Using poker odds & outs, you can calculate if you can profitably call a draw. Outs are cards which complete your draw. Odds are the winning probabilities to hit an out. In Texas Hold'em odds = outs / possible cards. To calculate the percentage by hand, use any of the following approximations:. For example, using the Goodapproximation, if you have 9 Outs, then you have a 19% chance on the turn, a 19% chance on the river, and a 38% minus 19% of 19% (close to 20% of 20%, which is 4%) equals a 34% chance on the turn and river combined.

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.

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

Poker Strategy Odds Outs Against

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:

Poker Strategy Odds Outs College Bowl

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.

Part #2 Of Our Beginners Poker Tournament Guide
Poker Odds, Outs and Expectation All Clearly And Concisely Explained!

Poker odds are a critical factor in success in online poker tournament strategy. While alone information on odds and outs will not make a player an instant winner, this knowledge will certainly give them an instantly profitable advantage over those players who do not understand these simple poker concepts correctly.

A good way to begin looking at poker odds and outs is in terms of expectation. During any game of poker we will be faced with a number of ‘bets’ at various prices. When you bet with the odds in your favor then you have a positive expectation. That is to say that regardless of the outcome of any particular hand you will show a profit over time. If you bet or call when the odds are against you then your wagers have a negative expectation, that is you will lose money over time.

The most commonly referenced form of poker odds are known as ‘Pot Odds’. This describes the price you are getting when calling a bet from an opponent compared to the current amount of money already in the pot.

For example, if the total pot - including your opponent’s last bet - was $100 and you had to call a $20 bet then your current pot-odds are exactly 5/1. Pot odds are useful when working out whether your call has a positive expectation. In this example, assuming this was the final bet of the hand, then you simply need to work out whether you have a greater than 20% (1 in 5) chance of winning the hand. If you think this is the case then calling will show a profit over time if you think your chances are lower then calling will lose money over time and your hand should be folded.

Pot-Odds can also be used before the last card is dealt. Imagine you have King-Jack of spades and by the time the turn card is dealt there are 2 other spades showing. With 1 card to come you are sure that hitting a spade will win the hand for you. In this situation you need to compare the pot-odds being offered to your chances of winning the hand. In this case you are approximately 4.5/1 against hitting that last spade (see ‘outs chart’ below for more information on this).

Thus if you are getting better than 4.5/1 odds from the pot then calling will show a profit over time. If you are getting less than this price then calling will lose money over time and you should not usually call the bet.

Looking at the current odds that you are getting by calling a bet leaves out one very important factor. You may be able to win one or more additional bets after the last card has been dealt. This is especially significant in No-Limit Holdem Tournaments where you can bet any amount you like. The additional bets you might win if you make your flush (for example) are known as the Implied-Odds and need to be factored into your expectation.

To return to the King-Jack of spades example, the pot-odds after the turn has been dealt there is $30 in the pot and your opponent bets $10 more. Here you are getting odds of 4/1 with a 4.5/1 of completing your flush, pot-odds alone indicate a negative expectation from this bet. However after the river, if you do make your flush by hitting that last spade then you estimate that your opponent will call an additional $20 bet. Your implied odds are now the $30 in the pot + $10 bet from your opponent + $20 on the river for a total of $60. This means that the real odds of your $10 call on the turn were 6/1. If you take 6/1 odds on a 4.5/1 chance then you will show a profit each time – you will have a positive expectation for the bet.

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What are Poker ‘Outs’ and how are they calculated?

During the play of any hand there are a number of the unseen cards left in play that will improve your hand, and a number that will not. Any card that will improve your current holding is known as an ‘out’. Any hand that is not yet complete, for example 4 cards to a flush or 4 cards to a straight, is known as a ‘drawing hand’ or just ‘draw’. Poker odds can be used to assess whether your play has a positive expectation if you know the basic chart of ‘outs’ that will improve your hand.

A Full Outs Chart is Below - Here are the most common poker outs:

1. 4 Cards to a Flush with 2 cards to come: Odds = 1.9/1 (35%)
2. 4 Cards to a Flush with 1 card to come: Odds = 4.1/1 (19%)
3. 4 Cards to a Straight with 2 cards to come: Odds = 2.2/1 (32%)
4. 4 Cards to a Straight with 1 card to come: Odds = 4.7/1 (17%)
5. Inside Straight Draw, 2-3-5-6, 2 cards to come: Odds = 4/1 (20%)
6. Inside Straight Draw, 2-3-5-6, 1 card to come: Odds = 10/1 (10%)

As you gain experience in using poker odds and outs you will be able to quickly calculate your winning chances using simple math. After the flop in Holdem there are 5 cards which you have seen – and so 47 unseen cards. You calculate the number of cards that will help your hand out of those unseen cards and then divide this number by 47. For example if you calculate that 10 cards will improve your hand then (10/47) = 4.7/1 odds which is approximately 21% winning chance, with 2 cards to come then doubling the winning chances is close enough for most situations. Learning the most common outs from the chart below will help you make good decisions during a hand – remember that if you take positive expectation bets you will show a profit over time!

SNG Planet Tip: A quick way of calculating your chances of making a hand after the flop (with 2 cards to come) is the ‘Rule of 4’ – Simply Multiply the number of cards to make your hand by 4! For example if you have 4 to a flush on the flop then there are 9 unseen cards of your suit that will make your hand… 9*4 = 36% which is very close to the 34.97% shown on the outs chart above! With just one card to come you multiply by 2 instead.

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