If you are a fan of playing poker, you might be familiar with the popular game of 3 Card Poker. This fast-paced game is played with a standard deck of 52 cards, and the objective is to make the best possible hand out of three cards.
One common question that arises when playing 3 Card Poker is – what are the odds of getting a pair? In this article, we will explore this question and provide you with some useful information that can improve your chances of winning.
First, let’s understand what we mean by a pair in 3 Card Poker. A pair is a hand that contains two cards of the same rank and one card of a different rank.
For example, if you have two 7s and one 4 in your hand, you have a pair of 7s. The probability of getting a pair depends on several factors such as the number of players at the table, how many decks are used, and whether or not there are any wild cards.
Assuming that we are playing with one deck of cards and there are no wild cards involved, let’s calculate the odds of getting a pair in 3 Card Poker. There are three ways to get a pair out of three cards:
1) You can get two cards that have the same rank on your first draw.
2) You can get two cards that have the same rank on your second draw after discarding one card.
3) You can get one card that has a certain rank on your first draw and then get another card with the same rank on your second draw.
Let’s break down each scenario and calculate its probability:
1) Probability of getting two cards with the same rank on your first draw:
The first card you draw can be any card from the deck (52 options). The second card must match the rank of the first card (4 options for each rank since there are four suits).
The third card can be any card except the first two (48 options). Therefore, the probability of getting a pair on your first draw is:
(52/52) x (4/51) x (48/50) = 3.92%
2) Probability of getting two cards with the same rank on your second draw:
Assuming that you have already drawn one card and it is not a pair, there are now only 51 cards left in the deck. The probability of getting a pair on your second draw is:
(8/51) x (47/50) = 5.88%
The numerator of this fraction is 8 because there are eight cards left in the deck that have the same rank as the card you drew initially.
3) Probability of getting one card with a certain rank on your first draw and then getting another one with the same rank on your second draw:
The first card you draw can be any card from the deck (52 options).
The third card must be different from the first two cards but must match their rank (3 options for each rank since there are three remaining cards with that rank). Therefore, the probability of getting a pair through this scenario is:
(52/52) x (4/51) x (3/50) = 0.24%
Now that we have calculated all three probabilities, we can add them together to get the overall probability of getting a pair in 3 Card Poker:
3.92% + 5.88% + 0.24% = 9.04%
Therefore, if you play enough hands of 3 Card Poker, statistically speaking, you should get a pair about once every eleven hands.
It’s important to note that these calculations assume that you are playing with perfect strategy and always making the best decisions based on the cards in your hand and the dealer’s up card. If you deviate from optimal strategy, your chances of getting a pair can increase or decrease depending on your choices.
In conclusion, the odds of getting a pair in 3 Card Poker are relatively low but still significant enough to make it a common occurrence during gameplay. By understanding the probability of getting a pair, you can adjust your strategy accordingly and make better decisions when it comes to placing bets and discarding cards. Good luck at the tables!
