the club and headed for a seat at one of the service tables. The tea I ordered arrived about the same time as Bib Ladder who took a break from a 20-40 Omaha game to say a few words.
After exchanging greetings he started, ``I was down in the state of Washington playing at one of the casinos near Seattle. The only game going was $4-$8 hold'em so I joined in. Man, it was my first experience with one of those no fold'em hold'em games I've read about. Everyone, and I mean everyone, was calling and raising with any two cards. I tried playing only quality hands and got eaten alive. It seemed as if a straight or flush made it every hand. I don't think I've ever seen so many flushes.
So it got me to thinking about the chances of a board occurring which allows a flush. To me I see all that green felt as a meadow on which we romp and play this game of poker. So I think of boards which allow flushes as flushing meadows. Here are my calculations. Can you take a look at them?''
``Very poetic terminology, Bib. Sure, I'll look at what you did.''
``There are two live ones in that Omaha game who seem prepared to keep me in groceries for the next month or so. I think I'll return to the game. See ya later.''
Below are Bib's calculations.
We are going to determine the probability of a flushing board given no
information on what any of the players is holding. This means we must
determine the total number of flushing boards possible from 52 cards.
The total number of possible boards is
Boards of types (0,0,0,5), (0,0,1,4), (0,0,2,3), and (0,1,1,3) are
flushing boards. The number of boards of these types is the sum
After I had checked Bib's calculations, I had a chance to talk with him again.
``Bib, your calculations are correct. Did you think about seeing what happens to these numbers from the standpoint of an individual player? There are two possibilities for the player: either she has two suited cards or two unsuited cards.''
``No, I didn't think about that. It would be interesting to see if there are some differences.''
``Let's do it!''
In the next article we explore flushing board probabilities from an individual player's viewpoint.