No Limit Holdem 101: Holdem Math Part 1 (Counting Outs)

One of the most critical concepts to master in poker is math. We will start out discussion of the math of holdem poker with the basic bulding block of counting outs.


This is intended to be a series of articles about playing on-line no limit holdem cash games. There will be times where I venture into live poker and times where I venture into SNGs, MTTs, Satellites, and games other than no limit holdem, but for the most part this will target no limit holdem cash games.

For the second installment of this series, I am going to tackle one of the most important aspects of poker: math.

When I first wrote this article to encompass everything I wanted to discuss about the math of holdem, it was so lengthy it was almost unreadable. So I’m going to break it into several parts.

The first math topic I’ll cover is the starting point for all holdem math: counting outs.

There are 169 starting card combinations in Holdem (if suits are discounted). It is important to know the general value of these combinations of hands. There are many decent starting hands chart that will give you a guide on which hands you should be playing. I’m not going into that in this installment, but I will go into that in a future installment. For this installment, I’m going to stick with the concept of outs.

You will be making your pre-flop decisions based on expected value of starting hands, reads on your opponents, position, etc., but one of the most critical factors in decision making after the flop is outs.
For a simple definition, an out is a card that can come in the community cards that will improve your hand.

As a simple example, if you hold the Ace of hearts and the two of hearts (Ah2h) and the flop is the seven of hearts, six of hearts, and King of spades (7h6hKs) then you have missed your hand (at least slightly) but you need to know what cards might come on the turn and the river to make you a winner. In this example, any heart will give you the nut flush. Since there are 13 hearts in the deck, 2 hearts in your hand, and 2 hearts in the community cards, there are 9 hearts (13-2-2=9) that you don’t know where they are that will make the nut flush for you.

Pretty simple so far, right? 13-2-2=9. Not hard math at all.

Just make sure the outs you are counting are actually outs. The real idea here isn’t to count outs to make just any hand, but rather to count your outs to make the winning hand. If you hold the King of clubs and the three of clubs (Kc3c) and your opponent holds the Ace of clubs and the 2 of clubs (Ac2c), then you can make your flush and still loose the hand. The point of this is to make sure that you are counting outs to a winning hand.

It is also important to understand the concept of discounting outs. There are a couple of different categories that this falls into.

The first is an out that will make you a hand, but will make your opponent a bigger hand. For example, you hold a pair of Queens and your opponent holds a pair of Aces. The flop is King, Jack, Ten. Now obviously if the turn or river is a Queen you will make a set of Queens but your opponent will make a straight (and the bigger hand.)

The important concept here is that you must always consider your opponent’s hand when counting your outs. Ignoring your opponent’s hand will over inflate your calculations and lead to making poor decisions.

The second is a concept that I have not seen expressed very often, but I think it important none-the-less. This is the concept of discounting outs that your opponents may hold in their hand. I think this concept applies almost exclusively to flush draws. If you are counting odds towards a flush draw, you need to consider the very real possibility that one or more of the players at the table was dealt cards in that suit as well. If you are at a 9 handed table (meaning your have 8 opponents) and have suited cards in your hand, then each of your opponents has somewhat less than a 50% chance of holding a card of the same suit as your cards. Against 8 opponents that means the odds say they will hold between 3 and 4 of the outs you need to make your hand. That means the 9 outs you thought you had have suddenly shrunken to 5 or 6 outs after the flop and is not as nearly attractive as the 9 outs.

There are 4 suits in the deck of cards, but there are 13 different ranks. The math gets much murkier if you are trying to deal with the rank of the cards dealt and is really much too complicated to even consider the mathematical possibilities trying to discount outs based on rank.

Some out there may well not agree with the concept of discounting your flush draw based on probabilities that someone holds a card of your suit, but I think that if you are going to use probabilities, then you had best consider all the probabilities (or at least those you can get a handle on).

That’s it for this installment. Count your outs correctly and you are on your way to making holdem math work for you.

In the next installment I’ll deal with calculating the percentages of making a hand and converting those percentages into odds.