What is the Probability of Getting 13 Cards of the Same Suit?
When playing a card game, it is not uncommon to wonder about the probability of being dealt a certain hand. One such hand is a 13-card flush, which is a hand in which all 13 cards are of the same suit. But just how likely is it to be dealt such a hand?
Calculating the Probability
To calculate the probability of being dealt a 13-card flush, we need to consider the following factors:
- There are 52 cards in a standard deck.
- There are 4 suits in a deck (clubs, diamonds, hearts, and spades).
- A 13-card flush requires all 13 cards to be of the same suit.
Given these factors, the probability of being dealt a 13-card flush can be calculated as follows:
(Number of ways to choose 13 cards from one suit) / (Total number of ways to choose 13 cards from a deck)
The number of ways to choose 13 cards from one suit is 4, since there are 4 suits in a deck. The total number of ways to choose 13 cards from a deck is 52 choose 13, which is 635,013,559,600.
Therefore, the probability of being dealt a 13-card flush is:
4 / 635,013,559,600 = 6.31 x 10^-12
Conclusion
As you can see, the probability of being dealt a 13-card flush is incredibly low. In fact, it is so low that it is unlikely that you will ever be dealt such a hand in your lifetime. However, this does not mean that it is impossible. If you play enough card games, you may eventually be dealt this rare hand.
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