Poker: Pot Odds and Equity

Overview

This instructable will cover the concepts of pot odds and equity and one of the ways you can use them to improve your poker game. These concepts are applied to gain insight to a given hand using information like pot size and number of outs. It is intended for beginner to intermediate level players who are already familiar with basic poker terminology such as raise, call, action, outs, and many others. If you do not feel comfortable with these terms or any of the basics of poker, I recommend becoming more familiar with them before attempting to learn more advanced concepts such as pot odds and equity.

Materials

This is an abstract concept and does not require any materials to learn, but having a deck of cards can help visualize the gameplay examples that are used, and having a pencil/paper can be useful for doing the initial math that is involved.

Step 1: Getting Started

Background Information

Calculating your pot odds and equity in a hand in poker are vital in giving you the information you need to make the statistically correct decision. Doing so won’t reveal your opponents hand to you, or if you will win the hand, but it will give you very useful statistical information on how advantageous your hand is, and since poker can consist of many difficult decisions it is vital to collect as much information as possible. One of such difficulties is deciding whether or not you should call an opponent's raise, and pot odds and equity can be applied together to give you a great estimation of what you should do.

Step 2: Pot Odds

What are Pot Odds?

The first of the two concepts, pot odds, is simply the ratio of the amount of money currently in the pot to the amount of money you must pay in order to make a call. For example, if there are are $1000 in the pot and you must pay $500 to call, then the pot odds are 1000:500, or 2:1 simplified. If there were $1500 rather than $1000, your pot odds would be 1500:500 instead, or 3:1.

How to Calculate Pot Odds

Normally pot odds are simply expressed as a ratio, but I believe the overall concepts of both pot odds and equity are easier to understand if they are both expressed as a percentage because percentages are easier to compare to one another than fractions. So, to calculate the percentage form of this, simply take the number representing your share (the number on the right) and divide it by the sum of both numbers. So if your pot odds were 2:1, the percentage would be 1 divided by 2+1, or 1/3, to give you 33% pot odds.

Step 3: Equity

What is Equity?

Pot odds on their own, however, do not quite give you all of the information you are going to need. In order to apply this information, you must use another concept called equity. Equity is simply your chance of winning the hand by the end of the river. This chance can either be represented with a ratio or a percent, but again, we will be using the percentage form.

How to Calculate Equity

In order to calculate your equity you must consider your number of outs, or possible cards that would win you the hand. Consider the following example:

Imagine that there are only 2 of you left in the hand, and your opponent has a pair of jacks. Drawing either the straight, or a pair of aces or kings will beat his jacks, so you have 10 outs to win out of 45 remaining cards (3 aces, 3 kings, and 4 queens). Using an odds calculator shows that this gives you about a 38% chance of hitting one of those draws and winning the hand, which means that you have a 38% equity in the hand.

Step 4: Equity (Continued)

Simplifying Equity

However, you are not an odds calculator, and making complicated calculations or memorizing odds tables are both very difficult and can require a large amount of time during a game. It is therefore considered much more practical to use the rule of 2 and rule of 4. These rules simply mean that if there is one card left to be drawn (just the river) you can approximate your percent chance to hit one of your outs by multiplying the number of outs by 2. And likewise, if there are 2 cards left to be drawn (both the turn and the river), multiply your number of outs by 4. In this example, if you have both the turn and the river left, multiplying 10 outs by 4 would give you 40%, which isn’t exactly 38%, but it is quite close and it is a worthy sacrifice to lose some accuracy in order to easily and quickly make these calculations. The above table shows the odds corresponding to 1-15 outs using this system.

Step 5: When to Not Call

How to Apply These Terms

Now that you have calculated both your pot odds and your equity you are ready to combine the two to decide if you should make the call or not. In the previous example, you have 38% equity in the hand. In other words, if you played this hand through 100 times you could expect to win it 38 of those times, and furthermore, you can expect to win back 38% of every dollar that goes into the pot. So how do you know if you should call a raise? Essentially, your equity must be greater than your pot odds. If this is the case, the profits from the 38 times you win the hand would be greater than the costs from the 62 times you lose.

This is where pot odds come in. Consider again the example, but this time, let’s be a little bit more specific: there is currently $100 in the pot, and your opponent raises $500 dollars. If you were to call, it would cost you $500 dollars to try to win a $600 total pot, so your pot odds would be 6:5, or 45%. Your equity in the hand is 38%, which is less than 45%, so you should not call his raise.

Why?

But why exactly is that? In order to understand why your equity should be greater than your pot odds, think about the implications of these two numbers. Your pots odds are 45%, so if you call you are contributing 45 cents of every dollar that goes in. However, your equity is only 38% so over the course of many hands you can only expect to win back 38 cents for every dollar that goes in. So for every 45 cents you contribute, you are only getting back 38 cents. In the long run, you are losing money, and that is why you should not call in this situation.

Step 6: When to Call

Now, let’s change the conditions so that there are $1000 dollars in the pot. Your opponent raises 500$, so there are $1500 total and you are faced with a $500 call. This time, your pot odds are much better, at 3:1, or 25%. Your equity hasn’t changed; it’s still at 38% and over the course of many hands you will win 38 cents for every dollar in the pot. But this time around, your equity is greater than your pot odds, and you are only contributing 25 cents for every dollar in the pot. You are spending 25 cents to make 38 cents for each dollar, so this time around you can expect a call to be profitable.

Step 7: Final Thoughts

Hopefully you now have an understanding of pot odds, equity, and how they can interact to give you information. This is a very useful technique for giving you tangible, statistical information on a hand, and learning it can give you some insight into the mathematical aspect of poker. After all, while being able to read your opponents is very important, poker still boils down to a game of numbers, and using these numbers to your advantage can give you the edge over your opponents.

The kind of scenario in the example used by this tutorial is but one of many applications of pot odds and equity, and there are many more advanced concepts that build on these, such as fold equity and implied odds. If you are able to incorporate this technique into your game successfully, I highly encourage you to learn more about the advanced features of poker.