I have just started looking at Combos for No Lmit Holdem.

I was wondering what is more important the number of combinations your opponent may hold or the number of outs.

How are they related? Or they are not related?

For example.

Flop
7s 7c 3h

Opponent calls your bet after the flop

A few hands your opponent could hold are 43 or AK-A8, A6-A4

There are 128 combos of Aces and only 12 for 43

There are 4 outs for an Ace and 3 outs for a three

However there is 16% chance of hitting an ace (turn & river) and 128 possibilities your opponent holds an Ace and 12% of hitting a three with only 12 combos.

Does the number of combos affect the odds/chances or is that seperate beast?

Maybe this doesn't make sense but there just feels like there is some relationship between the two

Let’s go back to basics. One of the key elements for a poker decision is determining your winning chances. To do that you need to estimate your opponent’s range and compare that with your hand. If you have a guess of his hand, you may then be able to estimate the number of outs he needs to beat you. Basically, this is what you did with your example (not sure why villain has 4 ace outs, though).

Mathematically, you can express this as follows, assuming a post flop situation:

Pr(Opponent wins) = Sum[ Pr(Hi) * (Outs|Hi)*4 ] [ = 1- Pr(You win)]

where

Pr(Hi) = probability villain holds hand Hi

H1, H2, … , Hn is the range of hands you assign to villain

Outs|Hi = number of outs villain has with hand Hi that will give him the win

4 = using the 4x rule for win probability given the outs quantity

Given hand Hi has Ci combos, then a simple estimate for villain’s hand holding is

Pr(Hi) = Ci / (C1+C2+…+Cn)

Based on your characterization of villain and betting actions so far, this simple equation may be modified to give more weight to certain combos. Note also that villain’s outs will likely depend on your hand. For example a card that will give him a set may give you a flush or straight so such cards are not outs for the villain.

So to answer your basic question, villain’s combos and outs together provide an estimate of his card equity – and that determines your card equity, which is an important factor in an EV decision analysis.

As a final comment, as with any math analysis of this type, adjustments often should be made to account for non-quantifiable elements and other factors such as tells, tournament standing, meta-game issues, stack sizes, etc.

Great, thanks for that. Thats awesome.

I'm not much of a maths person so is there any chance of showing an example of the formula.

By the way do you think this can be helpful. I have just finsihed Ed Millers book on Hand Reading and I have just been practising various hand combos with flop and turn cards.

Finally I thought there are four aces still left in deck but I suppose if an ace is in his range there is only three?

I have a nice example of this for QQ vs villain range of AA, KK, JJ, AQ+ using weighted combos. It is in a Word table and I don't know how to display that in this forum without getting into all sorts of column alignment problems.

So, PM me with your email address and I'll send you the table or maybe someone can tell me how to import a Word table so it displays correctly,

Won't do anything till tomorrow though. It's late back east.