Odds of two players getting three-of-a-kind in a game of poker?

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SUMMARY

The odds of two players obtaining three-of-a-kind in a game of poker depend on the number of players and the specific rules of the game. The initial assumption of squaring the probability for one player does not accurately reflect the shared community cards. The discussion highlights the importance of considering the total number of players and the deck configuration when calculating these probabilities. Ultimately, the complexities of poker hand rankings and shared cards must be factored into any probability assessment.

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timon
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from another thread on probability:

What are the odds of two players getting three-of-a-kind in a game of poker?
My first idea was to square the chance for three-of-a-kind for one player, but that doesn't seem right to me since it doesn't take the shared cards on the table into account.
 
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How many players? How many decks? Do you count a hand as a 3-of-a-kind even if a better hand is possible?
 


never mind, solved.
 

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