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StrategyPoker Basics

Ranges & Equity (2): Combos & Card Removal

Before this lesson, it is recommended that you read the following article:

You are already familiar with the concept of ranges and know how to notate them. Now let's imagine your opponent has a range of QQ and AK. Which hand is more likely?

You might assume that each hand is equally likely, since QQ and AK both represent one specific starting hand.

However, the correct answer is quite different. There is a 27% chance that your opponent has QQ and a 73% chance that he has AK. The reason for this is that the two hands are each made up from a different amount of poker card combinations - called combos.

Counting combos is necessary to analyze ranges correctly; in this lesson you will learn how to do this. We will also take a look at how your cards, your opponent's cards, and the board each influence the combos and the way we count them.

How to count combos for specific hands and ranges

There are four queens in the deck and therefore six possible combinations of cards that give us the hand QQ. However to make AK, there are 16 possible card combinations. Four aces combined with four kings gives you 4 x 4 = 16 combinations.

Note that the order of the cards within a combo doesn't matter; QcQd is the same hand as QdQc.

The sum of all combos for a specific range (or part of a range) is an important factor in assessing how likely it is that your opponent has a certain hand. The more combos there are in a hand or range, the more likely it is that you are facing this range and vice versa.

For easy documentation, we use the "#" symbol to indicate the amount of combos that make up a range. The range QQ, AK has 6 + 16 = 22 combos which means that the short form for writing this is:

QQ, AK (#22)
A combo is a specific combination of two cards that make up a certain hand. The sum of possible combos for creating a certain hand, or range of hands, is important information when estimating the hand strength of your opponent based on his range.

The following table gives you an overview of the number of possible combos for certain categories of starting hands:

Hand category
Possible combos
Example
Pocket pair 6 QQ
Offsuit hand
12 AKo
Suited hand
4 AKs
Suited/offsuit hand
16 AK

Card removal influences counting combos

Card removal refers to the fact that the dealt community cards and your own hand directly influence the likelihood of certain hands or the number of combos in your opponent's range.

For example, we know that a pocket pair consists of six combos, and that a specific suited hand consists of four combos; this can change depending on the community cards that hit the flop. Let's look at the following situation:

We're assuming our opponent has a range of either sets or an open-ended straight draw, and we want to determine which is the more likely holding.

Notating ranges isn't an issue for you anymore, so you know his range is QQ, 99, 44, JT.

Given what you have already learned, it is natural to assume that QQ, 99, and 44 have six combos each and that JT has 16 combos. This makes 18 set combos and 16 OESD combos, making a set more likely.

But this doesn't take the board into account. Cards on the board can't be used in your opponent's range; villain can't have a card that's already on the table. This effect is called card removal

Since the Qh is already on the board, there are only three queens left that could make up QQ as a hand. 

This means that there are only three combos that make a set with QQ. There are only nine combos that make a set with any of the three community cards.

Without card removal
With card removal  (on Qh9c4d)

 

For an OESD on the other hand, a board like Qh9c4d still allows for all 16 combos to be available, since there is no jack or ten on the board.

In total, there are 16 combos for an OESD as opposed to 9 combos for a set. Therefore the chances of an OESD are 64%; 36% for a set.

By determining the exact number of possible combos that make up a certain hand strength utilising card removal, you can calculate the likelihood of this hand strength within a range. This is a very important tool to make optimal decisions based on your analysis of the situation.

Card removal includes your own hand

Card removal doesn't just include the cards on the board, but also includes your own hand.

How many combos are there for your opponent to hold QQ in the hand below?

In this situation, there are even fewer queens available for making a set than previously. Due to card removal, you have to exclude the Qh on the board as well as the Qs in your own hand, leaving only the Qd and the Qc - exactly one combo.

The effect of card removal

Card removal doesn't just play a big role in affecting the likelihood of sets, but also when you are facing hands that are far more common, such as top pair.

On a board such as Qd6c3h there are only 12 instead of the usual 16 combinations that make up a hand like AQ: 4 aces x 3 queens = 12.

If we assume that you also have a queen in your own hand (maybe QsTc), then there are only eight combos left for AQ; 4 aces x 2 queens. If you have an ace yourself, say AsTc, there are nine combos left for AQ; 3 aces x 3 queens.

The following table shows you how card removal influences the possible combos for different hands:


  Hand
With card removal on: Qd6c3h Without card removal
    You have QsTc You have AsTc  
AQ
12
8
9
16
AQs
3
2
2
4
Q6
9
6

16
Q6s
2
1

4
QQ
3
1
6

Summary

Combos are combinations of individual cards that create a certain starting hand. The number of possible combos is different depending on the type of starting hand:

  • Pocket pair: 6 combos
  • Suited hand: 4 combos
  • Offsuit hand: 12 combos

Card removal means taking into account that community cards and cards in your own hand cannot be included in your opponent's range. This influences the likelihood of villain holding certain hands depending on the board and your cards.

Next steps

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Discussion
 

Comments (40)

#1 genia2q, 10 Jul 13 16:51

Wow, that was very confusing, I will have to find a way so that I can understand it and put it in practice, thank you.

#2 yuli06, 10 Nov 13 13:58

Thanks

#3 SkelterAAA, 09 Mar 14 08:59

A bit confused with this one:<br /> "to make AK, there are 16 possible card combinations. Four aces combined with four kings gives you 4 x 4 = 16 combinations.<br /> and later....<br /> Offsuit hand AKo = 12 combos<br /> Which is it for AK...12 or 16?

#4 SkelterAAA, 09 Mar 14 09:03

Sorry, i understand now....AK unsuited (12) with AK suited (4) = 16

#5 SkelterAAA, 09 Mar 14 09:40

Difficult stuff to say the least :)

#6 CustardKid, 05 Jun 14 21:03

Ill try explain this I was confused at 1st until I got a pen and paper out lol<br /> <br /> AKs = 4 possible combos of AKs<br /> AKo = 12 possible combos of AKo<br /> AK total combos = 16<br /> <br /> you are trying to work out how many combos of ak villain has on a flop, now say there is a flop of:<br /> <br /> As-Kd-3d<br /> <br /> there is 3 aces left and 3 kings in the deck so its 3x3=9 possible combos left.<br /> <br /> now lets look a this flop:<br /> <br /> As-Kd-Ks<br /> <br /> there is 3 aces, but only 2 kings left in the deck so 3x2=6 possible combo's<br /> <br /> I hope this helps for you guys<br /> <br /> I am still learning myself so please do correct me if I'm wrong

#7 Jaquare, 12 Jun 14 14:01

right is you are not holding an A or a K yourself! Good article!! Thanks again!!

#8 rebelbhoy67, 10 Jul 14 20:18

brill

#9 wirra, 17 Jul 14 07:49

ok

#10 STEPVN, 31 Jul 14 16:16

I am confused :/

#11 Mandator, 20 Aug 14 19:35

This is an article that you have to read carefully and more than once to be understood... Also, write down some notes about it. That helps a lot

#12 biggood, 02 Sep 14 21:29

I hope this helps me in the games

#13 tashaleigh3, 09 Oct 14 10:00

ok:)

#14 catblank, 14 Oct 14 09:01

ok

#15 Ambrosh, 05 Nov 14 19:34

i am bignuer in the poker game pls say me how i play that

#16 BenBlakeIsTilting, 14 Nov 14 05:35

good article

#17 bbqpkr, 10 Dec 14 07:00

Thanks for this, really useful - took a while to get my head around though!

#18 hud400, 18 Mar 15 20:46

The charts showing the changes under different situations of hands<br /> and boards should help many especially those with decent grasp of math.

#19 mirth, 25 Mar 15 17:46

so far this is the most diffiult of the lessons to underrstand. will take a while to be able to calculate this quickly in the midst of a hand

#20 totalfish, 27 May 15 21:14

what an article!!! i didn't understand the concept of compos and card removal until now, and the video was very clearly explained all this! THANKS PS FOR THIS VIDEO! guys read it fist then watch the video and then take a paper and a pencil and work it out, i found my own way to calculated fast, its easy you will do it also. thank take the quiz as many time until you answer all the questions right and you know the reason why!

#21 PokarFace, 16 Jul 15 03:38

Right now I'm mind blown, but everything takes practice before it becomes a killer instinct :)

#22 dddq8842, 23 Sep 15 10:41

I can't sleep if I dont understand this. Its driving me nuts.

#23 CANeZ, 17 Oct 15 10:48

Number of specific hands can be calculated with the number of combinations; n over k. Lets say we wamt to calculate the number of ace pairs possible it is 4 over 2 = 4 × 3/2 = 6. But if we are to calculatr the number of possible AK-s without considering suit: (8 over 2) - 12 = 28 - 12 = 16. First is the combinations posaible from all aces and kings but we have to substract from it the pairs(AA, KK) calculated before.

#24 gohomeman2690, 31 Oct 15 15:24

ok

#25 Edimieras, 08 Nov 15 07:48

Hard to get it at first, but it might come in handy a bit.

#26 6attitude9, 08 Nov 15 21:31

stuff to learn

#27 minsa0123, 12 Nov 15 05:45

I am confused

#28 bubamarasr, 20 Jan 16 18:42

Read it. Thank you.

#29 setyaida, 25 Jan 16 11:06

Confused but its Good idea

#30 hassux, 25 Jan 16 21:25

badi nik kiss emou

#31 ptpokermyth, 26 Feb 16 16:32

i liked :)

#32 Rey2016, 29 Feb 16 18:47

thank you, very good article

#33 sedinbsng, 01 Apr 16 19:23

ok

#34 pharaonsgold, 07 Apr 16 00:35

nice

#35 CroZoZo, 26 Apr 16 13:20

nice

#36 TetonSouix, 16 May 16 02:20

good article

#37 Tezza459, 25 May 16 15:23

I enjoy being on this site because I have been learning so much about Poker and is making me a wiser gambler

#38 armorrrat, 08 Jun 16 19:05

Good stuff. Complicated and it takes time to put it in practice, but when you do - you'll rock.

#39 hardkandy, 31 Jul 16 22:29

I really liked this article.. got my brain thinking and learning.. will be very useful if applied correctly to complement other reads on villian.. good stuff.

#40 Robinsko, 09 Aug 16 18:10

??????