# Three of a kind

## Introduction

In poker, a Three of a Kind is a hand where a player has three cards of the same rank along with two other cards of different ranks. This hand is quite powerful, ranking seventh among all possible poker hands.

Let’s understand all the hand rankings before diving into the concept of Three of a Kind. Later we will also understand the probabilities.

## Poker Hand Rankings

Here are the hand rankings in poker:

• Royal Flush: It is the highest hand ranking of Poker which consists of Ace, King, Queen, Jack, and 10 of the same suits.
• Straight Flush: It is the second highest hand ranking in the game of Poker, consisting of five consecutive numerical number cards of the same suit.
• Four of a Kind: When the player has four cards of the same rank in the hand.
• Full House: In this, the player has a Three of a Kind and One Pair in the same hand.
• Flush: The player has 5 cards with the same suit in the hand in the flush.
• Straight: When the player has 5 cards in a straight numerical order in the hand.
• Three of a Kind:  Here, the player has three cards of the same rank in the hand.
• Two Pair: In this, the player has two pairs of the same rank in hand.
• One Pair: The player has two cards of the same rank in one pair.
• High Card: When the player has the highest ranking card(s) in the hand.

## What is Three of a Kind?

Three of a Kind comprises three cards of the same rank and two cards of different ranks. It ranks third highest, following a Straight. Obtaining Three of a Kind is less difficult than achieving higher-ranking hands like a Flush. As it ranks seventh in hand rankings, Three of a Kind is relatively common.

In the event of two players holding Three of a Kind, the winner is determined by the highest card value among their three cards. For example, consider two players, A and B, with the following hands:

• Player A: King of Spades, King of Clubs, King of Diamonds, 7 of Clubs, and Jack of Hearts.
• Player B: 5 of Clubs, 5 of Diamonds, 5 of Hearts, Queen of Spades, and Ace of Spades.

In this scenario, Player A's Kings hold a higher value than Player B's 5s , making Player A the winner.

## How Does a 3-of-a-Kind Hand Rank?

• Three of a Kind is a poker hand where a player holds three cards of the same rank, accompanied by two unrelated cards.
• It ranks seventh in the hierarchy of poker hands, below a Straight and above Two Pair.
• In terms of strength, Three of a Kind beats Two Pair but is surpassed by a Straight, a Flush, a Full House, Four of a Kind, a Straight Flush, and a Royal Flush.

## Three-of-a-Kind Poker Probabilities

The mathematical probabilities and odds of achieving a Three of a Kind hand in poker depend on various factors:

• Pocket Pair: The odds of flopping Three of a Kind when holding a pocket pair are approximately 10.8%, equating to 1 in 9.3 hands.
• Choosing the Trio: Initially, you need to choose a rank for the trio, which offers 131 choices. Subsequently, you select three cards of that rank, providing 4 combinations.
• Overall Probability: The probability of being dealt pocket aces or any other pocket pair is approximately 220 to 1, considering there are 13 types of cards in a deck.

These statistics indicate that while Three of a Kind is not the most common hand, it still occurs frequently enough in poker games.

### How many hands can a Three of a Kind beat?

A Three- of a Kind hand can beat two types of hands: One Pair and a High Card. It ranks below a Straight and above a Two Pair in poker hand rankings.

### How many ways can we get a Three of a Kind?

If we follow the card suit condition, then there are 54,912 ways to make Three of a Kind hand and only 848 ways to achieve it. The technical probability of getting the Three of a Kind is 2.1128% or once in every 46 hands.

### Is getting a Three of a Kind too difficult?

Players have a decent probability of getting a Three of a Kind. After the High Card, One and Two pairs, Three of Kind is a hand that can be achieved by a player very easily.

### What poker hand has Three of a Kind and a Pair?

A Full House hand consists of Three of a Kind and a Pair. It ranks higher than Three of a Kind but lower than Four of a Kind in poker hand rankings.

## Conclusion

Understanding why a Three of a Kind hand is important reveals how useful it can be. It's the seventh-best hand you can have. Even though it's not as good as a Flush or a Full House, it still helps you win games quite often.

When you start with a pair in your hand, there's about an 11% chance you'll get Three of a Kind. Plus, you have some freedom in picking which three cards match. So, while it's not the absolute best hand, having Three of a Kind can make a difference when you're playing poker.

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