Royal Flush (Straight Flush) A royal flush is essentially the best possible hand that you can get in poker, but it’s still just a straight flush. So the odds of being dealt a royal are exactly the same as being dealt any other straight flush. You just need to have two hole cards that can make a royal, i.e., anything between a 10 and an Ace. Straight flush hands that differ by suit alone, such as 7 ♦ 6 ♦ 5 ♦ 4 ♦ 3 ♦ and 7 ♠ 6 ♠ 5 ♠ 4 ♠ 3 ♠, are of equal rank. An ace-high straight flush, such as A ♦ K ♦ Q ♦ J ♦ 10 ♦, is called a royal flush or royal straight flush and is the best possible hand in high games when not using wild cards. So - the odds of hitting a royal flush would be 4/2,598,960, which would work out to 1/649,740. So, you should hit a royal flush every 650,000 hands that you play or so. Poker hands odds & outs: a crash course-guide on poker odds, pot odds, probabilities & odds charts so you can win at Texas Hold’em at the tables or online.
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- If you ever wanted to know some of the odds and probabilities of Texas hold'em poker, from the chances of flopping a flush (0.8%) or set (12%) to the odds of an overcard coming on the flop when you.
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
What are the odds of hitting a straight flush in Texas Holdem What about the same straight flush 3x in 6weeks We play a home game and a player hit a straight flush 5-9 diamonds 2 out of 4 weeks. 2 weeks later she hit 4-8 diamonds straight flush. In Texas Hold'em, there are a total of 2,598,960 different five card poker hands. This includes the four royal flushes (Diamonds, Spades, Clubs and Hearts). So - the odds of hitting a royal flush would be 4/2,598,960, which would work out to 1/649,740. So, you should hit a royal flush every 650,000 hands that you play or so. Poker hands odds & outs: a crash course-guide on poker odds, pot odds, probabilities & odds charts so you can win at Texas Hold’em at the tables or online. One of the most important things that a poker player should know is what their poker odds are in a given situation.
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.
Related Lessons
Texas Holdem Table Odds
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There are 10 different hands ranks in Texas Hold’em – from a Royal Flush to a Straight to a lousy High Card. Here’s a comprehensive list of all Texas Hold’em poker hand rankings:
- In Texas Hold'em, there are a total of 2,598,960 different five card poker hands. This includes the four royal flushes (Diamonds, Spades, Clubs and Hearts). So - the odds of hitting a royal flush would be 4/2,598,960, which would work out to 1/649,740. So, you should hit a royal flush every 650,000 hands that you play or so.
- Multiplying that by 2 gives you 18, or around an 18% chance to complete your flush on the turn. Multiplying it by 4 gets you a 36% to complete it by the river. The actual percentage odds for a flush draw hitting on the turn and then by the river are 19.1% and 35% respectively, getting you pretty close with the 2 and 4 hack.
- Quora Texas Holdem Poker- Odds of making a Royal Flush - YouTube For example, there are 4 different ways to draw a royal flush (one for each suit), so the probability is 42,598,960, or one in 649,740.
You can also print and download the Official Texas Hold’em hand ranking as a PDF file.
There is only possibility of one royal flush occurring in any one round. So it be 1 in 2.6 million of that occurring. But the odds slightly increase on turn and river. Unlike 5/7 card stud poker, then it be 1 in 650,000 of it occurring.
Chart: Poker Hand Ranking
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Download the poker hand ranking charts image or PDF:
- Official Poker Hand Rankings Image
- Print: Poker Hand Rankings PDF
Official Poker Hand Rankings
- Royal flush: A straight from a ten to an ace with all five cards in the same suit.
- Straight Flush: Any straight with all five cards in the same suit.
- Four of a Kind or Poker or Quads: Any four cards of the same rank. If two players share the same four of a kind (on the board), the larger fifth card (the “kicker”) decides who wins the pot.
- Full House or Boat: Three cards of the same rank along with two cards of the same rank. In short: trips and a pair.
- Flush: All five cards of the same suit (not necessarily consecutive). The highest card determines the rank of the flush.
- Straight: Five consecutive cards (not necessarily the same suit). Aces can count as either high or low cards, but not as both at once. Meaning, a straight cannot go “around the corner”.
- Trips: Three cards of the same value. If two players have the same trips the highest kicker decides who wins the pot.
- Two Pair: Any two cards of the same rank together with two other cards of the same rank.
- One Pair: Any two cards of the same rank.
- High Card: Any hand that is none of the above hands.
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Poker Hand Rankings Explained
- If two players have a Straight or Straight Flush, the higher Straight or Straight Flush wins.
- If two players have a quads, the player with the highest quad wins. If they are identical, the highest kicker wins.
- If two players have a flush, the player with the highest card in the flush wins. If they are identical, the second highest card decides, then the third highest, and so on. The suit of the flush does not matter.
- If two players have a full house, the player with the higher trips wins. If they are identical, the player with the higher pair wins.
- If two players have two pairs, the player with the bigger pair wins. If they are identical, the player with the higher pair wins. If they are also identical, the player with the highest kicker wins.
- If two players have a pair, the player with the higher pair wins. If they are identical, the highest kicker wins, then the second highest, then the third highest.
- If two players have a high card, the highest card wins. If they are identical, the second highest card decides, etc.
How many Poker Hands are there?
There are only 10 distinct poker hand ranks, but if you randomly deal 5 cards from a deck of 52 cards there are exactly 2,598,960 possible card combinations.
Poker Hand Odds for 5-Card-Poker
The poker hand ranking charts are based on the probability for each distinct hand rank. More unlikely combinations are ranked higher. Those are the probabilities and odds for all 5-card poker hands:
Poker Hand Odds for Texas Hold’em
If you’re playing Texas Hold’em, you have 7 cards to chose your hand from. There are 133,784,560 to deal 7 random cards. This changes the odds and probabilities for all poker hands a bit. Those are the probabilities and odds for all Texas Hold’em Poker hands:
Technically it’s more likely that you’re dealt at least a pair in Texas Hold’em than holding only high card. But “High Card” still remains the lowest rank.
FAQ: Poker Hand Rankings
Does 2 pairs beat a straight?
When playing Texas Hold’em (or any other popular poker variant) 2 pairs are always ranked below a straight.
Does 3 Aces beat a straight?
3 Aces are just trips (or three of a kind) in poker. When playing regular Texas Hold’em a straight is ranked above trips. There are however rule variations where trips can bet a straight, namely Short Deck Hold’em, a poker variant where all cards below 5 are removed.
Does 5 of a kind beat a royal flush?
In regular poker variants there are is no 5-of-kind rank. When playing with wildcards (joker) 5 of a kind are possible. In this case 5 of a kind are the highest possible poker hand and beat a royal flush.
Does a full house beat 3 aces?
Every full house always beats trips, no matter the rank of the trips. Even trip aces are always ranked below every possible full house.
Does Royal Straight beat flush?
A Royal Flush is the best possible poker hand and of course always beats any other flush.
Does straight beat a full house?
Every common poker variant, including Texas Hold’em, ranks a Full House above a straight. So no, a Straight never beats a Full House in Poker.
What beats a royal flush?
In all regular modern poker variations (including Texas Hold’em and Omaha) a Royal Flush is always the highest possible hand rank. A higher rank is only possible when playing with a Joker. In this case 5 of a kind (4 Aces plus Joker) beats a Royal Flush.
What can beat a flush in poker?
A Flush is a very strong hand in poker. The only hands that beat a Flush are Full House, Quads, Straight Flush, and Royal Flush.
How rare is a royal flush?
A Royal Flush is extremely rare. When playing Texas Hold’em you’ll only get one every 31,000 hands. And that assumes you never fold. The hand is so rare that most poker players can remember all Royal Flushes they have been dealt in their life time.
What are the odds of hitting a straight flush?
Straight Flushes are almost as rare as Royal Flushes. When playing Texas Hold’em you will hit a Straight Flush roughly every 3,600 hands (assuming you never fold any hand that can make a Straight Flush).
Can you have 3 pairs in poker?
There is no “3 pair” hand rank in poker. When playing Texas Hold’em it’s technically possible to have three pairs, but since a poker hand only consists of 5 cards only the 2 highest pairs are in play. For example, if you hold Q-J and the board reads Q-J-6-A-A you only have two pair: Aces and Queens.
Does Royal Flush have to be spades?
A Royal Flush can be any of the 4 suits, spades, hearts, diamonds, or clubs. It’s just that usually a Royal Flush is depicted in spades or hearts. Nevertheless, it doesn’t matter which suit, a Royal Flush is always the best Texas Hold’em Poker Hand.
How many kickers can you have in poker?
A poker hand can consist of up to 5 kickers. A player with no pair only has kickers. A player with one pair has 3 kickers, a player with trips has 2 kickers, and a player with 2 pair or quads has 1 kicker.
Is Ace a 1 in poker?
When building a straight an Ace can be used as a virtual “1” in poker. Meaning, A-2-3-4-5 is a straight. There are also lowball poker variations where the Ace counts as the lowest card.
Is an Ace 2 3 4 5 a straight?
Yes, the ace can count as the lowest card in a straight and function as a “1” when combined with 2-3-4-5.
Is JQKA 2 a straight?
A straight cannot go “around the corner”, the Ace can only be either the highest or the lowest card, not a card in the middle. So no, J-Q-K-A-2 is no straight in poker.
Is Queen King Ace 2 3 a straight?
A straight cannot go “around the corner”, the Ace can only be either the highest or the lowest card, not a card in the middle. So no, Q-K-A-2-3 is no straight in poker.
Is there a kicker on a straight?
For a straight you need to use all 5 cards. There are no cards left for a kicker. The rank of the straight is determined by the highest card. E.g. an ace-high straight beats a queen-high straight.
What is a flush in poker?
A flush in poker is hand which consists of 5 cards of the same suit. The same color (red or black) is not enough. It has to 5 spades, hearts, diamonds, or clubs.
What is the highest royal flush in poker?
There are no distinctions between the 4 possible Royal Flushes in poker. A Royal Flush in spades is as good as a Royal Flush in hearts, diamonds, or clubs.
What is the highest suit in Texas Hold’em poker?
Only in very rare occasions (for example when dealing for the button) the suits are ranked in poker. In this case the ranking is: 1. spades, 2. hearts, 3. diamonds, 4. clubs. Suits are otherwise generally not ranked in poker. A Flush in spades is as good as a flush in any other suit, only the ranks of the cards matter.
What is the lowest pair in a game of poker?
In poker the lowest possible pair is a pair of Deuces (twos).
How do you win bad beat jackpots in poker?
To win a bad beat jackpot in poker you need to lose with a very strong hand, usually a strong Full House (Aces Full). It’s also necessary that both, the winning hand losing player, user both of their hole cards. E.g. losing with quads on the board does not count.
What are the odds of hitting a bad beat jackpot in poker?
The odds of hitting a bad beat jackpot in poker depend on the rules for the jackpot. If you have to lose with Aces Full or better your odds of hitting the bad beat jackpot are 1:58,948. If you have to lose with quads or better your odds are 1:624,609 (assuming a 10 player table where nobody ever folds).
What is a bad beat in poker?
If you lose with a very strong hand against an even stronger hand this is called a “bad beat”. It is also a bad beat if you lose an all-in while being far ahead and you opponent wins by catching some miracle cards.
Chances Of Hitting A Royal Flush In Texas Holdemlush In Texas Hold Em
Texas Hold'em Royal Flush Odds
How many 5 stud poker hands are there?
5 Card Stud is one of the oldest poker variants where each player is dealt 5 cards. There are exactly 2,598,960 different 5 stud poker hands possible.
How many poker hands are there?
There are only 10 distinct poker hand ranks, but if you randomly deal 5 cards from a deck of 52 cards there are exactly 2,598,960 possible card combinations. If you’re playing Texas Hold’em, you have 7 cards to chose your hand from. There are 133,784,560 to deal 7 random cards.
Ultimate Texas Holdem Royal Flush Odds
What happens if two hands tie in poker?
It’s possible (and not too uncommon) for two players to have the same hand in poker. In this case the pot is split and both players receive half the pot.
What happens if two people have a royal flush?
When playing Texas Hold’em it’s almost impossible for two players to have a Royal Flush. For that to happen the 5 community cards need to form a Royal Flush. In that case all players in the hand win and split the pot.
What happens if two poker hands are the same?
If two players have the same hand, the pot is split and both players win half of it. This can happen for example if both players have the same cards (e.g. Ace-King) and nobody makes a Flush.
How do you hit a royal flush on video poker?
In Video Poker you can win the jackpot when you hit a Royal Flush. To maximize your chances you should always keep all suited cards 10 or above (if you have at least 2) and discard the rest. You will see a Royal Flush roughly once every 40,000 spins.
What are the odds of hitting a royal flush on a video poker machine?
The odds of hitting a royal flush directly are only 1 in 649,739. But since you can draw one time your odds increase. If you play perfectly your odds of hitting a royal flush are roughly 1 in 40,000.
Chances Of Hitting A Royal Flush In Texas Holdemas Hold Em
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