There Are Over 4.6 Billion Ways to Deal a Poker Hand
The game of poker is one that has been around for many years, and it seems to only continue to grow in popularity. There are a variety of different ways that people can play the game, and each offers its own set of challenges and possibilities. No two games are ever exactly alike, as the cards that are dealt and the players’ strategies will always result in a unique experience.
There are a total of 52 cards in a deck, which means that there are 4,164 possible combinations of hands. When factoring in different suits, this number grows to 6,598,960. There are also 10 different ranks of cards, so when multiplying these two numbers together, there are over 4.6 billion possible ways to deal a poker hand.
Of course, not all of these combinations are created equal. Some hands are much stronger than others, and it is important for players to be aware of which ones they should be targeting. The following is a list of the five strongest possible hands in poker:
A royal flush – This is the strongest hand possible in poker, and it consists of an ace, king, queen, jack, and ten all of the same suit. It is very rare to get this combination, but it can be worth huge sums of money when it does occur.
A straight flush – This hand is made up of five consecutive cards all of the same suit. It is less rare than a royal flush but still quite difficult to obtain.
Four of a kind – This hand consists of four cards with the same rank plus any other card. It is beats both a full house and a flush.
A full house – This hand is made up of three cards with the same rank plus two other cards with the same rank. It beats both a pair and two pairs.
A flush – This hand consists of five cards all of the same suit but not necessarily in sequential order. It beats both hands with fewer than five cards (a pair or two pairs) and three of a kind.
How Many Ways Can a Poker Hand Be Dealt?
There are 52 ways to deal a Poker hand, where each card can be dealt in one of four different ways. The order of the cards also matters, so there are only 4 possible hands when two cards are dealt (e.g., 2♥ 2♦).
The most common Poker hand is two pairs, which can be dealt in 11 different ways. Other common hands include three of a kind (6 ways), a straight (4 ways), and a flush (3 ways).
The least common Poker hand is four of a kind, which can only be dealt once out of the 52 possible hands. Other rare hands include a full house (3 ways), a straight flush (2 ways), and a wild royal flush (1 way).
There Are 10,000 Possible Poker Hands
There are 10,000 possible poker hands. The probability of being dealt any given hand is 1 in 10,000. This can be calculated by multiplying the number of cards in a deck (52) by the number of ways those cards can be arranged (52 factorial, or 3,628,800).
Poker hands are ranked from best to worst according to their strength. The five strongest hands are royal flush, straight flush, four of a kind, full house, and flush. In descending order, the remaining poker hands are three of a kind, two pair, one pair, high card.
How Many Poker Hands are There?
The answer to this question is a little more complex that you might think. Mathematically, there are 2,598,960 different poker hands. However, not all of these hands are equally likely to occur.
There are 169 different types of straight flush, for example, which means that there is only 1 out of every 31,574 possible hands that is a straight flush. On the other hand, there are only 4 different kinds of full house (containing three of a kind and a pair), so there is 1 out of every 694 possible hands that is a full house.
This means that the chances of getting any specific hand are quite small. In fact, the odds of getting any given hand are about 1 in 54 million!
There are More Than 2 Trillion Ways to Deal a Poker Hand
In any poker game there are many different ways that the player can be dealt a hand. Each of these combinations will result in a different playing experience and strategy. Dealing a poker hand is an art form that some develop over time while others are just naturally good at it.
The first thing to understand when dealing a poker hand is the order of the cards. In most games, the order goes from highest to lowest, Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2. There are variations of this rule but for the most part this is how the hands rank. It is important to remember this ranking when dealing as you do not want to give someone a strong hand by mistake.
Another thing to keep in mind when dealing a poker hand is whether the game is being played Stud or Draw Poker. In Stud Poker each player is dealt five cards face up with one card face down which is called the “hole card”. In Draw Poker each player gets five cards but all are face down. After all the players have received their cards, they then have the opportunity to exchange any number of cards with the remainder of the deck (this is called The Draw). After everyone has completed their draw, the best five-card poker hand for each player is then revealed and scored.
Now that we know how the cards rank and what type of game we are playing Meierkord’s 5-card Draw Poker variant which uses a stripped deck (the ace through six lowball ranking), let’s take a look at some of the different ways that hands can be dealt.
There are exactly 2,598,960 different possible five-card poker hands when using a stripped deck (the ace through six lowball ranking). This number is arrived at by multiplying 52! (52 factorial) by 12 (since there are 12 unique ranks in a stripped deck). To put this into perspective, there are only about 1 million different possible hands in a standard deck of 52 cards! So as you can see, there are many more possibilities when using a stripped deck which makes for much more interesting and varied games.
Now let’s take a look at some specific examples of how different hands can be dealt:
Royal Flush: This type of hand consists of an Ace high straight flush – A♥ K♥ Q♥ J♥ 10♥ – and is the highest possible hand in poker. There are only four ways this can happen out of 2,598,960 possible hands (1/654,746).
Straight Flush: This type of hand consists of five consecutive rank cards all in the same suit like K♦ Q♦ J♦ 10♦ 9♦ There are only 720 possible straight flushes out of 229860 possible hands (1/3155).
Four-of-a-kind: This type if hand consists four cards of identical rank like 4♥ 4♦ 4♣ 4♠ There are 16384 ways to get four-of-a-kind out of 2598960 total hands (1/1581).
Full House: A full house occurs when you have three cards of one rank and two card another rank like 3♣ 3♦ 3♥ J♣ J♦ There are 13424 full houses out on 2598960 total hands (1/191).