1. What Are The Odds Of Flopping A Straight In Texas Hold Em
2. Poker Hand Odds Texas Holdem
3. Texas Holdem Odds Calculator
4. Texas Holdem Odds And Statistics

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.

In Texas Hold em, what are the odds of making a one gap or two gap inside straight by fifth street starting from the flop? D from Cherry Hill, USA For the benefit of my readers, this question asks what is the probability of filling in a one or two gap inside straight with two more cards, with 47 left in the deck.

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.

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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.

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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.

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Once you familiarize yourself with basic Texas Hold ‘em play, hand rankings and dealing, you should learn about the odds and probabilities associated with different aspects of the game. While it may be impossible to calculate precise odds mid-hand, particularly given you’ll never see your opponents’ cards until all decisions have been made, knowing when to play (and when not to play) different hands typically requires more than just good instinct.

In Texas Hold ‘em, winners are often decided before the community cards are even laid out, so the chances of being dealt a strong starting hand is something many players think.

Calculating Texas Hold ‘em Odds

What Are The Odds Of Flopping A Straight In Texas Hold Em

To understand the odds of drawing any particular starting hand, you’ll have to consider all of the factors that go into the deal of a hand. Considering a shuffle to completely randomize the order of the cards, the biggest factors that will affect a draw are the number of players at the table and your own position relevant to the dealer. Also consider that there are four cards of any given value in each deck and there are 169 different hole card combinations. That being said, there’s a roughly one in 1326 chance that players will be dealt any specific hand, so it’s important to know what kind of odds you should keep in mind whenever you step to the poker table.

Pre Flop

You have a 55:1 chance of being dealt a pair of Jacks or higher.

Your Texas Hold’em experience will begin with your hole cards, and while you cannot change the cards that are dealt your way, it’s good to know what to expect. While World Series of Poker reruns may make it seem like someone at the table will be dealt pocket kings every hand, starting with a monster hand is rarer than you may imagine. For more on Pre Flop strategy see our guide here.

Quick Odds

While an extensive list of the probabilities for preflop hands could fill a book, here are some quick odds to consider when you’re peeking at your cards for the first time.

• Being dealt a pocket pair: 16:1
• Being dealt suited cards: 3.2:1
• Being dealt suited connectors: 24:1
• Being dealt AK: 82:1
• Being dealt two cards of jack or higher: 10:1
• Being dealt AA, KK, QQ or JJ: 55:1

The Flop

The flop is a game changer in every sense of the words. With more cards in your hand, players will get their first real taste of what the final outcome will look like. That being said, players will want to think about the odds for how their hand could turn out before they start placing or calling bets. For more on Post Flop strategy see our guide here.

Quick Odds

Though the presented odds may be mathematically accurate, they do present a best case scenario that you won’t always find yourself in at the table. These calculations don’t take into account the probabilities of the card or cards you are looking for turning up as burn cards or in your opponents’ hands, so keep that in mind when considering your next move.

• Hitting a pair on the flop: 2:1
• Pocket pair improving to three of a kind on the flop: 7:1
• Flop being three of a kind: 424:1
• Odds of flopping a flush with suited hole cards: 118:1

The odds of flopping a straight can be a bit harder to pin down. Depending on your starting hand, there are any number of card combinations that could lead to a flopped straight. Those hands that have the more flexibility when it comes to straight draws, particularly middling connectors (those between 5 and 9), have the strongest chances of hitting on the flop because there are more cards that could allow for their straight to hit. The wider the gap between your starting cards, the worse your chances are.

The Turn and River

Naturally, as the hand progresses and fewer cards remain to be dealt, the odds of making any particular hand become slimmer and slimmer. That being said, you’ll want to look at the odds for a hand from beginning to end as well as those from stage to stage.

Quick Odds

Your odds change as each new card is dealt.

Over the course of a full hand, these scenarios could play out

Poker Hand Odds Texas Holdem

• One pair on flop improving to two pair or a set by the river: 4:1
• Catching an ace on the turn or river: 7:1
• Open ended straight hitting by the river: 2:1
• Gutshot straight draw hit by the river: 5:1
• Pocket pair improving to set by river: 10:1
• Going runner runner for a flush: 23:1
• Going runner runner for a straight: 67:1

Pot and Implied Odds

In addition to the odds that your cards will pair or better, experienced players know that pot odds, that is, the ratio of the size of the pot to the cost of a call, play an important role in proper Hold’em strategy. With all of the risks that are inherently involved in games like poker, players won’t get far if they don’t decide to gamble every so often – and pot odds allow you to make smarter decision when it comes time to place your money on the line. Pot odds take into consideration the likelihood of making a hand to establish a decent risk vs. reward ratio.

Texas Holdem Odds Calculator

Another important statistic for players to keep in mind is ‘implied odds,’ which factor in the likely size and frequency of any betting that may come in later rounds of play. These come into play post flop and will be a factor until the river is dealt, and unlike most other Texas hold ’em odds, implied odds will be entirely based on your read on your opponents’ betting habits and aggression.

Texas Holdem Odds And Statistics

To calculate effective pot odds, consider your position in the hand and relative strength, then make a note of the amount of money currently in the pot. If you’re in a position to call, think of how much you stand to win should your hand come out ahead, as establishing a solid return on investment can help turn a questionable call into a big win. If no one has bet, then pot odds can help you deduce what size bet you will want to make in order to shift the statistical probabilities in your favor. With a sound bet, you could either make the continued investment not worth the potential gain or place a value wager designed to elicit a call from any remaining opponents. You will have to decide whether or not your chances of winning are worth risking the amount you could lose if you are wrong – a fine line for some players, but one that must be crossed often. For more on Texas Hold’em pot size and strategy see our guide here.