Yes. That is what I did. I'm glad you followed my reasoning.
Glad to hear it.
My object was mainly to explain how to create a table to be used in combinatorics leading to computing probability. The original title was,
"How to Make a Chart to find the Probability of being dealt two particular ranks as part of an Omaha-8 hand."
I used as an example calculating the probability of getting dealt a particular two cards of different ranks. And as a sub-example, the two ranks I chose were aces plus deuces.
But I didn't like that original title, tried some changes, and finally settled on a title I thought would be less confusing and would have more widespread appeal, "Calculating the Probability of Being Dealt Ace-Deuce in Omaha 8 or Better." I think it's that change of title that has led to confusion by you over my purpose in writing the article. My fault. Sorry.
Except for the following: Using one of the most fundamental results of combinatorics, the Inclusion-Exclusion Principle, it is absolutely trivial to compute the number of A2 combinations as
where "binom(n,k)" is the binomial coefficient n!/(k!(n-k)!).
binom(52,4) -2 binom(48,4) + binom(44,4)
That's beautiful. Took me a while to comprehend it, and I don't know how you came upon it, but that's beautiful.
This avoids considering all subcases, and reduces the possibility of making mistakes. It also allows for generalisation to count other classes of hands.
"2 binom(48,4)" evidently means "2*binom(48,4)."
Thus binom(52,4) -2 binom(48,4) + binom(44,4) =
Very elegant!! Thank you.
And then 17,316/270,725=0.06396
Nifty! Very elegant method! Again, thank you.
From my own perspective, there are often different methods to go about finding probabilities, some more elegant than others.
In the article to which you're referring, I specifically wanted to illustrate the general method of constructing a chart to use in calculation of probability. The chart method is a general method I often use and I thought the method would be useful to others.
I had considered submitting an article as a reply, but since you are "less interested in a new mental trick to calculate probabilities" and no original mathematical work was done I didn't feel it would be appropriate.
I don't know what you're quoting. Doesn't sound like something I'd write. And the magazine editor asserts he didn't write it either. (I believe him).
Of course this raises the question how those criteria were applied to the original article.
I don't understand. I wrote an article illustrating how to construct a chart to find the probability of being dealt a particular two rank combination in a four card Omaha-8 hand. It's something that, in my opinion, is very practical and that might be of interest to serious Omaha-8 players and students of the game. I submitted the article for possible publication, and it was accepted.
I plan to submit another along the same lines for next month. The goal, really, is to illustrate, by example, a method to construct a chart to calculate probabilities. I'll approach the problem from a different perspective. I'm not sure what the title will end up being.
I try to write the Omaha-8 articles I submit on a level sharp, interested readers will understand and will be able to apply. The Omaha-8 articles I write are written for the on-line 2+2 poker magazine rather than for a mathematics journal. (No offense to mathematicians is intended).