Does 3 of a Kind Beat a Straight

Introduction

One common question that puzzles new Poker players is – does 3 of a kind beat a straight?

Spoiler alert: the answer is no—a straight-out ranks three of a kind in standard poker rules.

Both hands are strong in their own right, but understanding the hierarchy between them can make a huge difference in how you play your cards.

In this article, we will explore why a straight beats 3 of a kind in poker.

What is a 3 of a Kind?

Three-of-a-kind, also known as trips or a set, is when a player holds three cards of the same rank plus two unrelated cards. For example, if you have 7♠ 7♥ 7♦ Q♣ 3♠, you have three of a kind with sevens. While this is a strong hand, it can be vulnerable to hands like straights and higher.

Three of a kind is generally stronger than two pairs, one pair, and a high card but weaker than straights, flushes, and full houses.

What is a Straight?

A straight occurs when a player has five sequential cards, each of different suits. For instance, 4♠ 5♦ 6♣ 7♥ 8♠ forms a straight ranging from four to eight. Aces can be used as either the highest card (as in the sequence: 10♠ J♣ Q♥ K♦ A♠) or the lowest (such as in A♠ 2 ♣3 ♦4 ♥5 ♠), depending on how they fit into the hand. In poker, a straight is considered relatively strong and ranks higher than hands like pairs, two pairs, and three of a kind.

Why Does a Straight Beat 3 of a Kind?

The reason a straight beats three-of-a-kind lies in the probability of making the hand and its inherent strength. Although strong, a three-of-a-kind is easier to form than a straight one. For example, the chances of getting straight on the flop are less common than achieving three-of-a-kind. Poker hand rankings partially reflect how likely or challenging it is to create each type of hand.

Example:

Let’s look at two hands head-to-head:

Player A’s hand (Three of a Kind): 7♠ 7♥ 7♦ 2♣ J♠

Player B’s hand (Straight): 4♠ 5♠ 6♦ 7♣ 8♥

Even though Player A has three of a kind, Player B wins with a straight. The consecutive nature of Player B's hand gives them the higher-ranked hand.

Can 3 of a Kind Be a Winning Hand?

While a straight beats three of a kind, it doesn’t mean three of a kind is not a strong hand. In many situations, three-of-a-kind can still win large pots, especially against weaker hands like pairs or two pairs.

Example:

Player A’s hand (Three of a Kind): K♠ K♦ K♥ 5♣ 9♠

Player B’s hand (Two Pair): Q♦ Q♠ 8♦ 8♠ 6♣

In this case, Player A’s three of a kind of kings will easily beat Player B’s two pairs (queens and eights).

Straight vs. 3-of-a-Kind

Probability

Here are the probabilities of being dealt a straight or three-of-a-kind in Texas Hold’em:

Probability of Three of a Kind:

The probability of getting three of a kind in a five-card hand is approximately 2.1128%.

This translates to odds of around 1 in 47 hands.

Probability of a Straight:

The probability of making a straight in a five-card hand is approximately 0.3925%.

This means the odds of forming a straight are about 1 in 254 hands.

A straight is much less likely to occur than three of a kind. Because straights are more difficult to form, they are considered stronger and are ranked higher in standard Poker hand rankings.

Hand Combinations

Let’s explain why the straight is rarer than three of a kind.

Three-of-a-Kind Combinations:

A three-of-a-kind requires three cards of the same rank plus two additional unrelated cards (known as ‘kickers’). In a standard deck of 52 cards, the number of ways to get three of a kind can be computed as follows:

First, choose which rank (2 through Ace) will form your trips. There are 13 possible ranks.

Once you choose a rank, you need to pick three out of the four available cards of that rank. There are C(4, 3) = 4 ways to select three cards from four.

For the two remaining cards, you must pick two different ranks from the remaining 12 ranks. C(12, 2) = 66 ways to choose two different ranks.

For each of these two chosen ranks, there are four suits to choose from for each card, so there are 4 x 4 = 16 combinations for the kickers.

Thus, the total number of ways to form three of a kind is:

 13×4×66×16 = 54,912 combinations.

Straight Combinations:

Five consecutive cards of different ranks form a straight. Here’s the breakdown of the combinations:

The rank sequences for a straight are limited to those with the lowest card from 2 to 10 (Ace can be high or low but cannot ‘wrap-around’ in standard poker).

Therefore, there are 10 possible straight sequences (e.g., 2-3-4-5-6 through 10-J-Q-K-A).

There are four suits available for each of these five consecutive cards. Therefore, the number of ways to choose five cards, one from each rank in the straight, is 4 x 4 x 4 x 4 x 4 = 1,024 combinations.

However, this total includes both straight flushes and regular straights. There are exactly 40 straight flushes (one for each sequence and suit), so we subtract these:

10×1024−40 = 10,200−40 = 10,160 straight combinations.

Comparison of Total Combinations:

The total number of possible five-card poker hands is 2,598,960.

The total number of possible three-of-a-kind hands is 54,912.

The total number of possible straight hands is 10,160.

The ratio of these two is approximately 54,912 / 10,160 ≈ 5.4. In other words, three-of-a-kind occurs more than five times as frequently as a straight.

Frequently Asked Questions

Does a straight-beat 3-of-a-kind exist in poker?

Yes. A straight one beats a three-of-a-kind because it occurs less frequently, making it a stronger hand. Forming a straight requires five consecutive cards, which is more challenging than matching three cards of the same rank. Poker hand rankings are based on the probability and difficulty of achieving each type, so hands that appear less often are ranked higher.

Can 3 of a kind beat any other hands?

Yes, a three-of-a-kind can outperform several hands, including pairs, two pairs, and high cards. Although it doesn't surpass a straight, flush, or full house in strength, it is still considered strong—particularly when opponents have lower-value hands like just one pair or high card combinations.

Should you fold 3 of a kind if there is a straight possibility?

It depends on the board and betting patterns. If you suspect your opponent may have hit a straight based on their actions, you might want to proceed cautiously. However, folding three is usually only necessary when the board heavily suggests a straight, and your opponent’s betting indicates strength.

Conclusion

In Poker, mastering hand rankings is essential for success. A straight always prevails over three-of-a-kind in all variations, such as Texas Hold'em, Omaha, and Seven Card Stud. This is due to the greater challenge of forming a straight and the superior strength of five consecutive cards compared to having three identical ranks.