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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

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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.


The probability of being dealt 4 aces in a 5 card poker hand?

Poker hands are combinations of cards (when the order does not matter, but each object can be chosen only once.)The number 52C5 of combinations of 52 cards taken 5 at a time is (52x51x50x49x48) / (5x4x3x2x1) = 2,598,960.The number of hands which contain 4 aces is 48 (the fifth card can be any of 48 other cards.)So there is 1 chance in (2,598,960 / 48) = 54,145 of being dealt 4 aces in a 5 card hand.The odds are 54,144 to 1 against. The probabilityis 1/54145 = (approx.) 0.000018469 or 0.0018469%.


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?


What is the probability of getting exactly three aces in a five-card poker hand dealt from an ordinary 52 card deck?

The probability of getting 3 aces in the order AAABB is; P(AAABB) = (4/52)∙(3/51)∙(2/50)∙(48/49)∙(47/48) = 0.0001736... There are 5C3 = 5!/(3!∙(5-3)!) = 10 different ways in which the aces can come out. So the probability of getting exactly three aces in a five card poker hand dealt from a 52 card deck is, P(3A) ~ 10∙(0.0001736) ~ 0.001736 ~ 0.1736%


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.

Related Questions

When you play poker cards game and you have straight Aces in your hand what that mean?

suited aces


What is the best pair in poker and why is it considered the most powerful starting hand?

The best pair in poker is a pair of aces (AA). It is considered the most powerful starting hand because it has the highest probability of winning before the community cards are dealt. A pair of aces gives you a strong advantage over other players and increases your chances of winning the hand.


Do you know why it is always recommended to split aces and eights in blackjack?

In blackjack, it is recommended to split aces and eights because it increases your chances of winning. Aces are powerful cards that can form strong hands, while eights are weak and splitting them gives you a chance to improve your hand. Splitting these pairs can help you maximize your potential to win in the game.


How do aces work in blackjack and what impact do they have on the game?

In blackjack, aces can be counted as either 1 or 11, depending on what benefits the player's hand. Aces are important because they give players flexibility in their hand values. Having an ace can increase the chances of getting a blackjack, which is a winning hand worth more than a regular win. Aces can also help players avoid busting, as they can be counted as 1 if needed to keep the hand under 21. Overall, aces can greatly impact the outcome of the game by giving players strategic options and increasing their chances of winning.


What if you get two aces in blackjack - how would you play them to maximize your chances of winning?

If you get two aces in blackjack, it is best to split them into two separate hands. This increases your chances of getting a high-value hand on each ace. By splitting, you have the opportunity to potentially double your winnings if you get a 10-value card on either ace, resulting in a strong hand like blackjack. Splitting aces is a common strategy in blackjack to maximize your chances of winning.


In a poker hand consisting of 5 cards find the probability of holding 3 aces?

Approximately 2%


What are the two aces in blackjack and how do they affect the game?

In blackjack, the two aces are valued at either 1 or 11 points each. They are considered powerful cards because they can be used flexibly to create a strong hand. If a player is dealt a hand with an ace, they have the option to use it as either 1 or 11 points, depending on what benefits their hand the most. This flexibility can greatly impact the player's strategy and chances of winning in the game.


How do you determine what are outs in poker and how do they affect your chances of winning a hand?

In poker, outs are the number of cards left in the deck that can improve your hand. To determine outs, you identify the cards that would give you a winning hand. The more outs you have, the higher your chances of winning the hand. You can calculate your chances of winning by dividing the number of outs by the number of unseen cards.


Is having two aces considered a blackjack in a game of cards?

No, having two aces is not considered a blackjack in a game of cards. A blackjack is when a player has an ace and a 10-value card (10, Jack, Queen, King) in their initial hand.


Why is it important to always split aces and eights in blackjack"?

Splitting aces and eights in blackjack is important because it gives you a better chance of winning. Aces are strong cards that can form a strong hand when split, while eights are weak cards that are better off separated to improve your odds of winning.


What is the best starting hand to play in Texas Hold'em according to the Hold'em hands chart?

According to the Hold'em hands chart, the best starting hand to play in Texas Hold'em is pocket aces (two aces as your hole cards).


What wins in Texas holdem a pair of kings and a pair of queens or a pair of two and a pair aces?

In Texas Hold'em, the hand with the higher pair wins. In this case, a pair of aces is higher than a pair of kings, queens, or twos. Therefore, the hand with a pair of aces and a pair of twos would win over a hand with a pair of kings and a pair of queens.