Does a straight flush beat a full house?

Why Does a Straight Flush Beat a Full House?

Certain poker hands can give a player a jolt of adrenaline, including the powerful straight flush and the mighty full house. But which one wins? Does a straight flush beat a full house?

The simple answer is: yes, a straight flush does beat a full house.

Now that you have an answer, let me explain why a straight flush beats a full house.

Why Does a Straight Flush Beat a Full House?

When you’re holding a hand like a full house or a straight flush, you know you’ve made one of the strongest possible hands. But why exactly does one topple the other? The answer lies in the math.

Straight flushes occur much less frequently than full houses, which is why the straight flush is higher on the hand rankings. While there are 3,744 possible ways to make a full house, there are just 36 ways to make a straight flush using a traditional 52-card deck.

Let’s dive deeper into the math.

does a straight flush beat a full house math

The Math Behind a Full House

A full house (aka full boat) occurs when a player makes both three-of-a-kind and a pair in the same hand. An example of a full house is:

Does a full house beat a straight flush?jc-clubs-new-cardsjs-spades-new-cards2c-clubs-new-cards2d-diamond-new-cards

This hand qualifies as a full house, jacks full of deuces. The three-of-a-kind part of a full house determines the strength of the hand against other full houses. For example, the hand above would beat 5-5-5-A-A (fives full of aces) in a head to head match-up.

Using a standard 52-card deck, there are 156 distinct ways to draw a full house. This doesn’t take suits into account.

For example, our JJJ22 full house from the examples above represents one distinct full house, regardless of the suits. Taking suits into account, there are 24 different ways to draw any individual distinct full house.

Multiplying 156 distinct full house hands times 24 possible suit combinations gives us 3,744 possible ways to draw a full house out of a 52-card deck.

The Math Behind a Straight Flush

Let’s take a look at an example of a straight flush. This hand occurs when a player holds five cards in sequential order that are all of the same suit:

4c-clubs-new-cards5c-clubs-new-cards6c-clubs-new-cards7c-clubs-new-cards8c-clubs-new-cards

The above hand qualifies as an eight-high straight flush. The straight flush is truly one of the most rare hands you can make in most poker games. It’s one of the strongest hands in poker, second only to the royal flush in hand rankings.

A 52-card deck yields nine ways to draw a distinct straight flush. The four suits give us four different versions of a distinct straight flush, and overall there are 36 ways to draw a five-card straight flush.

The straight flush, with 36 possible combinations, is a far more rare hand than a full house, with 3,744 possible combos.

A straight flush beats a full house in the standard poker rankings. In Texas Hold’em, you have a 0.0279% chance of making a straight flush with all five community cards on the board. This excludes the royal flush, which is an ace-high straight flush (like A♠ K♠ Q♠ J♠ T♠).

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Home > Why Does a Straight Flush Beat a Full House?
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About the Author

Geoffrey Fisk

Freelance writer and poker player based in San Diego, California.

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