Just got familiar to the concept and could really need some help on this.

I have an example and wonder if someone can correct my mistakes or lead me to the right path.

Playing Limit-Holdem 6 max and raises Ad 4d from HJ and get called by a maniac in the BB.

Flop comes Qs 6c 3c

He check-raises me.

Hypotechnical I know for sure he has 54, any Q or and 6 or a flushdraw.

How can I calculate his combos here?

According to my calculations:

55 combos to flushdraw - correct? (Heard this somewhere - dont know the math?)

54 / straightdraw = 12 combos - three unknown 4 and four unknown 5 - 3 times 4 = 12 combos...... correct?

Can I assume he is on a draw 67 combos here?

Next one is to calculate how many times he has a 6 or a Q:

3 unknown 6/Q times 4 different suits times 11 different kickers ( no Q/6, A or 4)
3 * 4 * 11= 132 combos

Should I calculate 2 * 4 different suits * 11 different kickers since I assume he has a Q or 6?

132+132 = 264

Since he could have 3 combos of aces or fours kickers to his Q or 6 it equals 3*3=9 + 3*3=9 = 18 more combos

18+18=36

264+36=300


If I am correct he has:

1 pair=300 combos
strightdraw=12 combos
flushdraw=55 combos

So he is on a draw 67/367=18,2 %

I am correct or where is the mistake?

to make this more complicated, he could do gutshot+flush draw, or even just gutshot, or a pair like 77 :P

or even air, it is a dry boards fellas so never discount it completely

Here are some good loose guidelines:

Any GSSD or OESD is worth 16 combos.

Any pair is worth 12 combos times the number of possible kickers.

Any high card is worth 16 combos times the number of possible kickers.

Any set is worth 3 combos.

Any two of one particular suit, with two already on the board, is worth 55 combos.

Any two pair is worth 9 combos.

Also, you might want to check this out. Counting combos by hand is kind of cumbersome, especially with large ranges, so I commissioned a program to do it for people. The open beta should be starting in a few days: http://www.youtube.com/watch?v=P6fYixwfjpo

this is how you can find out flush draw combinations:
http://en.wikipedia.org/wiki/Combination

55 combos is assuming that villain can have any suited hand, ie
n!/(k!*(n-k)! = 11!/(2!*9!) = 11*10*9!/(2*1*9!) = 110/2 = 55

where n is the total number of suited cards remaining in the deck and k is the number of cards in a poker hand (hole cards)

but if he wouldn't play any suited hand with a 2 in it,
10!/(2!*8!) = 45

and so on. though it's not totally accurate because he may play K2s but not 72s and such

I was wondering, how this method of counting combos can become handy during actual play. Even with a tool/program it will take time to click in villains range data, board, etc'.
Or is the idea to use this to analyze hands off-line ?

thanks !

When my opponents raised the river and I held a strong but not nut hand I would usually count the number of combos for better / worse hands to determine whether or not I wanted to re-raise for value. Also did tons of away-from the table combinatorial analysis to determine things like if my opponent held a hand that would fold to a particular bluff often enough for it to be profitable.