In our poker math and probability lesson it was stated that when it comes to poker; “the math is essential“. Although you don’t need to be a math genius to play poker, a solid understanding of probability will serve you well and knowing the odds is what it’s all about in poker. It has also been said that in poker, there are good bets and bad bets. The game just determines who can tell the difference. That statement relates to the importance of knowing and understanding the math of the game.

1. Poker Odds Chart Explained Calculator
2. Poker Odds Chart Explained Interpretation
3. Poker Odds Chart Explained Percentile

Poker Odds Explained – Pot Odds. Poker odds tell you how often an event fails to occur. In other words, how many times you’re going to lose versus how many times you’re going to win. A simple to way to use poker odds to your advantage is to compare them to pot odds and determine whether you’ll be able to play profitably or not. You will improve it on the turn: 9.2=18% and real poker odds are around 19%; You have a straight draw on the flop with 8 outs. You will improve it on the turn: 8.2=16% and real poker odds are around 17%; You have two over cards on the turn with 6 outs. You will improve it on the turn: 6.2=12% and real poker odds are around 13%.

In this lesson, we’re going to focus on drawing odds in poker and how to calculate your chances of hitting a winning hand. We’ll start with some basic math before showing you how to correctly calculate your odds. Don’t worry about any complex math – we will show you how to crunch the numbers, but we’ll also provide some simple and easy shortcuts that you can commit to memory.

Basic Math – Odds and Percentages

Odds can be expressed both “for” and “against”. Let’s use a poker example to illustrate. The odds against hitting a flush when you hold four suited cards with one card to come is expressed as approximately 4-to-1. This is a ratio, not a fraction. It doesn’t mean “a quarter”. To figure the odds for this event simply add 4 and 1 together, which makes 5. So in this example you would expect to hit your flush 1 out of every 5 times. In percentage terms this would be expressed as 20% (100 / 5).

Here are some examples:

• 2-to-1 against = 1 out of every 3 times = 33.3%
• 3-to-1 against = 1 out of every 4 times = 25%
• 4-to-1 against = 1 out of every 5 times= 20%
• 5-to-1 against = 1 out of every 6 times = 16.6%

Converting odds into a percentage:

• 3-to-1 odds: 3 + 1 = 4. Then 100 / 4 = 25%
• 4-to-1 odds: 4 + 1 = 5. Then 100 / 5 = 20%

Converting a percentage into odds:

• 25%: 100 / 25 = 4. Then 4 – 1 = 3, giving 3-to-1 odds.
• 20%: 100 / 20 = 5. Then 5 – 1 = 4, giving 4-to-1 odds.

Another method of converting percentage into odds is to divide the percentage chance when you don’t hit by the percentage when you do hit. For example, with a 20% chance of hitting (such as in a flush draw) we would do the following; 80% / 20% = 4, thus 4-to-1. Here are some other examples:

• 25% chance = 75 / 25 = 3 (thus, 3-to-1 odds).
• 30% chance = 70 / 30 = 2.33 (thus, 2.33-to-1 odds).

Some people are more comfortable working with percentages rather than odds, and vice versa. What’s most important is that you fully understand how odds work, because now we’re going to apply this knowledge of odds to the game of poker.

The right kind of practice between sessions can make a HUGE difference at the tables. That’s why this workbook has a 5-star rating on Amazon and keeps getting reviews like this one: “I don’t consider myself great at math in general, but this work is helping things sink in and I already see things more clearly while playing.”

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Counting Your Outs

Before you can begin to calculate your poker odds you need to know your “outs”. An out is a card which will make your hand. For example, if you are on a flush draw with four hearts in your hand, then there will be nine hearts (outs) remaining in the deck to give you a flush. Remember there are thirteen cards in a suit, so this is easily worked out; 13 – 4 = 9.

Another example would be if you hold a hand like and hit two pair on the flop of . You might already have the best hand, but there’s room for improvement and you have four ways of making a full house. Any of the following cards will help improve your hand to a full house; .

The following table provides a short list of some common outs for post-flop play. I recommend you commit these outs to memory:

Table #1 – Outs to Improve Your Hand

The next table provides a list of even more types of draws and give examples, including the specific outs needed to make your hand. Take a moment to study these examples:

Table #2 – Examples of Drawing Hands (click to enlarge)

Counting outs is a fairly straightforward process. You simply count the number of unknown cards that will improve your hand, right? Wait… there are one or two things you need to consider:

Don’t Count Outs Twice

There are 15 outs when you have both a straight and flush draw. You might be wondering why it’s 15 outs and not 17 outs, since there are 8 outs to make a straight and 9 outs for a flush (and 8 + 9 = 17). The reason is simple… in our example from table #2 the and the will make a flush and also complete a straight. These outs cannot be counted twice, so our total outs for this type of draw is 15 and not 17.

Anti-Outs and Blockers

There are outs that will improve your hand but won’t help you win. For example, suppose you hold on a flop of . You’re drawing to a straight and any two or any seven will help you make it. However, the flop also contains two hearts, so if you hit the or the you will have a straight, but could be losing to a flush. So from 8 possible outs you really only have 6 good outs.

It’s generally better to err on the side of caution when assessing your possible outs. Don’t fall into the trap of assuming that all your outs will help you. Some won’t, and they should be discounted from the equation. There are good outs, no-so good outs, and anti-outs. Keep this in mind.

Calculating Your Poker Odds

Once you know how many outs you’ve got (remember to only include “good outs”), it’s time to calculate your odds. There are many ways to figure the actual odds of hitting these outs, and we’ll explain three methods. This first one does not require math, just use the handy chart below:

Table #3 – Poker Odds Chart

As you can see in the above table, if you’re holding a flush draw after the flop (9 outs) you have a 19.1% chance of hitting it on the turn or expressed in odds, you’re 4.22-to-1 against. The odds are slightly better from the turn to the river, and much better when you have both cards still to come. Indeed, with both the turn and river you have a 35% chance of making your flush, or 1.86-to-1.

We have created a printable version of the poker drawing odds chart which will load as a PDF document (in a new window). You’ll need to have Adobe Acrobat on your computer to be able to view the PDF, but this is installed on most computers by default. We recommend you print the chart and use it as a source of reference. It should come in very handy.

Doing the Math – Crunching Numbers

There are a couple of ways to do the math. One is complete and totally accurate and the other, a short cut which is close enough.

Let’s again use a flush draw as an example. The odds against hitting your flush from the flop to the river is 1.86-to-1. How do we get to this number? Let’s take a look…

With 9 hearts remaining there would be 36 combinations of getting 2 hearts and making your flush with 5 hearts. This is calculated as follows:

(9 x 8 / 2 x 1) = (72 / 2) ≈ 36.

This is the probability of 2 running hearts when you only need 1 but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the 9 remaining hearts:

9 x 38 ≈ 342.

Now we know there are 342 combinations of any non heart/heart combination. So we then add the two combinations that can make you your flush:

36 + 342 ≈ 380.

The total number of turn and river combos is 1081 which is calculated as follows:

(47 x 46 / 2 x 1) = (2162 / 2) ≈ 1081.

Now you take the 380 possible ways to make it and divide by the 1081 total possible outcomes:

380 / 1081 = 35.18518%

This number can be rounded to .352 or just .35 in decimal terms. You divide .35 into its reciprocal of .65:

0.65 / 0.35 = 1.8571428

And voila, this is how we reach 1.86. If that made you dizzy, here is the short hand method because you do not need to know it to 7 decimal points.

The Rule of Four and Two

A much easier way of calculating poker odds is the 4 and 2 method, which states you multiply your outs by 4 when you have both the turn and river to come – and with one card to go (i.e. turn to river) you would multiply your outs by 2 instead of 4.

Imagine a player goes all-in and by calling you’re guaranteed to see both the turn and river cards. If you have nine outs then it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds given in the chart, but it’s accurate enough.

What about with just one card to come? Well, it’s even easier. Using our flush example, nine outs would equal 18% (9 x 2). For a straight draw, simply count the outs and multiply by two, so that’s 16% (8 x 2) – which is almost 17%. Again, it’s close enough and easy to do – you really don’t have to be a math genius.

Do you know how to maximize value when your draw DOES hit? Like…when to slowplay, when to continue betting, and if you do bet or raise – what the perfect size is? These are all things you’ll learn in CORE, and you can dive into this monster course today for just $5 down…

Conclusion

In this lesson we’ve covered a lot of ground. We haven’t mentioned the topic of pot odds yet – which is when we calculate whether or not it’s correct to call a bet based on the odds. This lesson was step one of the process, and in our pot odds lesson we’ll give some examples of how the knowledge of poker odds is applied to making crucial decisions at the poker table.

As for calculating your odds…. have faith in the tables, they are accurate and the math is correct. Memorize some of the common draws, such as knowing that a flush draw is 4-to-1 against or 20%. The reason this is easier is that it requires less work when calculating the pot odds, which we’ll get to in the next lesson.

By Tom 'TIME' Leonard

Tom has been writing about poker since 1994 and has played across the USA for over 40 years, playing every game in almost every card room in Atlantic City, California and Las Vegas.

Pot odds, equity and expected value are important interrelated concepts in poker. As a beginner it is important that you understand the basics if you want to get ahead of your opponents.

The math side of poker is often ignored by a lot of new players but by simply spending a bit of time learning these simple concepts you will be able to improve your game drastically.

So we will first go through each of them individually and then a full example to tie it all together in the next few articles.

Table Of Contents

Pot Odds: The Definition

The odds which are being offered to you when your opponent bets are called pots odds. Essentially it is how much you will win vs how much you have to risk – your risk to reward ratio.

This is particularly useful when in a situation where you're facing a bet with a drawing hand (such as a flush draw). Pot odds will tell you whether is it correct for you to call or fold based on what size our opponent bet and how many cards that will improve our hand.

We can also use pot odds to determine whether or not we can call a river bet based on how often we expect our opponent to be bluffing.

Pot Odds: Using Ratios

To take an example of when we are facing a bet on the river when we have A9 of diamonds:

On the river our opponent bets $26 into a $41.5. If we called would be risking $26 and our reward is $41.5 already in the pot plus our opponents bet of $26.

This means that we are getting odds of 67.5: 26 (67.5 = 41.5+26). This is approximately 2.6:1.

Pot Odds: The Percentage Method

We can also convert that into a percentage (percentages are typically more intuitive) the result is 28%.

So if we expect to win 28% of the time or more we can call profitably.

How did we get that number?

Take the amount we have to call ($26) and divide it by the amount we have to call plus how much is in the pot:

Pot odds percentage = 26/(26+67.5) = 27.8%

Here is a summary of the numbers of outs and the pot odds associated for number of outs:

Why Are Pot Odds Useful?

It first lets us determine our risk to reward ratio. We can then use this along with the strength of our and our opponents potential hands in order to make better decisions.

If we have a very weak hand we should not be willing to call very large bets, only smaller bet sizes; in other words we must have very good pot odds in order to call.

This makes sense – if someone was to bet $1 into a $100 pot on the river we will continue with almost all of our range.

The greater the pot odds (the smaller our opponent bets) the more likely we should be to continue with our hand. Conversely, the smaller the pot odds (the larger our opponent bets) the less likely we should be to continue with our hands. The larger our opponent bets the more the requirement for an extremely strong hand.

Implied Pot Odds

Implied odds is simply the additional chips we expect to win when we hit our hand.

For example if we were to hit a flush on the turn or river, the hand won't just end – we still have an opportunity to win more money from our opponent.

This will reduce the pot odds we need to call profitably. The exception to this is when our opponent has pushed all in – we call we cannot win any more chips.

The reason we call preflop with small unpaired hands is not because we expect to have the best hand all that often; but because we expect to win a large pot when we hit a big hand such as three of a kind.

The reason we call is because with a hand like three of a kind, we have large implied odds and if we hit our hand we expect to win a big pot.

Here is an explainer video of implied odds from GreenBeanVideos:

Poker Odds Chart Explained Calculator

A Real World Example of Implied odds:

The reason you go to College or University and get a degree is not because of the return you would expect immediately after graduation. It is because of the additional value a degree would bring you in the years after gradation through income, job opportunities etc. The same applied to poker.

Unfortunately implied odds cannot be directly calculated like pot odds – we have to guesstimate the amount our opponent will be willing to pay us off after we make our hand.

If we think our opponent has a very strong hand, and we stand to make a better one, we will have large implied odds.

If our opponent has a weak hand, we will have little implied odds.

Additionally, if we believe our opponent is a very bad player we will usually have large implied odds as he will be more likely to make mistakes and pay us with hands that he shouldn't have.

Finally, if he is a good player we will have significantly less implied odds.

Here is a quick recap on everything we covered on pot odds:

Pot Odds Calculator

You do not need a fancy piece of software to work out your pot odds. As we have seen, it is simply the ratio of the bet you have to call to the size of the pot (including your opponents bet). You can also use a calculator to calculate the the percentage odds (or roughly do it in your head, you don't need to be extremely accurate)

However, on of the best pieces of software you can use in conjunction with calculating pot odds from cardschat.com.

Poker Odds Chart Explained Interpretation

This piece of software can be used to work out your pot equity which we have discussed in detail in other lessons.

Poker Odds Chart Explained Percentile

Conclusions

You should now be able to work out pot odds and when coupled with our other lessons, you should have a basic grasp on the math of poker.

Follow up this lesson first with Pot Equity and Expected Value (EV)