Does a Flush Beat 3 of a Kind

Introduction 

Poker is a game of strategy. Knowing which hands outrank others can make a big difference in how you play and how often you win. One common question among Poker players is whether a flush beats three of a kind. The answer is yes — but why is that the case?

This article will explore the hierarchy of these hands and provide tips on playing when you have a flush or three of a kind.

What is a Flush?

A flush is a hand of five cards, all from the same suit, arranged in any sequence. For instance, if you hold five hearts, that constitutes a flush. The values of the cards matter only when two players each have a flush. In that case, the player whose card has the highest rank wins.

Here are a few examples of flushes:

• A♠ 7♠ 4♠ 3♠ 2♠ (Ace-high flush)
• J♣ 9♣ 6♣ 5♣ 2♣ (Jack-high flush)

A flush is a relatively strong hand in Poker because the odds of getting five cards of the same suit are lower than obtaining simpler combinations like pairs or three of a kind.

What is Three of a Kind?

Three of a kind, also known as ‘trips’ or a set, is a hand containing three cards of the same rank and two unrelated cards. This hand is strong, especially when the rank of the three matching cards is high.

Examples of three of a kind include:

• Q♣ Q♦ Q♠ 8♠ 4♣ (Three Queens)
• 7♠ 7♦ 7♣ K♦ 2♣ (Three Sevens)

Three-of-a-kind can be a powerful hand, especially when it might be tricky for opponents to detect. However, it does not carry the same strength as a flush.

Why does a Flush Beat 3 of a Kind

Here, we will break down the probability of getting a flush and three of a kind and the total number of combinations possible for each hand.

1. Calculating the Probability of a Flush

A flush consists of five cards of the same suit. Four suits are in a deck (hearts, diamonds, clubs, spades), and within each suit, there are (13, 5) = 1,287 ways to choose five cards.

However, this includes straight flushes (even rarer and higher-ranking), so we must subtract those to get the true count for non-straight flushes.

Total Flush Combinations (excluding straight flushes):
There are 10 possible straight flushes per suit. With 4 suits, we have 4 × 10 = 40 total straight flush combinations.

Therefore, the number of flush combinations without straight flushes is:

4 × 1,287 − 40=5,1084

Probability of Making a Flush in Texas Hold'em:
There are (52, 5) = 2,598,960 possible 5-card combinations from a 52-card deck.

Thus, the probability of a flush (excluding straight flushes) is:

5,108/2,598,960 ≈ 0.001965 or 0.1965%

2. Calculating the Probability of Three of a Kind

Three of a kind requires three cards of the same rank and two unrelated cards of different ranks.

 Step-by-Step Calculation for Three of a Kind:

• First, choose the rank for the three of a kind: 13 possible ranks.
• Choose 3 cards from the 4 available for that rank: (4, 3) = 4 ways.
• We need two different ranks for the two remaining cards (not matching the three-of-a-kind). There are 12 remaining ranks, and we need to pick 2: (12, 2)=66.
• These two ranks can come in any of the 4 suits, so we have 4 × 4 = 16 combinations for the remaining cards.

Total Three of a Kind Combinations:

13 × 4 × 66 × 16 = 54,912

Probability of Making Three of a Kind in Texas Hold'em:

Thus, the probability of making three of a kind is:

54,912/2,598,960 ​≈ 0.02113 or 2.113%

Comparing the Two Hands:

From these calculations, we can see why a flush beats three of a kind:

Rarity: The flush is rarer than three of a kind. With a probability of approximately 0.1965%, a flush is more difficult to obtain than three of a kind, which has a probability of approximately 2.113%.

Hand Rankings and Strength: Poker hand rankings are structured around these probabilities. The rarer a hand is to make, the higher it ranks. Since a flush occurs less frequently, it is mathematically stronger and ranks higher than three of a kind.

How to Play With a Flush or 3 of a Kind

Both hands are strong but have different rankings and strategies depending on the board. Here are some tips for playing each hand:

Playing a Flush:

Here’s how to approach playing a flush:

1. Bet Aggressively in Most Situations:

• A flush is usually a strong hand, so you will want to maximize value from your opponents. Most players are willing to call bets with weaker hands, such as two pairs or trips (three of a kind), so bet confidently when you have a flush.
• You can play even more aggressively with a high flush (e.g., an Ace-high or King-high flush) since fewer hands can beat you.

2. Watch Out for Paired Boards:

• Be cautious if the board is paired (for example, two 9s). A paired board could mean your opponent has a full house, which would beat your flush.
• In this situation, you might want to slow down and control the pot size by checking or calling rather than raising it.

3. Extract Maximum Value on Non-Threatening Boards:

• If the board has no pairs and you hold a flush, especially if it is the highest flush possible, you can continue betting or raising to build the pot.
• Avoid scaring off weaker hands with excessively large bets, especially if you believe your opponent may have hands like a lower flush, a straight, or trips.

Playing Three of a Kind:

Here’s how to play it effectively:

1. Bet Strongly but Cautiously:

• Trips are a powerful hand, especially if your three-of-a-kind is made with high-ranking cards like Aces or Kings. You can confidently bet and raise, especially against players who might have a top pair or two pairs.
• However, be wary of over-committing to the pot if there are flush or straight possibilities on the board.

2. Watch for Potential Flush and Straight Draws:

• Be cautious if the board has multiple cards of the same suit or consecutive ranks. Opponents could be drawing to a flush or straight, which would beat your trips.
• In these scenarios, checking or making smaller bets might be best to avoid giving away too much information or losing too many chips if they hit their draw.

3. Stay Alert on the River:

• If you are betting aggressively with three of a kind and the river brings a fourth card of the same suit or a possible straight, re-evaluate. An opponent calling along might have completed a flush or straight.
• Decide whether to check, call, or fold based on the strength of your trips and how much you have committed to the pot.

Frequently Asked Questions

Why does a flush beat three of a kind?

A flush beats three of a kind because it is a rarer hand. In Poker, the hand ranking system prioritizes rarity, making a flush (five cards of the same suit) stronger than three of a kind (three cards of the same rank). The odds of getting a flush are approximately 0.2%, compared to 2.1% for three-of-a-kind.

How to play a flush?

Play a flush aggressively, but be cautious if the board is paired, as it could mean a full house is possible. If you hold a high flush, you can bet confidently to build the pot, but consider opponents' tendencies and the potential for higher hands.

How to play three of a kind?

Bet confidently with three of a kind, but be mindful of flush or straight possibilities on the board. If there are possible draws, consider smaller bets to control the pot. Disguise your hand by slow playing, especially if your trips are from a pocket pair.

Conclusion

In Poker, knowing the value of your hand is just the beginning. While a flush beats three of a kind, the real challenge lies in how you play these hands to maximize gains and minimize losses. By understanding the strengths and weaknesses of each hand, you can make more informed decisions at the table.