Simple way to find combinations of hands?

[Popinjay]

This is how I was I was calc-ing combinations. Preflop how may combos of AA are out there? I did (4 aces * 3 aces)/2 = 6. Then for AK I did (8 aces or kings * 4 ace/king)/2 = 16. That works right? but then say on the flop there is a King on the board and you have AA. How many AK are out there? (5 aces/kings * what?)/2

I don't think my method works for that on the flop. Can someone show me the easiest while still accurate method for figuring out hand combinations?

[fnord_too]

For non pairs, not caring about suitedness, take the number of each rank and multipy them together. In your example, you have AA and there is a K on the board.
There are two aces left and 3 kings, so there are 6 ways to make AK (2Aces *3Kings).

For suited, just count the suits you see neither Ace nor King (two or one depending on whether the board K matches one of your aces).

For specifically non suited, it is just the first number minus the second.

The reason you divide by two the way you are calculating combinations is because you are generating the combination as a series of events, so you double count all your combinations. (A /images/graemlins/heart.gifA /images/graemlins/spade.gif is the same as A /images/graemlins/spade.gifA /images/graemlins/heart.gif, but both get counted individually). In the case with AK, you can count combinations directly so you don't double count, if that makes sense.

You should pick up a book on probability and combinatorics (or take a class if you have the opportunity). You will find the material easy, but very useful and time saving none the less.

[gergery]

[ QUOTE ]


You should pick up a book on probability and combinatorics

[/ QUOTE ]

What do you recommend?

[fnord_too]

[ QUOTE ]
[ QUOTE ]


You should pick up a book on probability and combinatorics

[/ QUOTE ]

What do you recommend?

[/ QUOTE ]

No specific rec's, but they usually have a few in Barnes & Noble and Border's Math section.

[Derek in NYC]

Why do you need to buy a book? Just draw a picture, or if you can't figure it out by drawing a picture, try to arrange the combinations manually with actual cards. (You don't need the whole divide by 2, since the pictorial solution takes care of the problem that the order of the combination doesnt matter.) This is a very straightfoward multiplication issue.

[Popinjay]

Actually I do have a book that is very good. I was just too lazy to go look in it, plus 2+2'ers can explain better a lot of the time. the book is highly recommended however, it's called: Mike Petriv's Hold Em Odds book