Poker is a popular card game that has a lot of different variations. One of the most common variations is 2 card poker, also known as Texas hold’em. As the name suggests, this game involves each player getting just two cards and then trying to make the best possible hand with those cards and the community cards that are dealt later in the game.
But, have you ever wondered how many 2 card poker hands are there? Well, in this article we will explore this question in detail.
To start with, it’s important to note that there are a total of 52 cards in a standard deck of playing cards. These cards are divided into four suits – clubs, diamonds, hearts, and spades – with each suit containing 13 cards. And since we’re talking about 2 card poker hands here, we need to calculate the number of possible combinations of two cards from a deck of 52.
To do this calculation, we can use the formula for combinations: nCr = n!/r!(n-r)! where n is the total number of items and r is the number of items being chosen at a time. In our case, n = 52 (the total number of cards) and r = 2 (since we’re choosing two cards at a time).
Using this formula gives us:
52C2 = 52!/2!(52-2)! = (52×51)/2! = (2652)/2 = 1326
So there are a total of 1326 possible combinations of two cards from a standard deck.
Now let’s look at how many different types of hands you can make with those two cards.
In poker, the value of your hand is determined by its rank. The highest rank is a royal flush which consists of an Ace, King, Queen, Jack and Ten all in one suit. The lowest rank is just a high card where the highest card in your hand is used to determine its value.
In between these two extremes, there are many other ranks such as pairs, two pairs, three of a kind, straight, flush, full house, four of a kind and straight flush.
To calculate the number of different types of hands you can make with two cards in poker, we need to consider all possible combinations. There are a total of 169 different hand combinations possible in 2 card poker. Here’s how they break down:
– One pair: There are 13 possible pairs (one for each rank). For each pair, there are 6 possible combinations of suits (since there are 4 suits and you’re choosing 2). So the total number of one pair hands is 13×6 = 78. – Two pairs: There are C(13,2) = (13×12)/2 = 78 ways to choose two different ranks for your two pairs. For each combination of ranks, there are C(4,2)xC(4,2) = (6×6) = 36 ways to choose the suits for your two pairs. So the total number of two pair hands is 78×36 = 2808. – Three of a kind: There are C(13,1) = 13 ways to choose the rank for your three of a kind. For each rank choice, there are C(4,3) = 4 ways to choose which three cards will be that rank and C(12,1) ways to choose the rank for your other card. So the total number of three of a kind hands is 13x4x12 = 624. – Straight: There are C(10,1) =10 possible starting ranks for a straight (Ace can be high or low but can’t wrap around). For each starting rank choice there are only four possible ways to form a straight with the second card. So the total number of straight hands is 10×4 = 40.
– Flush: There are C(13,2) – 13 = 78-13 = 65 ways to choose two different ranks for your two cards such that they don’t form a pair. For each rank choice, there are C(4,1) = 4 ways to choose the suit for your first card and C(3,1) = 3 ways to choose the suit for your second card since you can’t pick the same suit as the first card. So the total number of flush hands is 65x4x3 = 780. – Full house: There are C(13,1) = 13 ways to choose the rank for your three of a kind and C(12,1) =12 ways to choose the rank for your pair. For each rank choice there are C(4,3) and C(4,2) ways to choose the suits respectively. So the total number of full house hands is 13x4x6 = 312. – Four of a kind: There are C(13,1) = 13 ways to choose which rank will be four-of-a-kind. For each rank choice there are C(4,4)=1 way to choose which four cards will have that rank and (48) possible cards for your singleton (it can be any card except those in the four-of-a-kind). So the total number of four of a kind hands is 13 x (48). – Straight flush: There are only ten possible straight flushes in standard two-card poker (Ace-King through Ten-Nine). Each straight flush consists of two specific cards (e.g., Ace and King of spades), so we multiply by four (one combination for each suit). The total number of straight flush hands is 10 x 4 = 40.
So, in conclusion, there are a total of 169 different possible hands that you can make with two cards in poker. Knowing this may not guarantee you a win at the table but it certainly helps to understand your odds and the strength of your hand.
