➧ Do you know what poker math is and when to use it?
➧ Is it really that important for poker players to understand?
➧ Can you calculate in real time when a situation becomes profitable based on pot odds?

Let Team Fearless River show you how poker math works and how you can use it to improve your poker decisions and play your next session with more confidence.

Many people hate math, but there's no escaping its importance at the poker table. The truth is that you don't need to be an expert at poker math to beat the games. However, using poker math is something that differentiates the best poker players from the average ones.

So, if you want to upgrade your poker strategy and improve your win rate, make sure your poker math knowledge is up to par.

There are many different strategies in poker, but no matter which one you use or how your luck runs, poker is a game of probabilities.

When we use poker math, we use it to make the right decision and calculate if the odds are in our favor. This means poker math helps you decide whether a call is profitable.

Poker math tells us whether it's worth putting money into the pot to chase after a particular card and how likely you are to hit it.

To understand how poker math actually works you need to become familiar with two key elements: outs and pot odds. These two elements are crucial for the decision-making process.

So let's get started!

Poker Math: Outs

➧ What Are Outs? The cards that can come on the flop, turn, or river that are likely to improve your hand.

When evaluating a poker hand, the first step is to consider how many outs we have and how likely it is that an out will be dealt in the specific scenario.

To understand the basic concept of outs, you can watch Fearless River Strategy Episode 37, which explains how to do basic calculations to determine outs with easy-to-use shortcuts. If you haven't already reviewed the Strategy Episodes on outs and pot odds, you definitely should check those before diving into the world of poker math.

Poker Math: Pot Odds

➧ What Are Pot Odds? The odds a player gets to continue in the hand, specifically a ratio comparing the size of the pot to the size of the bet.

To determine pot odds, determine how much is in the pot and then compare that amount to how much it costs to call the bet. Note that any opponent's current bet is considered part of the pot.

Your poker decisions should be fundamentally based on pot odds. The key to profitable poker is understanding pot odds and basic math so that when it comes time for decisions, you will be able to consistently make profitable ones.

Understanding the odds is also key to playing draws effectively. After some practice, basic odds calculations won't take you a lot of time at the table and will help improve your poker strategy by using simple math. Your goal for learning about odds is to gain a repeatable skill to help evaluate decisions based on facts and data.

Math Shortcut: The Rule of 2

➧ The Rule of 2 is a shortcut to calculating your percentage chance of hitting one of your outs on the next card to come. To use the Rule of 2, multiply the number of outs x 2 and the result gives you the percentage chance of hitting one of your outs on the next card.

The best way to learn is from an example: We have 9♣8♣ and the board is 3♥4♣Q♣. We have a flush draw and we are heads up on the flop. Our single opponent bets $1000 into $1000 pot. Remember that when talking about pot odds, we have to include any bet from our opponent that is already in the pot. So in this situation, there is $1000 in the pot plus our opponent's $1000 bet meaning the total amount that we could potentially win by continuing is now $2000.

The next step is to compare the total amount we could potentially win to the amount it costs us to call. In this case, it costs us $1000 to continue and there is $2000 in the pot. So our pot odds are 2:1. There are two units to win, and it costs us one unit to call.

As a rule of thumb, you can know that any time you are facing a pot-sized bet you're getting 2 to 1 pot odds.

Now put it together. With 9 outs, the Rule of 2 gives you roughly an 18% chance of hitting your flush on the turn. Getting 2:1, you need to win at least 33% of the time to break even. Since 18% falls well short, calling is not profitable on pot odds alone. That’s where implied odds come in, which we cover below.

What About the Rule of 4?

➧ The Rule of 4 is applied in mostly the same fashion as the rule of 2 except that it can only be used on the flop when one player is all-in and you are facing the decision to call.

Let's use that same example: We have 9♣8♣ and the board is 3♥4♣Q♣. We have a flush draw and your opponent goes all-in.

In this case, you would determine how many outs you have to make your flush, then multiply by 4 to determine the percentage chance of hitting your flush. There are 13 total cards of each individual suit and we can see 4 of them currently (2 in our hand and 2 on the board), so we can subtract 4 from 13 and get a result of 9 outs.

Then using the rule of 4 we multiply 4 x 9 for a result of 36, so we have roughly a 36% chance of hitting our flush draw on the next 2 cards to come. It is important to only use the Rule of 4 for situations where you are on the flop facing an all-in and guaranteed to see the next 2 cards if you call.

TNow put it together. If the all-in is about the size of the pot, you’re getting 2:1 and need 33% to break even. With roughly a 36% chance to hit by the river, calling is profitable.

Here Are Some Tips for Practicing:

When practicing your poker strategy, start paying attention to pot odds and how to apply the Rule of 2 or The Rule of 4 to determine your percentage chance of winning.

Watch additional Fearless River Strategy Episodes on this subject to get comfortable with poker math and keep in mind the fundamentals of pot odds at all times. Check out Episode 41 and Episode 39 for more about this topic and others we are discussing in this article.

Now that you have the basics on determining pot odds and outs, we can introduce another key concept of poker math, implied odds.

Poker Math: Implied Odds

➧ What Are Implied Odds? Implied odds are basically when we're not getting the correct direct pot odds to call the current bet, however, if we call now we anticipate winning more chips on future streets.

Implied odds are an important factor when determining profitable preflop calling. A common guideline is to call with speculative hands, like small pairs and suited connectors, only when the call costs about 5% of the effective stack or less, in multiway pots.

We're investing a small amount now with the expectation of being able to win a larger amount later. That's at the heart of implied odds. We are hoping to make up for the fact that we're not getting the right direct odds right now in exchange for the possibility of winning more chips on later streets.

When it comes to using implied odds for decisions on the flop and turn, it's crucial to understand when you are getting them. A few factors can help you determine whether or not you are getting implied odds in a specific situation:

➧ Look at Chip Stacks
You need to ensure that there are additional chips to win on a future street to make up the difference. If your opponents are all-in or nearly all-in, then you may not be able to win enough chips to make up for calling without proper odds on previous streets. As a general rule of thumb, the deeper chip stacks are, the easier it is to win additional chips on a future street and more likely you have implied odds.

➧ Look at Your Position
When you’re in position, you act last, so you’ll win more on average than when out of position. Of course, like in every rule, there are a few exceptions but it's rare to have an advantage from out of position. Once you have position, it's easier to extract more chips from your opponent on future streets. That means that your implied odds go up when you're in position and go down when you're out of position.

➧ Look at the Number of Opponents
The more opponents in the hand, the more likely you are to get paid off. When you have just one opponent, they often just fold if you take aggressive action. So if you hit your draw on a future street against one opponent, many times they'll just check and fold. In the case of multiple opponents, you're much more likely to get paid off as the likelihood that one of your opponents will have a hand that they will continue with increases. The more opponents you have postflop, the better your implied odds are with your draw.

➧ Estimate Your Opponent's Range of Hands
Ask yourself how likely your opponent is to have a good hand or a premium hand. For example, if an opponent had raised in an early position at the table, then you're more likely to extract chips from that opponent postflop after you hit your draw. That is because their range is comprised of more premium hands and they are much more likely to have a hand to pay you off with. When an opponent raises from an early position or otherwise indicates they have a narrow range of hands or premium hand, then your implied odds go up. It will be much easier on average to win chips from an early position opponent when you hit your draw.

➧ Look at How Disguised Your Draws Are
It is well known that some draws are more evident than others. The most obvious draws tend to be flush draws, and you can spot flush draws on the flop fairly easily. More disguised would be the straight draws. Your implied odds tend to go up as you get more disguised with your draws. While straight draws have one fewer out than flush draws (eight vs nine outs), they actually have better implied odds because the straight draw is often more hidden.

You’ve learned how to determine the two most critical components of poker math (outs and pot odds). Now it's time to practice.

Stay focused on practicing counting your outs, looking at your pot odds, calculating your hand odds, and analyzing whether you have implied odds. Review episodes multiple times and remember, practice makes perfect.

Our goal with Fearless River is to empower players to ask questions, help them stay focused on the key factors that affect play, and provide answers from winning professionals through a solid game plan. We’ve helped players from around the world of all experience and skill levels, and we can help you find your leaks and learn new strategies that can help you have more fun playing poker.

Good luck and good playing,
Team Fearless River