Poker Drawing Odds & Outs: Master Your Winning Hand!

July 4, 2023 Silas Everhart

Our poker math and probability lesson stated that “math is essential “in poker. 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 poker has good and bad bets. The game determines who can tell the difference. That statement relates to knowing and understanding the game’s math.

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 calculate your odds correctly. 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.

Table of Contents

Basic Math – Odds and Percentages

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

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 percentages 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 will apply this knowledge of odds to the poker game.

Counting Your Outs

Before calculating your poker odds, you must know your “outs.” An out is a card that will make your hand. For example, if you are on a flush draw with four hearts in your hand, then nine seats (outs) remain in the deck to give you a flush. Remember, thirteen cards are in a suit, so this is easily worked out: 13 – 4 = 9.

Another example would be holding a hand and hitting two pairs on the flop. 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 writing to a full house;

The following table briefly lists 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 lists more types of draws and gives 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 out is a fairly straightforward process. You 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 eight outs to make an explicit and nine 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 complete a straight. These outs cannot be counted twice, so our total releases for this type of draw are 15, not 17.

Anti-Outs and Blockers

Some outs will improve your hand but won’t help you win. For example, suppose you hold on to a flop of. You’re drawing to a straight, and any two or seven will help you make it. However, the loss 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 only have six good releases.

It’s generally better to err on caution when assessing your possible outs. Don’t fall into the trap of assuming that all your releases 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 only to include “good outs”), it’s time to calculate your odds. There are many ways to determine the odds of hitting these outs, and we’ll explain three methods. This first one does not require math; use the handy chart below:

Table #3 – Poker Odds Chart

As shown 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 still have both cards. 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 Adobe Acrobat to view the default PDF installed on most computers. We recommend you print the chart and use it as a reference source. 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 accurate, and the other is 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 nine hearts remaining, there would be 36 combinations of getting two hearts and making your flush with five 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 one, but this has to be figured. Of the 47 unknown remaining cards, 38 of them can combine with any of the nine remaining hearts:

9 x 38 ≈ 342.

Now we know 342 combinations of any nonheart/heart combination. So we then add the two varieties 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 the river), you would multiply your outs by two 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, it’s just a case of 9 x 4 = 36. It doesn’t match the exact odds 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). Count the outs and multiply by two for a straight draw, so that’s 16% (8 x 2) – almost 17%. Again, it’s close enough and easy to do – you don’t have to be a math genius.

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 study, 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 common draws, such as knowing that a flush draw is 4-to-1 against 20%. This is easier because it requires less work when calculating the pot odds, which we’ll get to in the next lesson.