Full houses, flushes, and straights are three very strong poker hands. But does a full house beat a straight? And does a full house beat a flush?
The simple answer is: yes, a full house beats both a straight and a flush.
Now that you have an answer, let me explain why a full house beats a straight and a flush in poker.
Why Does a Full House Beat a Flush or a Straight?
But straights and flushes are very strong hands too. So why does a full house reign supreme? The answer lies in the math.
Full houses occur much less frequently than flushes or straights, which is why the full house is higher on the hand rankings. There are “only” 3,744 possible ways to make a full house using a standard 52 card deck. Compare this to the 10,200 possible ways to make a straight and the 5,108 ways to make a flush and it becomes clear why full houses are ranked higher.
Let’s dive deeper into the math.
The Math Behind a Full House
Also known as a full boat, a full house is basically three-of-a-kind and a pair in the same hand. Even newcomers to poker probably know they’re holding a strong hand when a full house comes in.
Here are a couple examples of full houses:
The above hand is a full house, tens full of queens. The following hand also qualifies as a full house:
This hand is referred to as fives full of threes, or fives over threes. Keep in mind that it’s the three-of-a-kind part of a full house determines the strength of the hand against other full houses. For example, in a match-up between the two full houses above, tens full of queens would win.
Using a standard 52-card deck, there are 156 distinct ways to draw a full house. But this doesn’t take suits into account.
For example, our 555AA full house from the example 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. In Texas Hold’em, the world’s most popular poker game, the probability of making a full house is 2.6% with all five community cards on the board.
The Math Behind a Flush
A flush is any five cards of the same suit that are not in sequential order. An example of a flush looks like this:
This hand qualifies as an ace-high club flush. Flushes are still a great hands, but occur more frequently than full houses.
There are 5,108 possible five-card flushes in a 52-card deck. This excludes straight flushes and the royal flush, both of which beat a full house.
In Texas Hold’em, you have a 3.03% chance of making a flush with all five community cards on the board.
The Math Behind a Straight
A straight is any five cards in numerical sequence. Examples of a straight include:
This hand is known as an ace-high straight, or broadway straight. Another example of a straight looks like this:
This hand qualifies as a nine-high straight. A straight is another strong poker hand, but using standard poker hand rankings, a full house beats a straight.
Once again, the full house is a harder hand to get mathematically, making it a stronger holding than a straight.
There are only 10 distinct straights, but the different suits bring the number of possible straight combinations to 10,200 from a 52-card deck. Again, this excludes straight flushes and the royal flush.
In Texas Hold’em, you have a 4.62% chance of hitting a straight with all five community cards on the board.
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