[BruceZ]

The "sandbagging" was meant as an abstract compliment. You said irchans could do this much better, but it's an elementary problem which I believed you to be capable of doing perfectly well, so it would be impossible for anyone to do it better. That would be like saying someone else is a much better tic-tac-toe player than you. You either know how to play or you don't, and if you do then nobody can be much better. See? Maybe sandbagging was the wrong word. Nevermind, I was off my meds [img]/forums/images/icons/smile.gif[/img]

But I strongly disagree that your formula adresses the poster's question, even for the games you mention or any other that I can imagine. I'm not arguing about the specific numbers in the example; I'm saying the concept behind the formula you used is fallacious. The poster asked the probability of making a flush by drawing 3 cards to a 4 flush. It is extremely important to realize and point out that no matter what game we are playing or how these cards will be drawn; the number of unseen cards and the number of remaining flush cards after each card is drawn is, for the purpose of computing this probability, known before ANY of the cards are drawn. In other words, the formula should be:

p = 1 - (m1/n1)*(m1-1/n1-1)*(m1-2/n1-2)

There is no m2,n2,m3,n3 involved in computing this probability. We don't know what those numbers will be yet (hence the psychic comment) and we don't need those numbers to calculate the probability in question. Unseen cards are unseen cards, no matter if certain ones become seen later on.


PS: OK. I suppose you can argue that my formula is a special case of yours where n1=n2=n3 and m1=m2=m3. But this is the only special case we need to answer the type of question I'm sure the poster is asking. Your general formula applies to a contrived situation, and makes it look like we have to know how the number of unseen cards changes or we can't compute the probability. This would confuse just about everyone who didn't already know how to do the problem, and not really show them how to compute what they are interested in.