Does a Flush Beat a Straight in Poker

Introduction

Poker hand rankings are fundamental to understanding the game and making the right decisions at the table. Knowing which hands beat others is crucial, especially when faced with big bets or tough calls. One common question that players, especially beginners, often ask is, ‘Does a flush beat straight?’ The answer is yes; a flush does beat a straight. Let’s find out why and how these hands rank in poker.

What is a Straight?

A straight consists of five consecutive cards of different suits. For example, a hand with 8♦, 7♠, 6♣, 5♠, and 4♠ would be a straight. The strength of the straight depends on the highest card. So, a 10-high straight (10-9-8-7-6) would beat a 9-high straight (9-8-7-6-5).

What is a Flush?

A flush is a hand with five cards in the same suit, though they are not arranged sequentially. For instance, a combination like K♠, 10♠, 8♠, 5♠, and 2♠ qualifies as a flush. Similar to straights, the value of a flush is determined by its highest card, or ‘top card’. In cases where two players each hold a flush, the one with the higher top card emerges victorious.

Flush vs. Straight

The simple reason flush beats straight is that it is statistically less likely to occur. Poker hand rankings are determined by their probability, meaning the less likely it is to obtain a particular hand, the higher its ranking. A straight consists of consecutive cards from any suit and occurs more frequently than a flush. In contrast, a flush requires all five cards to be of the same suit, which is more difficult to achieve and, therefore, ranks higher than a straight.

Example:

Hand 1: Straight

8♦, 7♠, 6♣, 5♠, 4♥

This hand is straight, with the highest card being an 8.

Hand 2: Flush

K♠, 10♠, 8♠, 5♠, 2♠

This hand is a flush with a King as the highest card.

Hand 2 (flush) would win over Hand 1 (straight) in a showdown because a flush outranks a straight. Even if the straight had a higher top card than the flush’s top card, the flush would still win because of its superior ranking.

An easy way to remember that a flush ranks higher than straight is to consider suits versus sequences. In a flush, all the cards share the same suit, making it harder to put together than having sequential cards in varying suits.

Why Does a Flush Beat a Straight?

To find out the answer to the question ‘does a straight beat a flush in Poker?’, we can compare the probabilities of each hand occurring and strength of card combinations.

Hand Probability

Total Number of Possible Hands in Poker:

In a standard deck of 52 cards, a poker hand consists of 5 cards. The combination formula gives the total number of different 5-card hands:

(52, 5) = 52!/5! (52−5)! = 2,598,960 possible hands

Calculating the Probability of a Straight:

You need five consecutive ranks to form a straight, but suits don’t matter.

1. There are 10 possible straight sequences in poker (e.g., A-2-3-4-5 up to 10-J-Q-K-A).
2. Each card in the sequence can be one of 4 suits.

So, for each straight sequence, there are:

4×4×4×4×4 = 1,024 ways to combine suits

Since there are 10 different ways to make a straight (10 possible sequences):

10 × 1,024 = 10,240 possible straight hands

Adjusting for Straight Flushes:

A straight flush (which includes a royal flush) is the highest possible hand and involves all cards of the same suit. There are exactly 10 straight flushes possible per suit:

4 suits × 10 straight flush sequences per suit = 40 straight flush hands

Removing these 40 straight flushes from the total number of straights:

10,240 – 40 = 10,200 non-straight-flush straight hands

So, the probability of being dealt a regular straight is:

10,200/2,598,960 ≈ 0.0039 or 0.39%

Calculating the Probability of a Flush:

All five cards must be of the same suit to form a flush, but not in sequence. Let's calculate the total number of possible flushes:

1. There are 4 suits, and all cards in the flush must be from one of those suits.
2. Within a single suit, there are 13 cards, and we need to choose 5 cards.

The number of ways to choose 5 cards from 13:

(13, 5) = 13!/ 5!(13−5)! = 1,287 ways

Since there are 4 suits:

4 × 1,287 = 5,148 possible flush hands

Adjusting for Straight Flushes:

Since we calculated straight flushes already (40 hands), we subtract those from our flush count:

5,148 − 40=5,108 non-straight-flush flush hands

So, the probability of being dealt a regular flush is:

5,108/2,598,960 ≈ 0.00197 or 0.20%

Comparison of Probabilities:

• Probability of a Straight (non-straight-flush): ≈ 0.39%
• Probability of a Flush (non-straight-flush): ≈ 0.20%

The probability of getting a flush is lower than getting a straight one, making a flush statistically rarer.

Hand Combinations

Hand combinations, or ‘combos’, refer to how you can form a particular poker hand. Here is the number of hand combinations for both straights and flushes.

Straight Hand Combinations:

As previously calculated, there are 10,200 ways to form a non-straight-flush straight in poker. Here’s how those combinations break down:

1. Straight Sequences: There are 10 unique sequences that qualify as straights (A-2-3-4-5 up to 10-J-Q-K-A).
2. Suit Combinations per Sequence: The five cards can be four suits for each sequence.

4 x4 x 4 x 4x 4=1,024 combinations per sequence

3. Adjusting for Straight Flushes: Since straight flushes are the highest-ranked hands and are counted separately, we exclude them from regular straight combinations. There are 40 straight flushes, so:

10,240 total straight combinations − 40 straight flush combinations = 10,200 regular straight combinations

Flush Hand Combinations

Flushes involve all five cards of the same suit without necessarily being in sequence. The combinations for flushes are calculated as follows:

1. Single Suit Selection: There are four suits to choose from (clubs, diamonds, hearts, spades).
2. Card Selection within a Suit: We have 13 cards within each suit. We need to select 5 cards from these 13 to form a flush. The number of ways to choose 5 cards from a single suit is:

(13, 5) = 1,287 combinations per suit

3. Adjusting for Straight Flushes: From the total flush combinations (5,148), we subtract the straight flush combinations (40), leading to:

5,148 – 40 = 5,108 non-straight-flush flush combinations

• Straight Combinations: 10,200
• Flush Combinations: 5,108

Since there are fewer flush combinations than straight combinations, flushes are less common and thus rank higher.

Frequently Asked Questions

Does a straight beat a flush in cards?

No. A flush beats a straight in Poker. Hands are ranked based on their rarity, and there are fewer possible combinations of flushes compared to straights. This rarity makes flushes stronger, placing them higher in the hand rankings.

How often can you get a flush compared to a straight?

A flush occurs approximately once in every 508 hands, while a straight occurs about once in every 254. Flushes are about twice as rare as straights, contributing to their higher ranking in poker hand hierarchies.

Can a straight flush lose to a regular flush?

No, a straight flush combines both the characteristics of a straight and a flush. It ranks above an ordinary flush. In fact, it is one of the highest possible hands in Poker, surpassed only by a royal flush.

Conclusion

So, is a flush higher than a straight? Absolutely. Understanding the ranking hierarchy of Poker hands is essential for making wise choices at the table. Knowing that a flush outranks a straight one allows for more calculated decision-making. As you become more experienced in the game, this insight will help you focus on assessing your opponents, calculating odds, and executing strategies with precision.