Does Three of a Kind Beat a Straight?

Does Three of a Kind Beat a Straight?

Judging by how many people search for “does three of a kind beat a straight” on Google, it’s clear that many people don’t know the answer to this question.

In games using standard poker hand rankings, both three-of-a-kind and straights are quite strong hands. But which one is best in a head-to-head showdown?

The simple answer is: no, three-of-a-kind does not beat a straight. Straights are superior in head-to-head showdowns with three-of-a-kind.

Now that you have an answer, let me explain why a straight beats three-of-a-kind.

Why Does a Straight Beat Three-of-a-Kind?

While it may seem that it is easier to make a straight than three-of-a-kind, in reality, this is not the case. The reason why a straight beats three-of-a-kind lies in the math.

Straights occur less frequently than three-of-a-kind, which is why straights are higher on the poker hand rankings. While there are 54,912 ways to make a hand with three-of-a-kind, there are just 10,200 ways to make a straight using a standard 52-card deck.

Let’s dive deeper into the math.

math for does three of a kind beat a straight

The Math Behind a Straight

A straight is made when a player holds five cards in sequential order according to card rankings. Examples of straights include:

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The above hand is known as an ace-high straight, or “broadway” straight. Note that a broadway straight of all the same suit, like A♠ K♠ Q♠ J♠ T♠, qualifies as a royal flush, the strongest hand in poker.

For our comparison in this article, we’re talking about the regular version of the straight, with mixed suits. Another straight example looks like this:

7s-spades-new-cards6s-spades-new-cardsDoes a Full House Beat a Straight or a Flush?4c-clubs-new-cardsDoes a Full House Beat a Straight or a Flush?

The above qualifies as a seven-high straight. If this hand were all the same suit, like 76543, the hand is a straight flush.

In a 52-card poker deck, only ten distinct ways to draw a straight exist. A distinct straight doesn’t take suits into account, so AKQJT and 76543 are two of the ten possible distinct straights.

When you take suits into account, there are 10,200 ways to draw a five-card straight out of the 52-card deck. This excludes straight flushes and royal flushes. In Texas Hold’em, where players are trying to make the best five-card hand out of seven total cards, you have a 4.62% chance of making a straight with all five cards on the board.

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The Math Behind Three-of-a-Kind

Three-of-a-kind is made by holding three of the same-ranking card in a five-card hand. An example of a three-of-a-kind hand would be:

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The above hand qualifies as three-of-a-kind aces. Note that if the latter two cards are paired (like A A♠ A♣ 2♣ 2), the hand qualifies as a full house.

The 52-card deck offers 858 distinct ways to draw three-of-a-kind in a five-card hand. Factoring in the four suits gives you 64 different ways to draw each distinct three-of-a-kind.

In total, there are 54,912 possible ways to draw three-of-a-kind out of a 52-card deck. Compared to the 10,200 ways to make a straight, three-of-a-kind occurs more commonly, making the straight the more rare and stronger hand.

In Texas Hold’em, players have a 4.83% chance of making three-of-a-kind with all five community cards on the board. The math of making a five-card hand out of seven cards puts three-of-a-kind much closer to a straight as far as probability. The straight is still slightly more rare, however, and is the stronger hand in Texas Hold’em.

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About the Author

Geoffrey Fisk

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

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