# Does Three of a Kind Beat a Straight in Poker & Why?

7 minutes

Last Updated: December 14, 2022

You are probably here because you were wondering does three of a kind beat a straight? So, to give you the quick answer, no, three of a kind does not beat a straight in poker.

Now, if you want to learn the logic behind this rule and all other hand rankings in poker, we recommend that you read this article, as we will explain everything you need to know about straight vs. three of a kind in poker.

## A Three of a Kind in Poker

Three of a kind is a 5-card combination that consists of three cards of the same rank and two additional unrelated cards of different ranks, which are called the kickers.

Two examples of a three-of-a-kind combination in poker:

• 99956 – three-of a-kind, nines
• 8887K – three-of-a-kind, eights

Depending on how the three-of-a-kind combination is put together, different terms are used to describe this hand in Texas Hold’em.

### Set vs. Trips in Hold'em

If the three-of-a-kind combination is put together using one of the player's hole cards and two community cards, this combination is referred to as trips.

For example:

• Player A is holding A10 as his hole cards, and the board is K101069.

In this situation, the best 5-card combination that Player A can put together is 101010AK (trip jacks with an A and a K kicker).

Now, it is true that in this situation, Player A has used both of his hole cards to make the best possible hand. However, the A only plays as a kicker and not as a part of the main three-of-a-kind combination, and because of this, the combination is called trips.

If the three-of-a-kind combination is put together using both of the player's hole cards and one of the community cards, this combination is referred to as a set.

For example:

• Player A is holding 99 as his hole cards, and the board is 9JQ53.

In this situation, the best 5-card combination that Player A can put together is 999QJ (a set of nines with a Q and a J kicker).

As you can see, Player A is using both of his hole cards to make the three-of-a-kind combination, and because of this combination is called a set.

It is very important to learn the difference between these three-of-a-kind combinations because, although in theory these hands are ranked in the same way, in practice, a set is much stronger

Your opponents will have a harder time putting you on a three of a kind when you hold two cards from the combination in your hand.

### Rules for Ranking Three-of-a-Kind Combinations in Poker

There are three main rules that we use in poker to rank three-of-a-kind combinations:

1. Rank of the cards that make the three-of-a-kind combination
2. The rank of the stronger kicker
3. The rank of the weaker kicker

Example of how three-of-a-kind combinations are ranked:

• Hand 1) 777JQ vs. Hand 2) 666JQ

In this example, the situation is pretty clear and we use the first rule: rank of the cards that make the three of a kind combination. On the first hand, the rank of the cards that make trips is 7 and on the second hand, the rank of the card that makes trips is 6.

Since a 7 outranks a 6 in poker, the first three-of-a-kind combination outranks the second.

Example 2:

• Hand 1) 999KQ vs. Hand 2) 999QJ

In this example, we can’t use the first rule since both combinations consist of the same three of a kind rank, so we will use the rule of the stronger kicker.

In the first combination, the stronger kicker is the king, while in the second hand the stronger kicker is the queen. Since a king outranks a queen in poker, the first three-of-a-kind combination outranks the second.

Example 3:

• Hand 1) 101010A7 vs. Hand 2) 101010AJ

Here, we can’t use the first rule since both combinations consist of the same three of a kind rank nor the second rule, since the stronger kicker is of the same rank in both hands. Thus, we will use the rule of the weaker kicker.

In the first combination, the weaker kicker is the seven, while in the second combination the weaker kicker is the jack. Since a jack outranks a seven in poker, the second three-of-a-kind combination outranks the first.

## A Straight in Poker

In poker, a 5-card combination that is made of five sequential cards with at least one card being a different suit from the others is called a straight.

Two examples of straights in poker:

• KQJ109 – a king-high straight
• 87654 – an eight-high straight

If a 5-card combination consists of five sequential cards of the same suits, this straight combination is called a straight flush, i.e. KQJ109 – a queen-high straight flush.

Lastly, if a 5-card combination consists of five sequential cards of the same suit with the highest card in the combination being an Ace, this straight flush combination is called a royal flush.

The four possible royal flush combinations in poker are:

• AKQJ10 – a royal flush in hearts
• AKQJ10 – a royal flush in clubs
• AKQJ10 – a royal flush in diamonds
• AKQJ10 – a royal flush in spades

When it comes to straight combinations and how they rank against each other, the royal flush is the highest ranking straight combination and the highest ranking overall combination in poker.

The straight flush is the second strongest straight combination and the second strongest combination in poker.

Finally, an “ordinary” straight is the weakest straight combination and the 6th strongest hand overall in poker.

### Rules for Ranking Straight Combinations in Poker

The rule for ranking straight in poker is pretty simple; each straight ranks based on the highest card in the combination.

For example,

• Hand 1) 109876 vs. Hand 2) J10987 – a ten-high straight vs. a jack-high straight

In this situation, the second combination – the jack-high straight, outranks the first combination – the ten-high straight, because the highest card in the second combination (J) outranks the highest card in the first combinations (T).

This same rule also applies when ranking straight flush combinations.

## The Total Number of Straight Combinations in Poker

The standard card deck used for poker consists of 52 cards divided into four suits (hearts, diamonds, spades, and clubs) and 13 different ranks (A, K, Q, J, T, 9, 8, 7, 6, 5, 4, 3, 2).

This information allows us to calculate the following:

• There are 10,200 possible five-card straight combinations
• There are 36 possible five-card straight flush combinations (9 for each suit)
• There are 4 possible royal flush combinations (1 for each suit)

Since we already know that the royal flush is stronger than the straight flush and the straight flush is stronger than the ordinary flush we can conclude that the main rule for ranking hands in poker is “the lower the chance of getting a specific combination in poker, the stronger that specific combination is.”

## Does a Three of a Kind Beat a Flush In Poker?

Now that we know what three-of-a-kind and straight combinations mean in poker, it is time to explain why three of a kind do not beat a flush in poker from a mathematical standpoint.

As you can see, we have listed all the hand rankings in poker based on their strength in the table below. Furthermore, using this table in the correct way can help you understand the logic behind hand rankings easier.

 Hand Combinations Probability Odds Royal Flush 4 0.000154% 649,739-to-1 Straight Flush 36 0.00139% 72,192-to-1 Four of a Kind 624 0.02401% 4,164-to-1 Full House 3,744 0.1441% 693-to-1 Flush 5,108 0.1965% 509-to-1 Straight 10,200 0.3925% 254-to-1 Three of a Kind 54,912 2.1128% 46-to-1 Two Pair 123,552 4.7539% 20-to-1 One Pair 1,098,240 42.2569% 1.37-to-1

We can see from the table that the straight is ranked as the sixth overall hand in Texas Hold’em while the three of a kind is ranked one place lower, but why is that?

Well, as we mentioned before, there are 10,200 possible combinations of the straight in poker which means that the odds of getting one of these combinations on any given hand are 254-to-1 or 0.3925%.

Now, if we look at the three-of-a-kind combination, we can see that there are 54,912 possible combinations of this hand. Thus, the odds of getting a three-of-a-kind hand on any individual hand are 46-to-1 or 2.1128%.

Since hands in poker are ranked based how hard it is to make them, a straight beats three of a kind. The odds of collecting a straight are much lower than the odds of making three of a kind.

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