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Poker Hands Using combinations, calculate the number of each poker hand in a deck of cards. (A poker hand consists of 5 cards dealt in any order.) a. Four of a kind b. Straight flush d. Full house Factorials, Permutations, and Combinations Factorials n! Type the value of n. Press MATH and move the cursor to PRB, then press. PokerListings.com’s Poker Odds Calculator is the fastest, most accurate and easy-to-use poker odds calculator online. It’s just like what you see when you watch poker on TV. Use it in real-time to know exactly what your chances of winning and losing are at any point in a poker hand – be it on online poker sites or playing live poker.

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In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Frequency of 5-card poker hands

The following enumerates the (absolute) frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand by the total number of 5-card hands (the sample space, five-card hands). The odds are defined as the ratio (1/p) - 1 : 1, where p is the probability. Note that the cumulative column contains the probability of being dealt that hand or any of the hands ranked higher than it. (The frequencies given are exact; the probabilities and odds are approximate.)

The nCr function on most scientific calculators can be used to calculate hand frequencies; entering ​nCr​ with ​52​ and ​5​, for example, yields as above.

The royal flush is a case of the straight flush. It can be formed 4 ways (one for each suit), giving it a probability of 0.000154% and odds of 649,739 : 1.

When ace-low straights and ace-low straight flushes are not counted, the probabilities of each are reduced: straights and straight flushes each become 9/10 as common as they otherwise would be. The 4 missed straight flushes become flushes and the 1,020 missed straights become no pair.

Note that since suits have no relative value in poker, two hands can be considered identical if one hand can be transformed into the other by swapping suits. For example, the hand 3♣ 7♣ 8♣ Q♠ A♠ is identical to 3♦ 7♦ 8♦ Q♥ A♥ because replacing all of the clubs in the first hand with diamonds and all of the spades with hearts produces the second hand. So eliminating identical hands that ignore relative suit values, there are only 134,459 distinct hands.

The number of distinct poker hands is even smaller. For example, 3♣ 7♣ 8♣ Q♠ A♠ and 3♦ 7♣ 8♦ Q♥ A♥ are not identical hands when just ignoring suit assignments because one hand has three suits, while the other hand has only two—that difference could affect the relative value of each hand when there are more cards to come. However, even though the hands are not identical from that perspective, they still form equivalent poker hands because each hand is an A-Q-8-7-3 high card hand. There are 7,462 distinct poker hands.

Derivation of frequencies of 5-card poker hands

of the binomial coefficients and their interpretation as the number of ways of choosing elements from a given set. See also: sample space and event (probability theory).

• Straight flush — Each straight flush is uniquely determined by its highest ranking card; and these ranks go from 5 (A-2-3-4-5) up to A (10-J-Q-K-A) in each of the 4 suits. Thus, the total number of straight flushes is:
  • Royal straight flush — A royal straight flush is a subset of all straight flushes in which the ace is the highest card (ie 10-J-Q-K-A in any of the four suits). Thus, the total number of royal straight flushes is

    or simply . Note: this means that the total number of non-Royal straight flushes is 36.

• Four of a kind — Any one of the thirteen ranks can form the four of a kind by selecting all four of the suits in that rank. The final card can have any one of the twelve remaining ranks, and any suit. Thus, the total number of four-of-a-kinds is:

• Full house — The full house comprises a triple (three of a kind) and a pair. The triple can be any one of the thirteen ranks, and consists of three of the four suits. The pair can be any one of the remaining twelve ranks, and consists of two of the four suits. Thus, the total number of full houses is:

• Flush — The flush contains any five of the thirteen ranks, all of which belong to one of the four suits, minus the 40 straight flushes. Thus, the total number of flushes is:

• Straight — The straight consists of any one of the ten possible sequences of five consecutive cards, from 5-4-3-2-A to A-K-Q-J-10. Each of these five cards can have any one of the four suits. Finally, as with the flush, the 40 straight flushes must be excluded, giving:

• Three of a kind — Any of the thirteen ranks can form the three of a kind, which can contain any three of the four suits. The remaining two cards can have any two of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of three-of-a-kinds is:

• Two pair — The pairs can have any two of the thirteen ranks, and each pair can have two of the four suits. The final card can have any one of the eleven remaining ranks, and any suit. Thus, the total number of two-pairs is:

• Pair — The pair can have any one of the thirteen ranks, and any two of the four suits. The remaining three cards can have any three of the remaining twelve ranks, and each can have any of the four suits. Thus, the total number of pair hands is:

• No pair — A no-pair hand contains five of the thirteen ranks, discounting the ten possible straights, and each card can have any of the four suits, discounting the four possible flushes. Alternatively, a no-pair hand is any hand that does not fall into one of the above categories; that is, any way to choose five out of 52 cards, discounting all of the above hands. Thus, the total number of no-pair hands is:

• Any five card poker hand — The total number of five card hands that can be drawn from a deck of cards is found using a combination selecting five cards, in any order where n refers to the number of items that can be selected and r to the sample size; the '!' is the factorial operator:

This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.

Home > 5 Card Poker probabilities

Poker combinations are important. Poker, as we all should know by now, is a game of skill and luck.

Fate and the dealer decide what cards you start off with, and that can make the difference between winning and losing a game.

There are 52 cards in a deck, which means that you can get up to 169 different combinations for your starting cards.

The cards you are dealt at the start do not make or break your game, but they play a huge role in defining how you progress.

We look at the best poker combinations of cards which you should be looking out for if you want to win big in poker.

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Aces and Kings

Probably the best starting poker combinations you could game are a pair of Aces or Kings, irrespective of the suit.

The chances of someone getting a pair is exceptionally remote but if you do get such a pair always think about raising the pre-flop.

A word of caution though, these hands are tough to beat but are not unbeatable.

Also, if you are playing with a couple of Kings, there is the possibility of someone playing with a couple of aces, so always tread carefully.

poker combinations: Queens, Jacks and an Ace-King pair

The next highest possible poker combinations are also based on the highest cards.

Again getting a Queen pair or a jack pair is extremely rare but the chances of winning a hand significantly increase.

Of course, they can still be beaten if the right moves are made but this is a strong hand to play with.

The Ace-King pair is another strong hand to think about.

This combination works well and gives you a lot of opportunities to make strong hands.

This isn’t as strong as a starting pair of high cards, but it is a good bet for a win at the table.

Ace-Queen, Ace-Jack

The next best poker combinations to start a poker game with is the Ace-Queen pair.

This is similar to the Ace-King pair but has a few limitations since the Queen card is ranked lower than the King card.

The Ace-Jack combination ranks below the Ace-Queen pair.

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All the above pairs are made in the same suit, except in the case of a pair of cards which are of similar value.

Always the need to have same suit cards trumps cards of the same value.

So a Jack-Ace of the same color will trump, a Jack-Ace of different colors.

While these cards will undoubtedly play a huge role in deciding who wins a game.

It isn’t the end of the world if you are not dealt the above pairs.

There are many other ways to ensure you end up winning the game and we look at some of the best combinations of hands possible in the game of poker.

You might need to be a little sly in hoping that you get these cards from the dealer, but if you get the following combinations, you are guaranteed to win the game or at least do well.

Winner winner, chicken dinner!

Playing your way through the game is not easy but having the following hands will undoubtedly ensure victory and a nice amount of money for you to win.

Some of these hands are guarantees to win while some would require you to do some bluffing.

So without further to do, here are the best poker combinations you could have in a game of poker.

The Royal Flush

Royalty is vital in the game of poker and having a ‘Royal Flush’ is the best possible poker combinations of cards you could have after all the cards have been given to you.

A Royal Flush consists of the Ace, King, Queen, Jack and 10 of the same suit.

Nothing can beat this hand in a game of poker.

Straight Flush

Almost the next best thing to the Royal Flush, having 5 cards which are in a consecutive rank, for, eg, 5,6,7,8 and 9 of diamonds.

In case two players have a straight flush, the one with the higher denomination of cards wins.

Four of a kind

As the name suggests, having 4 cards of the same rank, high-value cards of the same rank will beat cards of a lower value.

Full House

Having three cards of the same rank and two other cards of a different rank.

In case of a tie, the highest ranking three cards of a player win the game.

Flush

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This happens when a player has five cards which are of the same color but are not in any specific order.

This can include high cards with low-value cards.

Three of a kind

Having three cards which are of the same rank/strength, and two cards which are of a different color or unrelated side cards.

Two pair

Having two pairs of cards which are of the same value; for example, having two 10’s and two 6’s in hand.

One pair

In this hand, two cards must have the same value; and the other three cards can be of any other denomination.

High card

Just having one high card in hand should win you the game. In case any of the above hands don’t take place.

So there you have it, the best starting poker hand combinations which can set you out for glory. And the best possible hand combinations at the end of the game before you go on to bet and win.

Remember, poker isn’t an easy game to pick up; there will always be a lot of people who try different tactics to get a slight edge.

While having a Royal Flush in your hand is a guaranteed win; the other options aren’t.

You need to keep your wits about it. And one way of doing it is by practicing and keeping yourself informed.

Poker Hand Combination

Also, you should use a few tools to aid your game like poker calculators and odds calculators. They might not help you out in the table games, but will help you make decisions faster and help solve tables better.