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# four of a kind

## Question

In five decks of cards, what is the least amount of cards you must take to be *guaranteed* at least one four-of-a-kind?

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40

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Assuming 52-deck card (no Jokers):

196

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What I meant in the previous post was proper four of a kind, where you have 4 cards of the same rank and

different suits.
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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

well this is embarrassing but for some reason i am getting a higher number, what am i missing?

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

well this is embarrassing but for some reason i am getting a higher number, what am i missing?

There are 13 types of card in each suit. If you draw 39 cards and still do not have four of a kind, then you must have exactly 3 of each type. The 40th card will match with one of the sets of 3 you already have, making four of a kind.

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

well this is embarrassing but for some reason i am getting a higher number, what am i missing?

There are 13 types of card in each suit. If you draw 39 cards and still do not have four of a kind, then you must have exactly 3 of each type. The 40th card will match with one of the sets of 3 you already have, making four of a kind.

Oops. for some reason i had it in my head that there were 14 card types... oopsies

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

well this is embarrassing but for some reason i am getting a higher number, what am i missing?

Do your decks have Jokers? (Wouldn't matter, anyway, since Joker helps making 4 of a kind.) I assume, standard deck is 52 cards 2 - 10, J, Q, K, A.

13 different ranks. You can pick 3 cards of each rank. 3*13 = 39. The 40th card will match in rank one of the 3-of-a-kind that you already have.

If the above assumptions are correct, but the answer is still wrong, I give up and would like to see a list of more cards than Sp posted not having at least 1 four of a kind.

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Assume that a four of a kind is defined as only needing to match the numeric (or letter?) value or in other words that suits do not matter.

In that case, like Sp said. And the number of decks does not matter.

well this is embarrassing but for some reason i am getting a higher number, what am i missing?

Do your decks have Jokers? (Wouldn't matter, anyway, since Joker helps making 4 of a kind.) I assume, standard deck is 52 cards 2 - 10, J, Q, K, A.

13 different ranks. You can pick 3 cards of each rank. 3*13 = 39. The 40th card will match in rank one of the 3-of-a-kind that you already have.

If the above assumptions are correct, but the answer is still wrong, I give up and would like to see a list of more cards than Sp posted not having at least 1 four of a kind.

2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards)

2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards)

2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A (13 cards)

then any card would make a 4th copy and thus a 4 of a kind. This is highly improbable for them to be drawn like this but still possible so this would be the max amount you need to draw, 40 cards, to guarantee a 4 of a kind.

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