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Well the short answer is that your chances are pretty slim. The long answer:
The total number of 13-card hands is 52-choose-13, which equals 52! / (13! * 39!). Any hand without any pairs must have exactly one of each value from 2 to ace. All there is to choose is the suit of each card, for 413 possible pairless 13-card hands. The probability of choosing one of these hands is the quotient of these two numbers, or 413 * 13! * 39! / 52!, which equals 4194304/39688347475, approximately 0.00010568 or 1 in 9462. Another explanation:
Say the first card in your hand is an ace. For the second card, you have to avoid the other three aces in the deck. There are 51 cards, and 48 of them are OK, so the probability that the second card doesn't pair the first card is 48/51. Suppose your second card was a king. For the third card, you now have to avoid all remaining aces and kings. There are 50 cards left in the deck and you have to Dodge six of them. So the probability that the third card doesn't pair either of the first two cards is 44/50. Each time you pick a card, there are three more cards you have to avoid, and one fewer card in the deck. So for the 4th card, you have to avoid 9 cards out of 49, giving a probability of 40/49. This continues until the 13th card, when the probability is 4/40. All these things have to happen one after the other, so you have to multiply the probabilities together:
48/51 x 44/50 x 40/49 x 36/48 x 32/47 x 28/46 x 24/45 x 20/44 x 16/43 x 12/42 x 8/41 x 4/40.
This gives the same probability as above (about 1 in 9462).
What else can I help you with?
What is the probability that a random selected poker hand contains exactly 3 aces given that it contains at least 2 aces?
To calculate the probability of a random selected poker hand containing exactly 3 aces given that it contains at least 2 aces, we first need to determine the total number of ways to choose a poker hand with at least 2 aces. This can be done by considering the different combinations of choosing 2, 3, or 4 aces from the 4 available in a standard deck of 52 cards. Once we have the total number of ways to choose at least 2 aces, we then calculate the number of ways to choose exactly 3 aces from the selected hand. Finally, we divide the number of ways to choose exactly 3 aces by the total number of ways to choose at least 2 aces to obtain the probability.
What is the probability of not being dealt a queen in a 52 card deck?
The answer will depend on the exact situation.If you are dealt a single card, the probability of that single card not being a queen is 12/13 - assuming you have no knowledge about the other cards.Here is another example. If you already hold three queens in your hand (and no other cards have been dealt), the probability of the next card being dealt being a queen is 1/49, so the probability of NOT getting a queen is 48/49 - higher than in the previous example.
What are chances of 4 aces being in a hand of 9 cards?
The probability of 4 aces being in a hand of 9 cards is: 9C4 ∙ (4/52)∙(3/51)∙(2/50)∙(1/49)∙(48/48)∙(47/47)∙∙∙(44/44) = 0.0004654... ≈ 0.0465% where 9C4 = 9!/[(9-3)!∙3!] = 126
What is the probability that a five-card poker hand contains the two of diamonds and the three of spades Enter the value in decimal format and report it to four decimal places?
How many solutions are there to the equation , where , i = 1, 2, 3, 4, 5, is a nonnegative integer such that
A deck of ordinary cards is shuffled and 13 cards are dealt. What is the probability that the last card dealt is an ace?
The odds of any card pulled from an ordinary deck of 52 cards being an Ace is 4 in 52 (4 aces in a deck of 52). This can be reduced to a 1 in 13 chance of any random card pulled from the deck being an Ace (or any other specific value, for that matter). That 13th last card dealt in a hand is no different than picking a random card out of the pack, regardless of what cards you deal before (face down or blindfolded or even face up, it doesn't matter). A more interesting question would be "what would the probability be of ANY of those 13 cards being an Ace?" Any takers?
How does the probability of getting 2 pairs in a poker hand compare to the probability of getting 3 of a kind?
The probability of getting 2 pairs in a poker hand is higher than the probability of getting 3 of a kind.
What is the probability of getting three pairs in a hand of Texas Hold'em poker?
The probability of getting three pairs in a hand of Texas Hold'em poker is very low, approximately 0.23.
What is the probability in a regular 52 deck of getting a hand with no diamonds given that the cards are red?
The answer depends on how many cards are in the hand.
What is the probability of being dealt a blackjack hand with an ace and a nine in a standard deck of cards?
The probability of being dealt a blackjack hand with an ace and a nine in a standard deck of cards is 4.83.
Is having 3 pairs a valid hand in poker?
No, having 3 pairs is not a valid hand in poker. In poker, a valid hand consists of the best 5 cards out of the 7 cards available to each player. Having 3 pairs would mean having 6 cards, which is not possible in a standard poker hand.
What is the difference between a poker hand with three of a kind and a hand with two pairs?
In poker, a hand with three of a kind consists of three cards of the same rank, while a hand with two pairs consists of two sets of two cards of the same rank.
Can you explain the rules of poker and how to determine the winning hand when a player has 2 pairs or 3 of a kind?
In poker, players aim to make the best hand using a combination of their cards and community cards. Two pairs beats one pair, and three of a kind beats two pairs. To determine the winning hand, compare the ranks of the pairs or three of a kind. If two players have the same hand, the one with the highest-ranking cards wins.
What is the difference between a poker hand with two pairs and a poker hand with three of a kind?
In poker, a hand with two pairs consists of two sets of two cards of the same rank, while a hand with three of a kind consists of three cards of the same rank.
Is 3 pair considered a hand in poker?
No, in poker, a hand consists of 5 cards. Three pairs do not make a valid hand in poker.
In a poker hand consisting of 5 cards find the probability of holding 3 aces?
Approximately 2%
Are three pairs a valid hand in poker?
No, three pairs is not a valid hand in poker. In poker, a hand consists of five cards, and three pairs would require six cards. The highest ranking hand in poker is a royal flush, followed by a straight flush, four of a kind, full house, flush, straight, three of a kind, two pair, one pair, and high card.
What is the Probability of getting a 6 of clubs and 7 of clubs?
If you are drawing two cards from a full deck of cards (without jokers) then the probability will depend upon whether the the first card is replaced before the second is drawn, but the probability will also be different to being dealt a hand whilst playing Bridge (or Whist), which will again be different to being dealt a hand at Canasta. Without the SPECIFIC context of the two cards being got, I cannot give you a more specific answer.
