No Limit Holdem 101: Holdem Math Part 5 (Putting It All Together)

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 sixth 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 fifth math topic I’ll cover is putting it all together.


We are almost experts on holdem math now. We know how to count our outs, how to convert those outs into percentage or ratios, how to calculate pot odds, and how to think in terms of implied odds.
Okay, so not experts, but we are getting a good grasp of the fundamentals.
Now we need to put it all together and actually use math to help us make a decision.
Example one: A flush draw.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. Both the blinds have stacks of about $200.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.

First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 2 is 24% of making our hand on the turn. That gives us 76 to 24 odds against making our hand. That’s right around 3.1 to 1.

Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.

Now we need to factor in implied outs. We are chasing a flush and an overcard. Both of these will be easy to see on the board and our opponent will likely shut down and abandon his Kings once the scare card hits the boards. We really can’t add anything to this with implied odds.

So we have 3.1 to 1 against us making the winning hand and we have 2 to 1 for pot odds. Since the odds against making our hand or less than our pot odds, we should not be making this call.

Example two: hidden straight draw with a low flush draw.
Same situation as above expect for the cards we hold. Now we have 5s6s. The action folds to the small blind who raises to $6. We decide to call and put another $5 in the pot bringing the total to $12. Again both players have around $200 stacks.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out with a pot sized bet of $12.

First we count our outs. There are 9 spades that we don’t know where they are and therefore could come on the turn or river to make our flush. So we have 9 outs. But do we really want to count these as this would make a very low flush. This depends on your read on your opponent. For the sake of argument, let’s say we just know that he’s playing an unsuited King. No need to discount any of our outs. We need to then add another 6 outs to make our straight draw (we’ve already counted the 3s and 8s as spades.) That gives us 15 total outs. So we have a 30% (15 x 2) chance of making our hand on the turn. So our odds are 70 to 30 against us making our hand. That’s 2 1/3 to 1 against making our hand.

Right now the pot is $24 with us having to make a call of $12. We are getting 2 to 1 to make the call.

So based strictly on the pot odds we should NOT be making this call (but it is fairly close).

But now we need to consider the implied odds and see if this makes for a good call or not. If any spade hits the board, our opponent is likely to shut down the betting. If however a non-spade 3 or 8 comes, our opponent is very likely to fire at this pot and we are now getting the right odds to make this call. We are getting no implied odds if we make the flush but high implied odds if we make the straight and that is more than enough add to the pot odds to make this an easy call.

Now you can see why in the last installment I referred to implied odds as more an art than a science. Implied odds require a high degree of predicting your opponent’s actions and that can be tricky indeed.

But wait a minute; isn’t it the rule of two and FOUR? What happened to the freaking FOUR? Good question.

The FOUR applies to your odds of making your hand on both the turn and the river and should be used in all-in situations after the flop. If the flop bet puts either you are your opponent all-in then that is where you use the FOUR as your factor to calculate your percentage of making your hand on the turn and river combined.

Example three: all-in on the flop.
We are playing a cash table with $1/$2 blinds. Before the flop we were in the big blind with the Ace of spades and the six of spades (As6s). The action folds to the small blind who raises to $6. We decide to call and put another $4 in the pot bringing the total to $12. The small blind has $36 left. You have him covered.
The flop is the Kc7s4s. You strongly suspect that your opponent has paired his King. He leads out by going all-in for $36.

First we count our outs. There are 9 spades that we don’t know where they are and therefore could come to make our nut flush. So we have 9 outs (unless we want to discount our outs for any reason). We also have an Ace with 3 Aces unknown. That gives us 3 more outs. 12 outs times 4 is 48% of making our hand on the turn. That gives us 52 to 48 odds against making our hand. That’s right around 1.1 to 1.

Right now the pot is $48 with us having to make a call of $36. We are getting 1.33 to 1 to make the call.

Our pot odds are greater than our odds of making the hands (1.33 is more than 1.1) so we should make the call.

I know some people use the rule of four for the flop regardless, but that is a mathematical error. The fact of the matter is the rule of four is your chance of making the hand on both the turn and the river. In order to use four you will have to calculate both the known bet on the flop and the unknown bet on the turn.

Now this doesn’t mean that you never use the rule of four on the flop unless there is an all-in involved. What it means is that you need to calculate the betting on the turn while you are on the flop in order to use the rule of four to justify your call on the flop. If you suspect your opponent will move all-in on the flop, then you can use those numbers to calculate your pot odds and compare those to your hand odds.

Yes. These calculations can get very tricky on the logic. Even though this about math it is based on your read on your opponent. If you don’t have a read on your opponent, then you are going to be hampered in some of the more complex aspects of holdem math.

Well, that’s it for the math of holdem (except I will be referring back to the math as we discuss further concepts in the future.)
In the next installment I’ll take a step back and talk about my basic theory behind holdem – Giving the other guy the chance to make a mistake.