No Limit Holdem 101: Holdem Math Part 2 (Converting Outs to Odds)

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 third 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 second math topic I’ll cover is making the numbers mean something by converting your outs into percentages or odds.

Now before all of those who got a “C” in algebra start heading for the door, let me tell you that Holdem Math is actually very easy. Holdem Math is as simple as 5th grade math. If you know your times tables, you can do the math needed for Holdem.
In the last installment we focused on how to count outs. Once we know the outs, we need to convert the outs to a number that gives a means of comparison to other numbers. I personally prefer to use percentages instead of odds, but some poker players (being gamblers) prefer expressing this in terms of odds.

The important thing is that you can produce a number that you are comfortable with in order to compare it to your pot odds (discussed in the next two articles.)

We will use a standard flush draw as our example. Lets say you have the Ace of Clubs and the two of clubs (Ac2c) and the flop is the six of clubs, the seven of clubs, and the King of spades. By counting outs we know that we have nine outs to make the nut flush.

But how do we express this in a way that has some meaning? We will use something called the rule of 2 and 4. This rule provides us with an APPROXIMATION of the percentage chance you have of making your hand. If you are trying to calculate the percentage of making your hand after the flop (with both the turn and river to come), multiply your outs by the number 4. If you are trying to calculate the percentage of making your hand on one street (after the flop to make it on just the turn or after the turn with just the river to come), multiply your outs by the number 2.

So in our nine out example above, we would have a 36% (9 x 4) chance of making our flush on the turn and river combined. We would have an 18% (9 x 2) chance of making the flush on the turn by itself and should the spade not come on the turn, we would again have an 18% (9 x 2) of making the nut flush on the river.

A true mathematician will point out that this is an APPROXIMATION. And that is correct the actual mathematically derived percentage based of the number of desired outcomes and the number of remaining unknown cards is 35% to make the nut flush on the turn and river combined, 19.2% to make the nut flush on the turn by itself, and 19.6%. We are trying to use the approximation as a tool so that we can actually do the math in our head on the fly, so we need to be comfortable with the differences.
Since we are working in a very limited universe (remember there are only 169 starting hand combinations) I highly recommend just finding and printing out an outs and odds chart and getting a general feel for the numbers behind the outs and how they compare to the approximations and whether or not you think you need to adjust the approximations.

True gamblers will want to express this percentage as odds (and there is come justification in this as you will need to compare this number to your pot odds, which we will cover in the next part of this series, to help with our decision making.)

So how do we express this as odds? To me this is more complicated math, but here it is and, as always, I’ll try to keep it simple.
Since we are talking percentages, we are always working with a base of 100% and dividing that 100% up in two parts to compare those parts to each other. If we have a 36% chance of making our hand, that means we have a 64% chance of NOT making our hand (100-36=64).

The way to express this in odds is to compare the ratio of the two numbers. The ratio here is 64 to 36 against you making your flush. You’ll need to reduce that down to something versus 1 to have a usable number to compare to pot odds. You can keep dividing each number by 2 until you get close and then you can estimate to have a usable number. 64 to 36 is 32 to 18 is 16 to 9. If this were 16 to 10 then it would be 1.6 to 1 against. It’s a little more than that against so add .2 to make it 1.8 to 1 against. Note here that the actual mathematical computation is 1.77 to 1. Please be careful when estimating as that can produce a number further off than you expect.

That is how to covert your outs into percentages (and odds). Don’t be intimidated by the math of this. The best thing to do is print out a chart and use that until you are comfortable with doing this math in your head.
In the next installment, we will talk about the basics of the next mathematical concept, pot odds.