»»WHAT IS POKER MATH? GUIDE TO POKER MATHEMATICS

# WHAT IS POKER MATH? GUIDE TO POKER MATHEMATICS

Poker
2023 Sep 1 8 min read

While many will view a poker game as that involving pure chance and luck, there is more than meets the eye.

The poker table can be a daunting place, regardless of whether you are a novice or experienced player, and even some modern poker players prefer competing in a high stakes environment.

But there is also poker math to take into consideration, including probabilities, which in turn, will affect the pot odds at poker tables.

In this guide, we will explain how the decision making process affects the pot odds in the long run, and how you can use poker to probe a seemingly certain probability of landing say suited connectors or producing a winning hand in the later streets.

## IS POKER LUCK OR MATH?

To label a poker game as being purely down to luck would be frankly ludicrous, as there are so many aspects to untangle.

When you play poker, there are other forces at play, and the poker math element shouldn’t be underestimated, especially when you assess the implied odds of making, for example, a flush or straight draw.

The successful poker player will be able to make more money from the preflop to the latter stages not simply through stifling opponent bets.

Moreover, they will be able to understand the value of poker hand equity, and apply some poker math to bolster their chances of grabbing more money from the total pot.

## MATH AND ITS IMPORTANCE IN POKER GAME

Regardless of the level you play poker at, whether it be as a beginner or at intermediate level, poker math has a big bearing on the actual game.

Things can change very quickly on poker tables, and this is something that doesn’t go unnoticed by most modern poker players.

Having position is crucial, and math is needed to work out some of the game’s most basic concepts, such as fold equity, the number of outs, or even the chances of gaining a royal flush in the big blind.

### WHEN TO USE MATHEMATICS WHILE PLAYING POKER

Poker math can provide some brilliant insights, not just into the pot odds, but also in terms of determining tactics for small blind calls.

Also, in particular pre flop situations, a game of poker can influence a player as to when they should make the call to put their opponent on the back foot or whether they should fold early if they fear their bet may not last several rounds.

In the later streets, a player may use poker math to their advantage to determine whether to make a semi bluff or a full bluff into getting their opponent to think they have a top pair or a full house.

There may be a time that you are holding a nut flush (best possible flush), and if you have an overcard, then you can pair an ace, which means you can top what your opponent bets.

You can also use poker math to calculate outs, where, for example, a flush draw boasts multiple outs (King of Clubs, 9 of Clubs, 8 of Clubs, and 5 of Clubs).

In the following section, we will look more closely at the pot, and assess the pot odds and how to calculate them.

## WHAT ARE POT ODDS AND HOW DO THEY WORK?

Is maths important in poker? In short, yes, it is, as it helps establish pot odds. The pot odds show what you stand to make at the end of the game if you are successful with your bet.

Let’s say the pot for a game stands at \$150, and your opponent bets \$100, then the total pot will stand at \$250.

The above number will therefore be the total pot that poker players seek to obtain. In the next section, we will explain the pot odds calculation process.

### HOW TO POT ODDS CALCULATION?

In terms of calculating pot odds, if we use the above example where the total pot is \$250, then some basic poker math can be applied:

Firstly, divide the size of the call by the size of the final pot for a game of poker. So, if the call size were \$100, then you would divide the call size by the pot size (\$150 call size/\$250 final pot size) which equals 0.6.

You would then need to multiply 0.6 by 100 to convert the decimal into a percentage (60%), which would show how often you could make a winning hand. If you went all in, then you would come out on top 60% of the time with hand combinations, so the odds would be in your favour.

You would therefore need to take into what your opponent makes and card equity to defy the odds and win if you play tightly in range.

## THE MOST IMPORTANT BASICS OF POKER MATH

Implied odds and understanding how poker math is a vital element for poker players, especially if they want to advance in a game.

As you’ll see, it’s not just about picking up habits gathered from reading an opponent’s bet on several occasions or what is in the total pot. It is also about assessing board texture, so you can land, for example, pocket aces or a royal flush.

In the following section, we will explain how winning players are canny at assembling top hand combinations to extract more cash from the pot.

### COUNTING OUTS IN POKER

Depending on which stage of the game you are at, counting odds is a principle part of poker math.

Counting odds isn’t that difficult, and the outs will show your chances of landing a better hand to stop your opponent from winning. Outs come out of the flop, and you will be working with five cards here.

So, for example, in a flush draw, you may be holding two hearts in the straight draw, and two hearts are sitting in the flop. As we know there will be 13 hearts in the 52-card deck, therefore, providing nine outs to make your straight flush.

In a straight flush draw, you may discover an ace, which is viewed as an overcard on the table, and landing any of the other aces could contribute to a top pair.

As such, if you are holding any of the aces and are still intact of the hearts, then the odds of winning the pot will dramatically increase when you hit enter in an online game come the streets or the river.

Inevitably, the more confident you are when you bet and understand drawing hands, then the more likely you are to win and land the pot.

Below, we have outlined a few flop situations where you can turn a good bet into an excellent wager:

• Inside Straight Draw – 4 outs to a straight.
• Open Ended Straight Draw – 8 outs to a straight.
• Set: 10 outs to a full house or four of a kind.

We have also provided a table showing specific outs for Texas Hold’Em and Omaha games.

Hold’Em and Omaha Draws

Specific Draws in Hold'Em and OmahaOuts
Flush draw with two overcards or a straight flush draw15 outs
Flush draw with one overcard12 outs
Flush draw9 outs
Open-ended straight draw8 outs
Two overcards6 outs
Gut-shot straight draw4 outs

### CALCULATING EQUITY

The implied odds for calculating equity are closely connected to the outs part of poker, and these are two elements of poker that will make the difference between a winning player and one that loses more often than they win.

So, as the number of outs begins to increase when competing for the total pot, there is a simple calculation that can be used, known as the rule of two and four, which will help with establishing a relationship between outs and equity for a current bet.

The formula is as follows:

Equity = (Amount of outs x 4) – (Number of Outs – 8).

Say there were 15 outs, we would do the following calculation:

Equity = (15 x 4) – (60-7). The Equity would therefore work out as 53%. The formula used is as true to the actual equity (54.1%), and it is quite reliable in terms of odds hitting say a two pair with a bet.

Therefore, when you are calculating implied odds for equity, you should only consider outs with a bet that will bolster your chances of claiming a win and landing cash from the pot.

## POKER MATH IS NOT DIFFICULT

Poker math essentially isn’t that difficult to get to grips with, and the more advanced you are as a player, the more confident you will feel with incorporating a strategy to bolster your odds of winning the pot.

Ideally, before you take part in a poker game and compete for what is in the pot, it is best to test out a game in demo mode first, so you can get a feel for the pace of it and understand the pot odds before trying to test yourself.

There are, of course, plenty of study materials out there and a bank of tutorials that explain pot odds in more detail, so you don’t feel lost.

In the next section, we will outline some poker math applications that dissect total pot odds and how to win in more detail.

## POKER MATH APPLICATION EXAMPLES

Poker, as you may have gathered by now, can inevitably be challenging, and if you want some tools to bolster your chances of claiming a pot win, then the following should be useful.

They are also available as iOS and Android apps, so you can download them and use them at a time that is convenient for you.

• Poker Odds Teacher – This is a fabulous free-to-use app for working out pot odds and outs, and it has been well received by Apple holders too.
• Fun Poker Math – As the name of this app suggests, this is designed to be more entertaining rather than placing too much of an emphasis on pot odds. You should see it more as a puzzle designed to push your mathematical skills to the limit.
• Enterra Poker calculator – This has a modern feel to it, and it comes with voice and picture input, so you can say a card, such as “Jack of Heart” and see what your win percentage be if you were dealt this card.

## POKER MATH IN TEXAS HOLD’EM

Poker math is critical when it comes to Texas Hold’Em, especially when it comes to pot odds, and players can use math as building blocks for how a game might transpire.

It ultimately boils down to the starting hand you have, and in multiplayer pots, you need to have a better starting hand on average than your opponents if you are going to stand a chance of claiming a win.

This version has a 52-card deck, and position will dictate your pot odds. So, for example, if you wish to complete a straight, you will be aware that there will be eight cards in the deck that will help you achieve your aim, while 38 won’t.

You can establish a ratio by dividing 38 and 8 which gives you 4.75 or a 4.75% chance of landing a straight.

Those players who appreciate poker math in Texas Hold’Em will be able to get the most out of high stakes situations.

## CONCLUSION

Whether you like it or not, poker math is part and parcel of the game, and those who will thrive, will be well versed in applying mathematics to their strategy to generate winning outcomes.

There are plenty of study materials and apps which will break down the key concepts for four suits, so have a read and see what you think.

### ⭐ What is EV (Expected Value)?

Expected value reflects the amount of money that a certain play will either win or lose. Ideally, you should make a play that has the higher expected value, such as a pocket pair, so you can end up taking more from the final pot.

### ⭐ What is a random variable in poker?

This is denoted by the value V and it represents the nine different values of cards from 0 to 8.

### ⭐ What are implied odds in poker?

The implied odds will represent the chances of scooping a big sum of cash if you make your combination by hitting the outs. Advanced poker players will have this at the forefront of their minds.

### ⭐ Is using poker math a chance to win big?

Poker math can make a big difference to a poker game, however, it is not the be-all and end-all. Strong players will have an innate understanding of the game to prevent an opponent winning.

### ⭐ Can poker math be part of your strategy?

Yes, you can use it for your strategy, but as mentioned before, you need to understand all areas of poker and have a solid knowledge of the rules to improve.