Poker Hand Rankings And Odds

1. Poker Hand Rankings And Odds Week 9
2. Poker Hands Odds Table
3. Poker Hand Rankings And Odds
4. Poker Hand Rankings And Odds Ncaa Football

When you first start playing poker it’s important that you are quickly able to recall hand rankings and the strength of the hand you’ve been dealt. Fortunately, it’s pretty easy to do so, as highlighted in this complete guide to the 10 strongest poker hands, with their rankings listed in order from highest to lowest. Furthermore, the rankings are standard for all the most popular types of poker games including No-Limit Hold’em, Pot-Limit Omaha and Seven-Card Stud.

Poker Hand Rankings And Odds Week 9

In addition to a poker hand rankings chart, also provided are answers to some of the most frequently asked questions regarding poker hand rankings, as well as the game of poker in general.

1. Royal Flush

A ‘Royal Flush’, otherwise known as a ‘Royal Straight Flush’ or ‘A Royal’, is the best possible hand in poker. It consists of ace, king, queen, jack and ten, with all five cards of the same suit, such as As-Ks-Qs-Js-10s.

Texas Hold’em is the most popular poker variant in the US. It is also the ranking game internationally, dwarfing other poker games by a long margin. This Poker Hands Guide is based on Texas Hold’em hand rankings, and it will reveal the best-kept secrets to forming winning hand combinations. Poker Hand Rankings - Texas Holdem Starting Hands Chart At the bottom of this page is a comprehensive listing of Texas Hold'em starting hands based on their EV (expected value). Expected value is the average number of big blinds this hand will make or lose.

This unbeatable hand is rare, though, with the odds of making a royal flush just 1 in 30,939 or 0.0032 percent using 7 cards. These odds apply to the game of Texas Hold’em where you build your hand using 5 cards, but still have 7 cards to choose from, namely 2 pocket cards and 5 on the board.

2. Straight Flush

A ‘Straight Flush’ consists of five cards in a row that are all in the same suit. It essentially combines a straight with a flush, with an example being Jc-10c-9c-8c-7c. This powerful hand rarely gets beaten, but in the eventuality of a showdown between straight flushes the player with the highest top card wins. Bear in mind that suits are irrelevant in poker and that only kickers are used to separate same ranked hands.

The odds of making a straight flush is 1 in 3,589, or 0.0279 percent.

3. Four of a Kind

A Four of a Kind, otherwise known as ‘Quads’, consists of any four of the same value cards in each of the four suits. For example Ks-Kh-Kc-Kd-2s is a four of a kind hand. In Texas Hold’em, if the community cards dealt complete four of a kind on the board, such as 10c-10s-10h-10d-7c, the player with the highest hole card wins. In the example provided, however, if none of the players have a card higher than a 7 the hand is drawn.

Four of a kind hands are strong and rarely beaten, with the odds of making such a hand 1 in 594, or 0.168 percent.

4. Full House

A ‘Full House’ is any three of a kind hand combined with a pair. An example of such a hand would be Ah-Ac-Ad-Kc-Kd, or “aces full of kings,” which is the best possible full house hand and would in turn beat a lesser-ranked full house, as well as a flush, a straight, or any other hand ranked lower on this list.

Also referred to as a ‘Full Boat’, the odds of making a full house is 1 in 37.5 or 2.60 percent.

5. Flush

A ‘Flush’ is fifth highest on the poker hand rankings list, and consists of five cards of the same suit, but not in consecutive order. An example would be Ac-Jc-9c-7c-5c or Qd-10d-7d-5d-2d. Between two flushes, the one with the highest-ranked card wins the hand, with an ace-high flush the best possible flush. Therefore, an ace-high flush beats a king-high flush, a king-high flush beats a queen-high flush, and so on. This is a hand that even a super tight poker player would play.

The odds of making a flush is 1 in 32.1, or 3.03 percent.

6. Straight

A ‘Straight’ consists of five consecutive cards in numerical order, but not of the same suit. In this hand, aces can count both as a high or low card. For example, the lowest possible straight, also known as the ‘Wheel’ or ‘Bicycle’, is five-high as in 5h-4d-3s-2c-Ad, while the highest referred to as ‘Broadway’ is ace-high as in Ad-Ks-Qh-Jc-10s.

The odds of making a straight is 1 in 20.6 or 4.62 percent.

7. Three of a Kind

A ‘Three of a Kind’ hand consists of any three cards of the same face value, and two non-paired cards. An example would be Ah-As-Ad, with a King and a Queen as side cards, which is also the best possible three of a kind hand. The term ‘Set’ and ‘Trips’ both refer to types of three-of-a-kind hands, but in a set you must hold a pair in your hand. By contrast, trips are when there is a pair on the board and you hold a third matching card in your starting hand, such as a 6c-6s-Kh-10h-5d board and you hold a 6d in your hand.

The chances of making a three-of-a-kind hand is 1 in 19.7, or 4.83 percent.

8. Two Pair

Any ‘Two Pair’ hand consists of two cards of the same face value together with another two cards of the same value. For example Jc-Jd-6c-6h-Kc. If two players both hold two pair then the player with the biggest pair wins. At the top of the two pair ranking order is aces and kings with a queen kicker.

Poker Hands Odds Table

The odds of making two pair or ‘Top Two’ as it is also known is 1 in 3.26, or 23.5 percent.

9. One Pair

A ‘One Pair’ hand means you have two cards of the same face value and three other non-matching cards. For example Ac-Ad-Qc-9d-3h or 10d-10h-7c-5d-2h. In a pair versus pair situation, like the previous example, the higher pair always wins, with two aces the best possible one-pair hand. Where two players have the same pair the player with the next highest card wins.

Also known as a ‘Pocket Pair’, the odds of making such a hand is 1 in 1.28, or 43.8 percent.

10. High Card

When a player has five unpaired cards the highest-ranked card plays. The highest possible high card in poker is an ace, which would beat a king high hand, and so on. For example, an Ac-Qh-10d-7s-3h hand would beat a Kd-Jc-9h-7c-5s hand.

The odds of not making a pair is 1 in 4.74, or 117.4 percent.

Poker Hand Rankings FAQs

Do hand rankings vary between different poker games?

All the most popular “high-card” poker games use the standard poker hand rankings based on five cards only and listed in order from highest to lowest. These include Hold’em, Omaha, Seven-Card Stud, and Five Card Draw. On the other hand, “low-card” games, known as Lowball, use an alternate low hand ranking in which the lowest possible hand wins. Badugi, 2-7 Triple Draw, and Razz are examples of such Lowball games.

Do my extra cards matter in poker?

When playing Texas Hold’em, it’s important to remember that the best five card hand takes the pot. If you and your opponent have the same hand, however, then the highest kicker comes into play. For instance, if your holding is A-9 versus K-10 for your opponent and the board comes Q-Q-Q-Q-8, then your quads and ace high hand would beat your opponent’s quads and king high hand. If, however, the highest kicker is a community card then its a split pot. An example of this would be if you had 10-9 versus your opponent’s 10-7 on a 10-K-K-A-Q board, as you both have two pair each, tens and kings, with a communal ace high card.

Which suit is ranked the highest in poker?

Most poker games do not rank one suit more valuable than another, with all suits considered of equal value. A spade Royal Flush, for instance, is considered of equal value as one comprised of either diamonds, hearts or clubs.

What is a ‘draw’ in poker?

A ‘draw’ or ‘drawing hand’ in poker is when a player’s hand is incomplete and needs an additional card or cards in order to become valuable. There are many types of draws associated with the game of poker, such as flush draws, straight draws, open-ended straight draws, and inside straight draw, to name but a few. A flush draw, for example, is a hand with four matching suited cards that needs another card of the same suit to improve to a flush. Similarly, a straight draw is where a player needs to hit one card of a certain rank in order to complete a straight.

What are the 10 best starting hands in Hold’em?

It can be difficult to rank the best starting hands in Hold’em because you’re always going to have hands where pocket aces get cracked. In general, however, the following 10 hands are considered the best versus any two random cards:

• 1. Pocket Aces
• 2. Pocket Kings
• 3. Pocket Queens
• 4. Ace-King Suited
• 5. Pocket Jacks
• 6. Pocket Tens
• 7. Ace-Queen Suited
• 8. Ace-King Offsuit
• 9. Ace-Jack Suited
• 10. King-Queen Suited

This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

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Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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The Poker Hands

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

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Counting Poker Hands

Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.

Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

Two Pair and One Pair
These two are left as exercises.

High Card
The count is the complement that makes up 2,598,960.

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

Probabilities of Poker Hands

Poker Hand Rankings And Odds

Poker Hand Rankings And Odds Ncaa Football

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2017 – Dan Ma