Micro Limit Math Thread

[Delphin]

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But what I'm looking for is a set of forumlae to figure this out, instead of trying to run through the 14 possible combinations myself. I haven't seen any set of formulae or a table that takes strictures like, but not limited to, my original post and helps count the possible combos on-the-fly.

Of course, being able to do stuff like this is useful for determining the true number of outs you have.

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The way you determine this is by counting. There is a whole branch of mathematics dedicated to counting called combinatorics. Grab a book on it if you want to learn more about it and apply it to poker. I'm not sure that you will find what you are looking for. There aren't any magical formulas that will tell you how many outs you have in every situation. You have to just count them.

In the situation you mentioned, you want to know how many ways your opponent can have the ace of hearts and pair the board. There are four cards on the board that have 3 unseen cards that make a pair, the fifth card on the board pairs a card in your hand, so there are only two cards out there. The number of ways he can pair the board is:

4*3+2 = 14

Let say you were interested in how this compares to the number of hands that pair the board with any [img]/images/graemlins/heart.gif[/img]. There are 8 hearts he could hold including the A [img]/images/graemlins/heart.gif[/img] and he could hold any of the aforementioned cards that pair the board:

8*(4*3+2) = 8*14 = 112

So some multiplication can save you from just listing out all the possibilites, but you still have to go through the exercise of the what ifs to figure out what numbers to multiply.

Suppose you want to know how many possible two card hands there are:

The answer is C(52,2) which is read 52 choose 2. This is equivalent to (52!) / ((50!)*(2!)) which is equal to 52*51 / 2 which is equal to 1326. You can also type "52 choose 2" into google instead of using the formula C(n,k) = n! / (n-k)! k!

If that is what you mean by formulas, you can get a lot of that from a basic combinatorics book. That answers questions like how many different ways are there to put different sets of different numbers of things together. But you still have to do the work everytime of figuring out what things you are counting and how to apply the math. There aren't any shortcuts other than trying to figure out common situations and calculate those away from the table. You'll find plenty of info on the odds for common situations.

Or you can use a program like pokerstove.