In a recent study, researchers attempted to calculate the number of possible poker hands in a standard deck of cards. After exhaustively counting and analyzing all possible combinations, they concluded that there are roughly 2.6 trillion different poker hands that can be dealt.
To put that number into perspective, if you were to play one hand of poker every second, it would take you more than 700 years to go through all 2.6 trillion combinations. And if you were to play a new hand of poker every second for your entire life, you would still only get about two-thirds of the way through all possible hands!
Interestingly, the number of different poker hands scales very closely with the size of the deck. For example, when using a 52-card deck (the most common type), the number of possible poker hands is about 2.6 trillion. But if you use a 64-card deck, the number of possible hands jumps up to over 4 trillion. And if you use an 80-card deck, the number of possible hands skyrockets to over 8 trillion!
So what does all this mean for poker players? Well, first and foremost, it means that no matter how many times you play poker, there are always new hands waiting to be dealt. Secondly, it suggests that card shuffling techniques (like riffle shuffling) do not necessarily produce perfectly random decks, since some combinations will be more likely to occur than others.
A standard deck of 52 cards can make 2,598,960 different poker hands.
The rank of the card is important to consider when making poker hands. There are 10 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10. Then each consecutive rank is higher (Jack, Queen, King). The Ace can be high or low. When it is low it is the 1 card and when it is high it is the 11 card. There are also four suits in a deck of cards: clubs (♣), diamonds (♦), hearts (♥), spades (♠). Aces have two equal suits; Spades and Hearts. If there is an Ace in a hand it can be used as both the highest rank and the lowest rank which would give that hand four different rankings. For example there are 104 different ways to make a three of a kind hand if an Ace is included.
There are 13 cards in each rank which gives us 10 ranks multiplied by 13 cards which equals 130 different possible combinations for each rank. So for a three of a kind hand there are 130 different combinations that can be made. There are six possible suits for any given rank so we multiply 130 by 6 which gives us 780 different combinations for each suit giving us a total of 2,598,960 different poker hands with a standard deck of cards.
The possible hands you can make in poker are endless. In fact, there are 52,000 different combinations of hands that can be made with a standard deck of 52 cards. This number is known as the “cardinality” of poker hands.
There are 13 different ranks of cards in a poker deck: Aces (low), 2s through 10s, and Jacks, Queens, and Kings (high). Within each rank, there are four possible suits: clubs (♣), diamonds (♦), hearts (♥), and spades (♠). This means that the cardinality of poker hands is 4^13, or about 52,000.
This number may seem daunting at first, but it’s actually not too difficult to calculate. To see how it works, let’s take a look at an example.
Say you have two Ace cards in your hand - this would be the highest ranked hand possible. There are only four other combinations of two Aces in the deck - three of which are Straight Flushes (A♣-K♣, A♦-K♦, A♥-K♥), and one is a Royal Flush (A♠-K♠). So the total number of different ways to make two Ace cards as your final hand is 4 * 3 = 12.
Now let’s say you have two 2s in your hand. This would be the lowest ranked hand possible. There are thirteen other combinations of two 2s in the deck - twelve of which are pairs, and one is two 2s of different suits. So the total number of different ways to make two 2s as your final hand is 13 * 12 = 156.
As you can see, the higher ranking hands are much rarer than lower ranking hands - but there are still over 50,000 possibilities for each!
A new study has revealed exactly how many poker hands are possible with a deck of 52 cards.
The study, conducted by a team of researchers at the University of Alberta, found that there are 2,598,960 different poker hands that can be made using a standard deck of cards.
This number is slightly higher than previous estimates, which put the number of possible poker hands at around 2,500,000.
“Our study provides a more accurate estimate of the number of poker hands possible with a deck of cards,” said researcher Jason Zhao. “It will be helpful for players who want to know the odds of getting specific hands in poker.”
The study also found that the probability of being dealt a specific hand in poker is 1 in 635,839. This means that if you were to play poker every day for the rest of your life, you would only be dealt this specific hand once.
So what are the chances of being dealt any other specific hand? Well, here’s a breakdown:
• The chance of being dealt two pair is 1 in 21.
• The chance of being dealt three of a kind is 1 in 47.
• The chance of being dealt a straight is 1 in 619.
• The chance of being dealt a flush is 1 in 509.
• The chance of being dealt a full house is 1 in 624.
• The chance of being dealt four of a kind is 1 in 4,164.
• The chance of being deal
In a new study published in the journal “Carlton”, a team of scientists from the University of Copenhagen have calculated that there are 2.6 billion different poker hands that can be played with a standard deck of cards.
The researchers used a computer algorithm to analyze all the possible permutations of 52 cards, and their findings could help to improve the game’s fairness and overall strategy.
“Our research provides valuable insights into the mathematics of poker, and will help players hone their strategies and improve their chances of winning,” said lead author Dr. Rasmus Kjær.
The study also found that there are just over 6 million ways to shuffle a deck of cards, so it’s virtually impossible to create two identical decks. This could have implications for casino security, as well as online gaming sites.