Poker Probability Of Flush
The probability of collecting royal flush in poker is 1 to 649 740. The odd to catch this combination on the flop with pocket broadway cards is equal to 0.0008%. If there is a potential royal flush on the board, the probability that it will be collected on the turn is 2%, and till the river – 4%.
The probability of getting a flush is the ratio of the number of ways of getting a flush divided by the total number of hands; it is 51 = 33/16660 =.17. Not very high odds - about 2 in every 1000 hands! Hand Details Combinations Probability; Royal flush 4,324 0.000032 Straight flush K-9 4,140 0.000031 Straight flush Q-8 4,140 0.000031 Straight flush.
Probabilitiesfor 6 card poker hands with misc. wild cards
Probabilitiesfor 7 card poker hands with misc. wild cards
Probabilitiesfor 8 card, 9 card, and 10 card poker hands with misc. wild cards
Lowball (Low Ball) poker probabilities with misc. wild cards (5 to 10 cards)
http://www.durangobill.com/LowballPoker/Lowball_Poker.html
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The probability of being dealt various poker hands has been printed in many other sources. We present the probabilities for a 5 card deal here, and then concentrate on how to calculate these numbers.
Poker Hand Number of Combinations Probability
--------------------------------------------------------
Royal Straight Flush 4 .0000015391
Other Straight Flush 36 .0000138517
Four of a kind 624 .0002400960
Full House 3,744 .0014405762
Flush 5,108 .0019654015
Straight 10,200 .0039246468
Three of a kind 54,912 .0211284514
Two Pairs 123,552 .0475390156
One Pair 1,098,240 .4225690276
High card only 1,302,540 .5011773940
Total 2,598,960 1.0000000000
(See Probabilitiesfor 5 card poker hands with misc. wild cards for additional details.)
The first calculation that must be made is to determine the total possible poker hands. A poker hand consists of 5 cards randomly drawn from a deck of 52 cards. Thus, the number of combinations is COMBIN(52, 5) = 2,598,960. Each of these 2,598,960 hands is equally likely. For each of the above “Number of Combinations”, we divide by this number to get the probability of being dealt any particular hand.
For the calculations, we will first split out the “No Pair” hands which include Royal Straight Flushes, Straight Flushes, Flushes, Straights, and “Nothings”. Then, we will look at all combinations that have at least 1 pair.
The cards in a hand without any pairs will have 5 different denominations selected randomly from the 13 available (2, 3, 4...Ace). Also, each of the 5 denominations will select 1 suit from the four available suits. Thus the total number of no-pair hands will equal:
COMBIN(13, 5) * (COMBIN(4, 1))^5 = 1287 * 1024 = 1,317,888.
A Straight Flush consists of 5 consecutive cards in the same suit and may have a high card of 5, 6, 7, 8, 9, 10, Jack, Queen, King, or Ace for a total of 10 different ranks. Each of these may be in any of 4 suits. Thus there are 40 possible Straight Flushes. An Ace high Straight Flush is a Royal Flush. Since there are only 4 different suits, there are only 4 possible Royal Straight Flushes. When we subtract the 4 Royal Straight Flushes from the total of 40 Straight Flushes, we are left with 36 other Straight Flushes that are King high or less.
A Flush consists of any 5 of the 13 cards from a particular suit. There are 4 possible suits. Thus the number of possible Flushes is: COMBIN(13, 5) * 4 = 5,148. However, this includes the 40 possible Straight Flushes. When we subtract these out, we are left with: 5,148 - 40 = 5,108 possible ordinary Flushes.
A Straight consists of 5 cards with consecutive denominations and may have a high card of 5, 6, 7, 8, 9, 10, Jack, Queen, King, or Ace for a total of 10 different ranks. Each of these 5 cards may be in any of the 4 suits. Thus there are 10 * 4^5 = 10,240 different possible straights . However, this total includes the 40 possible Straight Flushes. Thus we subtract 40, which leaves us with 10,200 possible ordinary Straights.
Finally, we come to the “Nothing” hands which are basically all the left over garbage. This is simply the total number of “No Pair” hands minus all the good stuff. This gives us: 1,317,888 - 4 - 36 -5,108 - 10,200 = 1,302,540 “Nothing” hands.
Now on to 1 pair or better. A hand with just 1 pair has 4 different denominations selected randomly from the 13 available denominations. 3 of these denominations will select 1 card randomly from the 4 available suits. The 4th denomination will select 2 cards from the available 4 suits. Finally, the pair can be any one of the four available denominations. Thus the calculation is: COMBIN(13, 4) * (COMBIN(4, 1))^3 * COMBIN( 4, 2) * 4 = 1,098,240 possible hands that have just one pair.
The calculation for a hand with two pairs is similar. We will have 3 random denominations taken from the 13 available. Two of these denominations will use 2 of the four available suits while the third denomination selects 1 of the four available suits. The singleton card may be any one of the three denominations. Thus, the calculation becomes: COMBIN(13, 3) * (COMBIN(4, 2))^2 * COMBIN(4, 1) * 3 = 123,552 possible hands with 2 pairs.
Three of a kind is calculated in a similar manner. There will be 3 different denominations from the 13 possible denominations. One denomination will select 3 of the 4 available suits while the other two denominations select 1 card from each of the 4 possible suits. Finally, the three of a kind can be in any of the three denominations. The calculation becomes: COMBIN(13, 3) * COMBIN(4, 3) * (COMBIN(4, 1))^2 * 3 = 54,912 possible hands with 3 of a kind.
The next calculation will be for a Full House. A Full House only uses 2 of the 13 denominations. One of these will select 3 cards from the 4 available while the other selects 2 cards from the 4 available. Finally the denomination that has 3 cards can be either one of the 2 denominations that we are using. This gives us: COMBIN(13, 2) * COMBIN(4, 3) * COMBIN(4 , 2) * 2 = 3,744 possible Full Houses.
The final calculation is for 4 of a kind. Again, we will select 2 denominations from the 13 available. One of these will select 4 cards from the 4 available (Obviously the only way to do this is to take all four cards.) while the other denomination takes 1 of the available 4 cards. The denomination that has 4 of a kind can be either one of the 2 available denominations. Thus, the calculation becomes: COMBIN(13, 2) * COMBIN( 4, 4) * COMBIN( 4, 1) * 2 = 624 different ways of being dealt 4 of a kind. (On the draw, ask one of the other players what the odds are of drawing to an inside straight. Then draw your card. It won't make any difference though as no one else will have anything, and they will all fold.)
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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.
Poker Probability Of Flush Rules
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.
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
Poker Probability Of Flush Valve
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.
Poker Probability Royal Flush
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.
Poker Probability Of Being Dealt A Flush
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.