Poker Royal Flush Probability
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:
The following table lists, for each hand, the number and probability of a given hand. Five-Card Stud (Natural) Probabilities Hand Number Probability Straight Flush 2 40 0.00002 Four-of-a-Kind 624 0.00024 Full House 3744 0.00144 Flush 5108 0.00197 Straight 10,200 0.00393 Three-of-a-Kind 54,912 0.02113 Two Pair 123,552 0.04754. Note that the probability of getting one when you are dealt your pocket cards is way lower than the probability of getting one after the board is complete, that is of course because you won’t go to the river on every hand. If you have five suited high cards, obviously that's a Royal Flush - in fact, 100 of them - and the probability is 1. If you have 4, you have a 1/47 chance of getting the fifth card, which means you have a 46/47 chance of not getting it, so you have a (46/47) 100 chance of not getting any royals in 100 of these hands, and a 1 - (46/47) 100.
You can also print and download the Official Texas Hold’em hand ranking as a PDF file.
Chart: Poker Hand Ranking
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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.
Poker Royal Flush Probability Calculator
Does Royal Straight beat flush?
A Royal Flush is the best possible poker hand and of course always beats any other flush.
Poker Royal Flush Probability Chart
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?
Poker Royal Flush Probability Table
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?
Royal Flush Poker Probability
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.
Poker Royal Flush Probability Charts
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.
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.
Relevant Resources
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
Click here for optimal strategy and expected value for Video Poker
http://www.durangobill.com/VideoPoker.html
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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