Texas Holdem Flush Probability

Aces can be high or low. An ace-high straight flush is called a royal flush, the best possible hand in poker. ♣ Betting Variations. Texas Hold'em can be played in three basic variations: Limit Hold'em: In Limit Hold'em, the amount you can bet or raise is fixed, according to the posted stakes. A bet placed before the turn card (4th community. Better, but this 1/117,600 probability is with exact cards in order. In Texas Hold'em it does not make a difference whether the flop comes A K Q or A Q K. So to account for this we multiply this fraction by 6 (1.2.3 = 6). P = 1/117,600. 6. There are 9 unknown cards left that could complete your flush so you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop). This is how Texas Hold’em odds are calculated. Rounded to the nearest tenth of a percent, 9/47 = 19.1, or a 19.1% chance to hit your flush on the turn. In Texas Hold’em a hand where aces, kings and queens pair up preflop is very rare. At a 9 player table this scenario unfolds roughly every 17,000 hands. The odds are 1:16,830 and the probability is 0.006%. Queens does happen every now and then, for example during this hand at the Bike. In the example of the four-flush, the player’s probability of filling the flush is approximately 36% after the flop (9 outs x 4) and 18% after the turn (9 outs x 2). Another important concept in calculating odds and probabilities is pot odds. Pot odds are the proportion of the next bet in relation to the size of the pot.

1. Texas Holdem Flush Probability Cheat
2. Texas Holdem Royal Flush Probability
3. Texas Holdem Flush Probability Rules
4. Texas Holdem Flush Probability Chart
5. Texas Holdem Flush Probability Calculator

To calculate the frequency of four of a kind, first note that there are 13 different ranks in which you can get four of a kind. For any given rank, the possible hands that give four of a kind in that rank all include the four cards of that rank as well as any three additional cards. There are C_48,3 = 17,296 different ways of choosing these three additional cards, so we have a total of 13 · 17,296 = 224,848 different four of a kind hands. This gives a frequency of (224,848/133,784,560) = 0.0017.

To find the frequency of straight flushes, sort all straight flush hands by the high card of the highest straight flush in the hand. For ace high straight flushes in any of the four suits you need the A - K - Q - J - 10 of the given suit and then any 2 of the remaining 47 cards. This gives a total of C_47,2 = 1,081 distinct hands. For straight flushes that are not ace high the same argument holds except that one of the remaining 47 cards would give you higher straight flush if it were in your hand (for example, if you have 10 - 9 - 8 - 7 - 6 in hearts, if one of your two other cards was a jack of hearts you would have a jack high straight flush). Therefore, in these cases there are only C_46,2 = 1,035 distinct straight flush hands. So the total number of straight flush hands is (1,081 · 4) + (1,035 · 4 · 9) = 41,584 hands (the nine in the second parenthesis comes from the fact that there are nine different possible non-ace high cards for straights - a 2,3, or 4 high straight can not occur). The corresponding frequency is then (41,584/133,784,560) = 0.00031.

To count the number of full house hands, we divide up the types of full houses by looking at the two cards that are not used as part of the final hand. These two cards can either be a pair (but of a different rank than the triple or the pair you are using for the full house, or else you would have four of a kind), one of the two cards could be of the same rank as your pair (giving you two triples and one card of some different rank), or the two cards could be of different ranks from each other, the triple, and the pair.

• We first consider the case of the unused cards being a pair. We can choose the rank for the triple in 13 ways. Once a rank is chosen we can pick the three cards for the triple in C_4,3 = 4 ways. We can then choose the two ranks for the two pairs in C_12,2 = 66 ways. For each pair, once we have chosen the rank we can choose the cards for the pair in C_4,2 = 6 ways. So we have a total of 13 · 4 · 66 · 6² = 123,552 full house hands of this type.
• Now we consider the case of two triples. We can choose the ranks for the triples in C_13,2 = 78 ways, and for each triple we can then choose the cards for the triple in C_4,3 = 4 ways. There are then 44 remaining cards from which to choose the last card of the hand, so we have a total of 78 · 4² · 44 = 54,912 hands of this type.
• Finally we consider the case of two cards of different rank from each other, the triple, and the pair. As above, the cards for the triple can be chosen in 13 · C_4,3 = 52 ways and the cards for the pair can then be chosen in 12 · C_4,2 = 72 ways. We can choose the two ranks for the remaining two cards in C_11,2 = 55 ways, and for each rank we can choose any of the four cards of that rank. This gives a total of 52 · 72 · 55 · 4² = 3,294,720 hands of this type.

Therefore, we have a total of 3,473,184 full house hands. This gives a frequency of (3,473,184/133,784,560) = 0.02696.

For additional calculations, as well as the frequencies for 5-card poker hands (which tend to be significantly easier to calculate), see for example Wikipedia.

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:

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

Texas Holdem Flush Probability Cheat

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?

Texas Holdem Royal Flush Probability

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?

Texas Holdem Flush Probability Rules

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.

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.

Texas Holdem Flush Probability Chart

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.

Texas Holdem Flush Probability Calculator

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.