Poker 10 Decks, 10 cards, independent 4 Aces

In summary, the probability of getting 4 aces (not necessarily distinct suits) out of 10 cards drawn from 10 standard independent decks is 10 * \binom{10}{4}\left(\frac{4}{52}\right)^4\left(\frac{48}{52}\right)^6, and for distinct suits, it would be multiplied by 4!. This calculation takes into account the different ways the 4 aces can be chosen out of the 10 cards.
  • #1
mattmns
1,128
6
Silly question of very little importance :smile:

My dad just asked me the following question: You have 10 standard independent decks (52 cards), you draw 1 card from each deck 1 at a time, what is the probability (count) of getting 4 aces (not necessarily distinct suits) out of the 10 cards you draw.
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I am thinking that the number of ways to get such a "hand" of 10 cards is the following:
[tex]\binom{10}{4}\left(\frac{4}{52}\right)^4\left(\frac{48}{52}\right)^6[/tex]

Reasoning being that you want 4 aces and there are 4 per deck, hence the (4/52)^4 and for the other 6 cards you want you have (48/52)^6, then 10 choose 4 for all the different ways you can get the 4 aces out of the 10 cards.

And if we wanted the aces to have distinct suits we would have 4! instead of 4^4

Does this look correct? Thanks.
 
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  • #2


Yes, your reasoning and calculation look correct. You have correctly accounted for the number of ways to choose 4 aces out of 10 cards and the probability of getting each ace in the chosen cards. The only thing to note is that the probability should be multiplied by 10 in order to account for the different ways the 4 aces can be chosen out of the 10 cards. So the final probability would be:

10 * \binom{10}{4}\left(\frac{4}{52}\right)^4\left(\frac{48}{52}\right)^6

For the case of distinct suits, you would indeed multiply by 4! instead of 4^4. Great job on your calculation!
 

What is Poker 10 Decks?

Poker 10 Decks is a variation of the popular card game poker, where players use 10 standard decks of cards instead of the usual one or two decks.

How many cards are used in Poker 10 Decks?

A total of 520 cards are used in Poker 10 Decks, with each deck containing the standard 52 cards.

What does "independent 4 Aces" mean in Poker 10 Decks?

"Independent 4 Aces" refers to the four aces in a deck of cards being unrelated to each other and not influenced by the presence or absence of other aces in the game.

How is Poker 10 Decks different from regular poker?

Poker 10 Decks differs from regular poker in that there are more cards in play, increasing the likelihood of higher-value hands and making the game more strategic.

What are some strategies for playing Poker 10 Decks?

Some strategies for playing Poker 10 Decks include paying attention to the number of cards in play, adjusting your betting based on the increased number of cards, and being aware of the potential for higher-value hands.

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