Hold'em odds book by Mike Petriv shows you how to calculate the "probability of flopping an open ended straight draw, flush draw, open ended straight flush draw, and flopping a flush draw OR an open ended straight draw with suited connectors, connectors, 1 gappers both suited and connected"...

It is difficult too find and relatively expensive (39.99 USD), considering the quality of the binding and the printing.

I searched far and low for a book that would answer all my questions on probabilities. It is the only one I found.

There is another book, Texas Hold'em odds by Catalin Barboianu. The reviews have been lukewarm, so I haven't purchased it yet. The author is a romanian mathematician, who is semi-literate in english.

Considering the avalanche of books on poker on the market, it is rather surprising to only be able to recommend a 1996 book, which is now out of print. People must simply be math-phobic.

The maths in Hold'em odds is basic and very simply explained, though not always rigorously enough to my taste. It is written by a poker player so all the subjects in your post are covered.

All basic poker probabilities boil down to simple combinatorics and basic logic.

Basically, you just need to know the combinatorics formula: C(n,k) = n!/(n-k!)k!. If you have a calculator, you don't even need to know that. If you don't have one yet, get a calculator where the combinatorics formula is available withou having to sift through the menu. I bought the Casio fx-991MS (20 CAD) just for that purpose.

Here is a simple way of expressing the flush draw probabilities which Aaron Brown has already done. I suspect he read Petriv's book, since he uses his method.

<u>Probability of having 2 suited cards</u>

C(13,2)/C(52,2) * 4 = 23.53%

<u>Probability of flopping a flush when holding 2 suited cards</u>

C(11,3)/C(50,3) = 0.84%

<u>Probability of flopping a flush draw when holding 2 suited cards (not a flush)</u>

C(11,2)*C((50-11),1)/C(50,3) = 10.9%


You can have a blind faith in BruceZ's posts in the Probabilities and Statistics forum. Brian Alspach is a mathematics professor who has published extensively on the subject. You can find his articles on the web. I wouldn't really recommend it, but Daniel Kinberg's has published a few articles on CardPlayer, which are geared towards the beginner but still enjoyable.

I'm still slogging through Petriv's book. Give me a month or so and I'll be able to answer your questions as competently as BruceZ.