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

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The odds of two players getting three-of-a-kind in poker depend on various factors, including the number of players and the specific cards dealt. Simply squaring the probability for one player does not accurately reflect the situation due to the shared community cards. The discussion highlights the complexity of calculating these odds, especially when considering the potential for better hands. Ultimately, the original poster resolved their confusion regarding the calculation. Understanding the nuances of poker probabilities is essential for accurate assessments.
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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.
 

Thread 'Deductive proof in logic formal systems'

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