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

Feb 24, 2009

timon

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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Feb 24, 2009

CRGreathouse

Science Advisor

Homework Helper

How many players? How many decks? Do you count a hand as a 3-of-a-kind even if a better hand is possible?

Feb 25, 2009

timon

never mind, solved.

1. What are the odds of getting three-of-a-kind in a game of poker?

The odds of getting three-of-a-kind in a game of poker depend on the number of players and the specific game being played. In a standard 52-card deck, the odds of getting three-of-a-kind are approximately 2.1%. However, these odds may vary in different poker variations such as Texas Hold'em or Omaha.

2. How do you calculate the odds of two players getting three-of-a-kind in a game of poker?

To calculate the odds of two players getting three-of-a-kind in a game of poker, you need to know the number of possible combinations for three-of-a-kind and the number of possible combinations for all hands. Then, divide the number of combinations for three-of-a-kind by the number of combinations for all hands and multiply by 100 to get the percentage. For example, in a game of Texas Hold'em with 2 players, the odds of both players getting three-of-a-kind are 0.2%.

3. What factors can affect the odds of two players getting three-of-a-kind in a game of poker?

The odds of two players getting three-of-a-kind in a game of poker can be affected by several factors. These include the number of players, the number of decks being used, the specific poker variation being played, and the skill level of the players. Additionally, the odds can also be affected by any wild cards or community cards that may be used in the game.

4. Is it possible for both players to have three-of-a-kind in a game of poker?

Yes, it is possible for both players to have three-of-a-kind in a game of poker. In fact, this scenario is quite common in games with multiple players and wild cards. In this case, the winner is determined by the highest ranking three-of-a-kind hand. If both players have the same ranking three-of-a-kind, then the winner is determined by the highest ranking side card.

5. How can understanding the odds of two players getting three-of-a-kind in a game of poker improve my gameplay?

Understanding the odds of two players getting three-of-a-kind in a game of poker can help you make more informed decisions and improve your gameplay. Knowing the odds can help you determine the strength of your hand and make better decisions on whether to fold, raise, or call. It can also help you anticipate your opponents' hands and adjust your strategy accordingly.