Learn all about the Poker math essentials: Odds, outs and equity. You will not only learn how to determine your odds and your equity, but also how to quickly convert the two into each other. Calculating Poker Odds for Dummies - A FREE, #1 guide to mastering odds. How to quickly count outs to judge the value & chance of winning a hand in 2020. You can also read the Party Poker Strategy Guide's article on poker odds as well, for a full treatise on how to calculate and work with odds. You can see that a pocket pair that misses on the flop usually only has 2 outs to beat a bigger pair and 22.5 to 1 odds to catch and make a set on the turn.
As daunting as it sounds, it is simply a tool that we use during the decision making process to calculate the Pot Odds in Poker and the chances of us winning the pot. Remember, Poker is not based on pure luck, it is a game of probabilities, there are a certain number of cards in the deck and a certain probability that outcomes will occur. However, we will repeat that briefly to talk about odds, as outs and odds in poker are connected in several ways. Outs are basically cards that we need to make a complete poker hand. Let’s say that we have an Ace and a Queen of hearts, and the flop showed a two and a seven of hearts, and a five of clubs.
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. Qt signal emitted but slot not called. 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.”
Instant Download · Answer Key Included · Lifetime Updates
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.
Poker Strategy Odds Outs College Bowl
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…
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.
We have already seen how the relative strength of a poker hand can increase or decrease as flop, turn and river is dealt. For example A♣A♠ is a big favourite against A♥K♥ pre-flop, but becomes a huge underdog if the flop comes Q♥8♥2♥.
If you have a hand that is probably behind, but has the potential to improve to a winner, you need to decide whether it is worth continuing with it through the various streets, and how much you are prepared to pay to do so.
This article explains the calculations required to make the right decision about “drawing hands”, ie, hands that will need to connect with later community cards to win.
In short, you need to identify the cards that will improve your hand (known as “outs”), and then determine how significant an advantage you will have. Finally you will need to calculate your odds of winning and whether the pot size makes the whole process worthwhile.
You need to use some basic mathematics to help you make correct decisions.
“Outs” are the cards left in the deck that improve your hand and hopefully win the pot at showdown.
Example with a flush draw
You are holding A♥3♥ and the flop is: 7♥9♣K♥. If another heart appears on the turn or river, you make the flush, and unless another player has a full house or better, you will win the hand. (The board isn’t paired, so none of our opponents can have a full house yet.)
There are 13 cards of each suit in the deck. You hold two of them, and another two are on the board. Four of the 13 hearts have therefore already been dealt, meaning that there are still nine hearts left in the deck. This means you have nine outs.
Example with a straight draw
You have J♠10♠ and the flop is 6♣Q♥K♥. Now any ace or nine will complete your straight. There are four aces and four nines in the deck, so you have eight outs.
If one card is missing to complete a straight, you have four outs. For example, if your hole cards were A♥J♠ and the flop was K♣Q♥7♦, your outs would be 10♠10♣10♥10♦.
Example with a straght draw and overcards
You have K♥J♥, and the board is A♠10♦2♣. One of the four queens in the deck will make you a straight. If your opponent has a middle pocket pair, e.g. 9♣9♥, then you have additional outs, as any king or any jack would give you a higher pair.
In this case, the number of your outs would increase to ten (four queens, three kings, and three jacks).
Example with a set against a flush draw
If you hold 7♦7♥ and hit a set on a board showing 2♠7♠J♠, you have a pretty strong hand. But it is not definitely a winner and could already be behind if any of your opponents has two spades in their hands.
However, you still have the chance here of improving your hand even further. There are seven cards that could make you a full house or better (a seven, three remaining twos and three remaining jacks), or the turn and river could be the same rank, which would also give you a full house.
Example with a straight draw AND a flush draw
You hold 6♥7♥ and the board is 4♥5♣J♥. You have both an open-ended straight draw and a flush draw. This means you have nine outs to make the flush and eight outs to make the straight. At the same time, you have to consider that two cards are counted twice (in this case the 3♥ and the 8♥), which have to be subtracted. Therefore you have a total of 15 outs here.
Although the term “out” typically refers to a card that improves your hand, there are also sometimes “hidden outs”, which help you because they reduce the value of your opponent’s hand.
Example of hidden outs
You hold A♣K♣ and your opponent has 3♥3♠. The board is J♦J♠5♣6♦. Not only would the three kings and the three aces give you a higher two pair than your opponent, but any six or five would help as well. This is because with a five or six, the board contains two pairs that are both higher than your opponent’s pocket threes, meaning that the fifth card, the kicker, would decide the outcome of the hand. Your ace is the best possible kicker.
In this instance, you have 12 outs, six of which are hidden.
Advanced players don’t only calculate their own outs when on a draw. They also ask themselves what hand their opponent has, and whether one of the cards they hope to appear might also give the other player an even better hand. Cards like this are known as “discounted outs”.
Let’s look at the straight draw example again:
You have J♠10♠ and the flop is 6♣Q♥K♥. You have calculated eight outs so far (four aces and four nines).
But how will your outs change if one your opponents has two hearts e.g. 7♥6♥ and is therefore drawing to a flush? In this example, two of your outs, i.e. A♥ and the 9♥, would give your opponent a better hand – even if you hit your straight. This means you have to discount both cards from your outs. You would now only have six outs, which significantly reduces your chances of winning the hand.
In general you should take a pessimistic approach when it comes to discounting outs, as it is better to discount one out too many than one too few!
Probability and Odds
There are two very simple rules of thumb for calculating the probability of improving your hand using your outs:
The probability of hitting a draw on the next card is: [number of outs] x 2
The probability of hitting a draw on the turn and/or river is: [number of outs] x 4
A flush draw on the turn
You have a flush draw on the turn (nine outs). The probability of hitting the draw is [number of outs] x 2 = [winning probability in percent]:
9 x 2 = 18%
A straight draw on the flop
You have a gutshot straight draw (four outs) on the flop and want to know the probability of making a straight with two cards to come. The rule of thumb is: [number of outs] x 4 = [winning probability in percent]:
4 x 4 = 16%
Probabilities can be displayed as a ratio or odds, which is very helpful when playing poker.
Odds describe the ratio between the probability of winning and losing.
The winning probability is calculated as before. The losing probability is therefore:
[Losing probability] = 100% – [winning probability]
It’s best to commit the most important odds to memory, instead of having to calculate them again and again.
Examples of calculating odds
With middle pair:
You are holding A♥8♣ on a board of K♠8♥3♣2♦. You’ve got middle pair. Assume that your opponent has top pair, with K♣Q♦ for instance.
You have five outs: three aces and two eights. The probability of improving your hand is 10% (5 outs x 2). The probability that your hand doesn’t improve is therefore: 100% – 10% = 90%.
The odds are now [losing probability] / [winning probability]
In numbers: 90% / 10%. This can be simplified (both sides divided by 10), with the result being odds of 9:1.
You have K♣Q♦ on a board of 10♠9♦5♣3♥. You assume that your opponent has top pair A♣10♥.
You therefore have ten outs (three kings and three queens for a higher pair and four jacks to make a straight) and your chance of winning is 20% (10 outs x 2). The probability that your hand will not improve is calculated as follows:
100% – 20% = 80%.
The odds therefore [losing probability] / [winning probability] are 80% / 20%, the result being odds of 4:1.
Certain similar situations appear frequently in Texas Hold’em, and you should try to memorise the odds of your hand winning in those instances. The odds that are of particular importance and appear often are highlighted in the chart below.
Calculating the odds of your hand improving is only the first step in deciding whether to continue in a pot. You then need to figure out whether the size of the pot itself is large enough to warrant pressing on.
For instance it would be pointless speculating $500 with a gutshot straight draw if you only stood to win about $50. You know that the odds of hitting your draw are slim, and the financial gain of making your hand are not good enough to make the risk worthwhile.
Most cases are slightly more tricky to calculate, but the principle is the same. You have to calculate what are known as “pot odds” – the ratio between the size of the pot and the bet facing you. Then you compare those odds with the odds of your hand winning.
The size of the pot refers to the chips that are already in the pot, as well as all the bets made in the current betting round. If the pot odds are higher than the odds of you winning, you should call (or in exceptional cases raise). If the pot odds are lower than your odds of winning, you should fold.
Example with nut flush draw
You have A♥2♥ on a flop of 6♥K♠9♥, so you have the nut flush draw. You have nine outs on the flop and currently the pot is $4.
Your opponent bets $1.
There is now $5 in the pot ($4 + $1), and it will cost you $1 to call. The pot odds are therefore 5:1.
According to the table above, your odds of hitting your hand are 4:1. That means that the pot odds are higher than your hand’s chances of winning and you should therefore call.
You are paying $1 with a 4:1 chance of winning five times that amount. It is a good call – and some players might even raise here.
Example with straight draw
You have 8♦7♣ on a flop of A♣4♥5♠. This is a gutshot straight draw, meaning you have four outs (any six) to make your hand. There is $25 in the pot.
Poker Strategy Odds Outs Against
Your opponent bets $5.
There is now $30 in the pot ($25 + $5), and it is $5 to call. Your pot odds are therefore 6:1.
However, according to the table the odds of winning the hand are 10:1. You don’t have the right pot odds to continue in this hand and should therefore fold.
You would be forced to pay $5 with a 10:1 chance of winning only six times that amount. It would be a bad call.
Facing an All in bet
If your opponent moves all in on the flop, you can make the same calculations as described above, but this time look at the “Odds Flop to River” column. If your opponent is all-in, you have the advantage that no further bets are possible. If you call, you therefore get to see not only the turn, but also the river without having to risk more chips.
Example with a straight draw versus All in
You have J♣10♦ on a flop of Q♥9♠2♣, which is an open-ended straight draw. You have eight outs on the flop.
There is $50 in the pot and your opponent moves all-in for $25. You therefore have pot odds of 75 to 25 ($50 plus the $25), and is $25 to call. When simplified, the pot odds are 3:1.
If you call you get to see both the turn and the river without any further betting. According to the column “Odds Flop to River” in the odds table, the odds of winning the hand are 2:1, and because the pot odds are higher, you should make the call.
Calculating odds, outs and probabilities can seem difficult and time-consuming, especially if you are a beginner. But the basics are quite simple to understand and the ability to make simple calculations can help you build a very solid foundation for your game. This part of poker is very well worth learning, especially if you intend to progress further in the game.
Poker Strategy Odds Outs Win
If you continually play draws without getting the right odds, you will lose money in the long run. There will always be players who don’t care about odds and call too often. These players will occasionally get lucky and win a pot, but mostly they will lose and pay for it. On the other hand, you might be folding draws in situations where the odds are favorable.
If you use the strategies in this article consistently, you can avoid mistakes and gain an edge over your opponents.
Join us on our Discord channel.