Royal Straight Flush Probability Texas Holdem

The following list shows the value of hands in descending sequence, with a description of the hand, the number of permutations and the probability of the hand occurring. It is worth memorizing this list in all its particulars. The five highest cards of the same suit. These conditions mean that there are nine straight flushes of a given suit. Since there are four different suits, this makes 4 x 9 = 36 total straight flushes. Therefore the probability of a straight flush is 36/2,598,960 = 0.0014%. This is approximately equivalent to 1/72193. A straight is highly likely in Royal Hold’em because only tens to aces are used. That means if you’ve made a straight on the turn, the chances are it will be beaten by a full house on the river, or the board will make a straight, too, for a split pot. The Royal Flush. The Royal Flush, as the name suggests, is the best possible hand in Texas Holdem. This hand combination is made up of the five highest cards in a deck – the Ace, King, Queen, Jack and the number 10. The royal flush must have all these characters of the same suit.

• Royal Straight Flush Probability Texas Holdem Odds
• Royal Straight Flush Probability Texas Holdem Tournaments

I am trying to determine the probability of the following occurrences in a Texas Holdem Game with 9 players.
On the flop:
Royal Flush versus queen high straight flush ( I.E board of 10 J Q suited versus AK and 89 of same suit)

There are combin(52,3) = 22,100 different flops, of which four (one of each suit) is Q-J-10, so the probability of the three flop cards being Q-J-10 suited is 1/5525.
I'm not 100% sure I am calculating this right, but here goes...
The probability that any of the 18 hole cards is the Ace of that suit is 18/49.
The probability that that player's other card is the King is 1/48.
The probability that any of the 16 remaining hole cards is the 9 of that suit is 16/47.
The probability that that player's other card is the 8 is 1/46.
The probability that one player in a nine-player game has a royal on the flop and another has a Queen-high SF is the product of these five numbers, or about 1 in 97,551,242.

Where did this happen at?

It didnt, just trying to determine the probabilities for promotional purposes.

I've seen a straight flush vs. straight flush bad beat jackpot once.

Flopped?<---very uncommon, hence my inquiry in my first post.
I like to know the probability of that as well (IE and three suited connect cards with each player holding the two straight flush cards for either side.)
with all 5 board cards, ive seen straight flush versus straight flush (each player using both hole cards) quite a few times in 25 years or so in card rooms

It didnt, just trying to determine the probabilities for promotional purposes.

There is a point in time that an outcome is so unlikely that a promotion based on it is BS.

There is a point in time that an outcome is so unlikely that a promotion based on it is BS.

I agree, players would recognize that point and it would likely have little affect. Trying to find the median.
Currently the Bad Beat is AAA1010 or better losing to 4 of a kind or better, both cards must play.

Royal Straight Flush Probability Texas Holdem Odds

Objective:
To add additional value to the jackpot ( I.E adding 5K 10K 15K ...or up to 50 or 100K) depending on the hands that qualify and when those hands are made.Hi all. I should have stumbled upon this forum sooner.

about 1 in 97,551,242.

I agree.
4 * C(9,2) / C(52,7) / C(7,3) / 3!!
Numerator: 4 suits, 1 valid flop combo for each suit, C(9,2) possible player matchups, 1 combo for the hole cards
Denominator: 7 cards dealt out of 52, then C(7,3) choices for which 3 are on the flop, then 3!!=3 possible ways to distribute the 4 hole cards between the 2 players involved (when it doesn't matter who gets the Royal and who gets the other).

Getting a royal flush is the hardest hand to obtain when playing poker online or in a casino. If you’re wondering what your odds are of being dealt a royal flush and other hands, you’ve come to the right place. We’ve developed this page to equip you with all the information you need to know about your poker hand odds.

In this detailed guide about your odds of being dealt a royal flush and other hands while playing poker, we’ll provide you with tons of information. You can check out the preview below to get an idea of everything we’ll cover. Feel free to click on one of these section titles if you want to jump ahead.

Breakdown of Potential Poker Hands

Before we dive into royal flush odds and other hands, we wanted to first ensure you’ve got a good understanding of the different hands possible when playing poker. Check out the sections below to look over all the different poker hands. We’ve listed them in the order of their rank when playing the game.

No Pair

This one should be pretty obvious. In casino poker and online poker, if you don’t have a single pair or higher in your hand, you have what’s considered a “no pair” hand. In this case, your hand’s value will depend on the highest card you’ve got.

Single Pair

If you end up getting a one pair hand, it means you’ve got two card values that match in your hand. For example, if you have two 4s, you have a single pair of 4s. While this isn’t a powerful poker hand, it does outrank anyone who has a no pair hand.

Two Pair

Kicking things up a slight notch from a single pair would be a two pair hand. In this scenario, you have two sets of matching card values. As an example, if you have two Ks and two 10s in your hand, it would be a two pair hand. In turn, it would outrank any players with just a single pair or no pair.

Three of a Kind

As the name implies, a poker hand that counts as three of a kind has three cards of the same value. For example, if you have three jacks in your hand, this would create a three of a kind poker hand. If you end up with the three of a kind hand, you’ll have a better hand than no pair, single pair, and two pair hands.

Straight (Not Royal or Flush)

Up next on the poker hand rank scale is a straight. Here, we’re only focused on standard straights, which means we’re not counting straights that are either flush or royal in nature (more on those in a moment). To make a straight, you’ll need all five cards in your hand to be in sequential order. As an example, if you had A, 2, 3, 4, and 5, you’d have a straight poker hand.

Flush (Not Straight or Royal)

Topping out straights and the other hands below it, a flush is another form of a poker hand. With a flush, you’ll have all five cards of your poker hand of the same suit. As an example, if all five cards in your hand are spades, you have a flush. For this particular hand, your cards do not count as a straight flush or a royal flush. We’ll touch on each of those below.

Full House

The next hand up the poker hand ranking scale is a full house. To make a full house with your hand, you’ll need to have a three of a kind paired with a two of a kind. If you have three 10’s and two 5’s, you’d have a full house.

Four of a Kind

One of the toughest hands to get when playing poker is a four of a kind. Here, you’ll need to have four cards of the same value in your hand. As an example, if you had four queens in your hand, you’ll have made a four of a kind poker hand. With four of a kind, there are only two other poker hands that can beat you.

Straight Flush (Not Royal)

Second from the top of the best poker hands possible is the straight flush. The flush portion of this name implies you’ll need all your cards to be of the same suit. However, to make a straight flush, they also must be in sequential order. For example, having 3, 4, 5, 6, and 7 of the same suit would provide you with a straight flush poker hand.

Royal Flush

The king of all poker hands is the royal flush. With a royal flush, it’s essentially a very specific straight flush. For starters, all your five cards must be the same suit. On top of that, it must be the 10, J, Q, K, and A of a particular suit to complete the royal flush.

Royal Straight Flush Probability Texas Holdem Tournaments

Poker Hand Odds for Five-Card Games

Up first, we wanted to start by presenting you with your odds of being dealt a royal flush and other hands when playing five-card games of poker. Most notably, this will include Five-Card Stud Poker. We’ve included a chart below which showcases your odds of being dealt each hand in conjunction with the potential combinations and associated probability.

One thing worth noting is that the chart below showcases your odds of having one of the hands in a five-card poker game. This data does not account for any possibilities of wild cards or draws, which may be present in select games like Five-Card Draw.

Poker Hand	Odds	Combinations	Probablity
Royal Flush	1 in 649,740	4	0.00015%
Straight Flush	1 in 72,192	36	0.00139%
Four of a Kind	1 in 4,165	624	0.02401%
Full House	1 in 693	3,744	0.14406%
Flush	1 in 508	5,108	0.19654%
Straight	1 in 254	10,200	0.39246%
Three of a Kind	1 in 46.2	54,912	2.11285%
Two Pair	1 in 21	123,552	4.75390%
Single Pair	1 in 1.37	1,098,240	42.25690%
No Pair	1 in 0.995	1,302,540	50.11774%

Chart Labels

• Odds: The odds of being dealt the particular poker hand in a five-card game.
• Combinations: How many different ways the poker hand can be made using all 52 cards in the deck.
• Probability: The statistical probability of being dealt the hand in a five-card poker game.

As you can see from the chart above, you’ve got the highest chance of being dealt a no pair or single pair hand when playing a five-card variant of poker online or in a casino. Interestingly, there’s roughly a 50% chance you won’t have a pair or better.

However, you can see just how tough it can be to get some of the other higher-ranking poker hands. Even two pair hands only happen about 5% of the time. And if you’re hoping for a royal flush, the odds of it happening are minuscule.

Things More Likely to Happen Than Being Dealt a Royal Flush

Since the royal flush is the hardest poker hand to achieve, we wanted to provide you with some visualizations to help you grasp just how rare it is. Check out the list of things below, which are more likely to happen to you than being dealt a royal flush when playing a five-card variant of poker.

Getting in a Car Accident
1 in 103

Getting Audited by the
Internal Revenue Service (IRS)
1 in 175

Winning an Academy Award
1 in 11,500

Losing an Appendage
in a Chainsaw-Related Accident
1 in 4,464

Going to the ER
With a Pogo Stick-Related Injury
1 in 103

Poker Hand Odds for Seven-Card Games

Up next, we wanted to provide you with royal flush odds and other poker hands when playing seven-card versions of poker. If you’re into games like Seven-Card Stud and No Limit Texas Hold’em, this is the section for you.

While the addition of two extra cards to work with doesn’t sound like much to some, it creates a dramatic difference. Instead of just 2,598,960 potential hand combinations, playing poker with seven cards brings the possibility of 133,784,560 hands. That means there are more than 50 times as many possible hand combinations thanks to those extra two cards in play!

This chart focuses on your odds of being dealt one of these hands in a game of seven-card poker. As with the previous five-card section, the poker probability and odds below do not take into account wild cards and draws from specific versions of poker.

Poker Hand	Odds	Combinations	Probablity
Royal Flush	1 in 30,939	4,324	0.00323%
Straight Flush	1 in 3,589	37,260	0.02785%
Four of a Kind	1 in 594	224,848	0.16807%
Full House	1 in 37.5	3,473,183	2.59610%
Flush	1 in 32.1	4,047,644	3.02549%
Straight	1 in 20.6	6,180,020	4.82987%
Three of a Kind	1 in 19.7	6,461,620	23.49554%
Two Pair	1 in 3.26	31,433,400	23.49554%
Single Pair	1 in 1.28	58,627,800	43.82255%
No Pair	1 in 4.74	23,294,460	17.41192%

Chart Labels

• Odds: The odds of being dealt the particular poker hand in a seven-card game.
• Combinations: How many different ways the poker hand can be made using all 52 cards in the deck.
• Probability: The statistical probability of being dealt the hand in a seven-card poker game.

Immediately, you’ll probably notice how much better your odds of getting most hands are. In the next section, we’ll provide you with even more information about how much better your chances are for each of these hands if you play a seven-card variant instead of a five-card one.

Thanks to the additional two cards, offering you the chance to make your best five-card hand, there are more potential combinations which can help you improve your starting hand.

How Much Better Your Odds Are Playing Seven-Card Poker

Now that we’ve broken down the difference in royal flush odds and other poker hands between five- and seven-card poker games, we wanted to help you visualize just how much better your odds are when playing a seven-card game. Check out the chart below to see why you might opt to choose a seven-card game if you’re hoping to land a significant hand like a royal or straight flush.

Poker Hand	Percentage Increase
Royal Flush	2000.00%
Straight Flush	1910.64%
Four of a Kind	600.00%
Full House	1702.13%
Flush	1439.38%
Straight	1077.02%
Three of a Kind	128.60%
Two Pair	394.24%
Single Pair	3.71%
No Pair	-65.26%

As you can see from the chart above, there’s a 2000% greater chance you’ll get a royal flush when playing a seven-card poker game instead of a five-card game. Other hands which have an increased chance of happening when you’re playing a seven-card variant of poker include the straight flush, full house, flush, and straight.

Interestingly, there’s one hand where you have a lower chance of getting it when playing a seven-card game of poker instead of a five-card game. That hand is the no pair hand. Intuitively, this makes sense since there are increased chances you’ll make at least a pair thanks to the expanded cards you’re playing with. In this case, your chance of getting a no pair hand is 65% less when playing a seven-card game as opposed to a five-card one.

Wrap Up

Thanks for stopping in to check out this page about poker probability and the odds of being dealt a royal flush when playing online poker and casino poker. If you’re planning to play poker soon, don’t miss our complete guide to real money poker. In it, you’ll find all sorts of helpful information, including terminology, strategies, and so much more.

If you enjoyed this page about the odds of getting a royal flush, you might also enjoy other pages we’ve developed in this series. Check out the choices below to explore some of our other “What Are the Odds?” pages.