You can set the calculator to determine the odds of you winning with that flush draw and compare that to the pot odds you received. If the poker hand simulator says you only win the hand 19% (4 to 1 odds) of the time, but you had to call a pot-sized bet to see the river (2. Pairs always look great, but often in one-on-ones you may be no more than a 50-50 shot to win the hand. Premium pairs should always be raised pre-flop, but 'set mining' with smaller pairs in Early.

• Poker Hands Chance Of Winning Calculator
• How To Win More Poker Hands
• Poker Hand Chances
• Poker Hands Chances Of Winning Golf
• Poker Games Winning Hands

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

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.

Poker Hands Chance Of Winning Calculator

Poker odds can appear confusing at first, but once you understand some of the basic fundamentals about how they work, not only will you have a much better understanding of the game itself, but you’ll also stand a higher chance of winning while playing the game.

In this post, we’re going to take a look at all forms of poker odds, from poker hand odds, how to calculate poker odds, the best poker winning hands, and more – and we’ll begin by taking a look at how exactly the odds work in conjunction with the game.

How Poker Odds Work

To look at how poker odds actually work, it can be handy to use an example of a football game. Let’s say the Chargers are playing the Eagles. A bookmaker may give the Eagles 3:1 odds to beat the Chargers. This means that for every $1 you staked, you would win $3, were the Eagles to win.

This, of course, roughly equates to the Eagles having a 1 in 3 chance of beating the Chargers – and this is the general ethos of how odds work, both in sports betting, and poker.

The higher the odds, the less chance you have of winning – and subsequently, the lower the odds, the more chance you have of winning.

Poker Hand Odds

One of the most common scenarios you’ll hear about odds in poker, is when looking at your “outs”. We’ll cover this in the section below – in this part of the guide, we’re going to look at the actual odds of getting some of the most popular and sought-after poker hands.

• Being Dealt Pocket Aces: Pocket aces are the premium starting hand in ALL Texas Hold’em games, and the odds of being dealt two aces is 0.4525% – equating to odds of 1:220. This means that you can expect to be dealt pocket aces once out of every 220 hands you play. (An interesting statistic is the chances of both you AND your opponent being dealt pocket aces. In this situation, the probability is just 0.0816%, equating to odds of 1:1,224!
• Hitting a Set on The Flop: Most players will always try to reach the flop when they hold a pair in their hand, pre-flop, as, if they’re able to make a 3-of-a-kind hand, they stand a very good chance of winning against their opponents. If you hold a pair pre-flop, the chances of hitting a set on the flop are relatively good; the probability is 11.7551%, equating to odds of 1:8.
• Hitting Quads: 4-of-a-kind is one of the strongest hands in Texas Hold’em, and it’s a hand that – despite being very hard to get – probability wise, isn’t actually too hard! The probability of making quads if you have a pair pre-flop, and make it all the way to the river, is 0.8163%, equating to odds of 1:122. Things become a little crazier when you look at the chances of two players hitting quads; in this case, the probability is just 0.0003%, equating to odds of 1:312,663!
• Royal Flush: The unbeatable hand – the hand all players dream of getting – a Royal Flush is the best possible hand in Texas Hold ‘Em poker, and cannot be beaten. Interesting, the board will only allow for a Royal Flush 1 in 59 times – and the odds of just ONE player making a royal flush at a full 9-person ring game is 1:3,628.

That’s just a few of the most common poker odds scenarios. It can be useful to have a rough idea of the odds for various hands and occurrences – but for the most-part, you don’t need to think into it too deeply, as the more important thing to worry about is the odds of you hitting your “outs”.

Outs and How to Use Them to Calculate Probability in Texas Hold’em

In Texas Hold’em poker, if you require an additional card, or more than one card to complete your hand, you’ll be looking to hit what’s known as an ‘out’.

For example, say you hold 5, 6 off-suit pre-flop, and the board comes King, 7, 8. You now have an up-and-down straight draw, meaning you need to hit either a 4 or a 9 to complete a straight – a strong hand that gives you a very good chance of winning over your opponents.

Now, in a 52-card deck, there are four 4’s, and four 9’s, which means you have 8 cards out of the 52 to hit your hand. However, you’ve already been dealt two cards – and there are three showing on the flop – which means the actual probability of hitting one of the cards you need is 8:47.

This means that approximately one in 6 times the turn card is dealt, you’ll hit your hand. Now, you may be thinking “why is this important” – and there are two reasons.

The first, is the simple fact that it’s good to know how likely you are to hit your hand. The second, and far more important reason, is that knowing how many outs you have allows you to make solid mathematical decisions, when faced with a bet. We’ll look at this in the following section.

Should You Call an Opponent’s Bet?

Using the example above, we can safely say that you’ll hit your hand – on average – once in every 6 times when the turn card is dealt.

Now, let’s say there is currently $40 in the pot, and your opponent bets $10. There are no other players in the hand.

In order to see a turn card, you must call $10. With the $40 in the pot, and the $10 your opponent bet, that means you’re required to risk $10, to have the potential to win $50. This means you’re getting 1:5 on your money – which means that over the long run, this would be a losing play, to call.

Now, say that there was $80 in the pot already, instead of $40. Now, when your opponent bets $10, you have to call $10 to have the chance of winning $90 – meaning you’re getting 1:9 on your money. In this scenario, it would almost always be a profitable decision to call, as, while you won’t always hit your hand, you’re getting odds that make it worthwhile, as over the long-run it would be a profitable, winning move.

That’s just one example, and of course, things become more complex when you start involving multiple players, and factoring in the possibility of re-raises. That being said, it should serve as a good starting-point for you to learn more about “outs”, and how they tie in with poker odds.

Tips to Improve Your Knowledge of Poker Odds

Like many things in life, having a firm grasp of poker odds and poker statistics takes time. There is no “quick-fire” way to memorize everything about odds, and how to use them in your game, and much of it comes from practice.

Thankfully, there are many great poker theory books available to purchase today, that you can use to improve your knowledge of the game and determine your odds of hitting your poker outs.
It’s worth pointing out that poker theory can become very complex – and even things like the poker outs example we looked at above can become difficult, when looking at things like reverse-implied odds.

As a general rule of thumb, the best thing to do is to simply stay calm while playing, and figure out how many cards you need to hit your hand. Calculate whether you’re getting the right pot odds to call to try and hit one of your poker outs – and don’t forget to factor in the fact that if there are multiple players to act after you, there’s a chance you may get raised and subsequently forced out of the hand.

Things to Remember

It’s important to note that many times, you’ll probably find that you simply don’t have time – or you forget – to work out the odds, especially when you’re in the middle of a hectic hand. However, try to brush up on your knowledge of poker winning hands from time to time, as you’ll find that this will soon become concreted within your brain, helping you to get a firm grasp on the game.

Frequently Asked Questions

Below, we’re going to finish this guide by answering a few commonly asked questions about poker odds.

How to Work Out Outs In Your Head

Like we just mentioned, there will often be times that it just seems too confusing, or hard to work out the odds in your head. When you find yourself in situations like these, one of the best pieces of advice we can offer, is to just slow down, take a deep breathe, and keep yourself calm and collected.

In most Texas Hold’em games, you’ll have ample time to think about the hand, and the odds – and if you’re looking for a quick way to work them out, it can help to brush up on some of the more common situations you’ll come across. For example, if you hold a pair pre-flop, and find yourself against a player holding two over cards, there is pretty much a 50/50 chance of you winning the hand.

Things like this can help – but above and beyond, it all comes down to practice as we keep mentioning, so spend a few minutes every day reading about poker statistics, and you’ll soon find that it becomes second nature to you!

What Are Outs?

The “outs” are the cards that you can hit to complete your hand. Say, for example, that you hold 2 cards that are suited hearts, and the flop contains another two cards that are hearts, and one spade. You “outs” are the remaining heart cards in the deck that can be drawn on the turn or the river, to help you complete your hand.

How to Count Outs

To determine how many outs you have, you simply need to work out how many cards there are in the deck that help you to complete your hand – and then minus the two hole cards you’ve been dealt, and the community cards currently visible.

Odds of Winning Poker

Some of the most common poker hands that you’d want to know the odds of, include an open-ended straight draw, which has odds of approximately 6/1, four-to-a-flush, which offers odds of around 4/1, an inside straight draw, which is approximately 10/1, and having a pair pre-flop which then turns into a set when the community cards are dealt, which is approximately 8/1.

How To Win More Poker Hands

Odds of Being Dealt Poker Aces

Poker Hand Chances

The odds of being dealt pocket aces in a standard Texas Hold’em game is around 220/1. This means that every 220 hands you play, you can expect to see pocket aces once – although, as is the case with ANY type of gambling, it could be 2,000 hands before you see aces… or you may see them back-to-back. It’s all a game of chance at the end of the day.

Chances of Winning with Pocket Aces

Poker Hands Chances Of Winning Golf

Pocket aces are – by far – the strongest starting hand in Texas Hold’em, and the chances of you winning with them largely depends on how many players are also in the hand with you. As a general rule of thumb, if you hold pocket aces on a 9-player table, you have odds of around 25% to win the hand at showdown – but the odds of you winning improve as more players drop out of the hand, so it can often be a good idea to play aces aggressively to avoid too many players joining the hand.

Poker Games Winning Hands

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