Does Three of a Kind Beat a Straight in Poker & Why Not?
If you are planning to get into poker, the first thing that you should do is learn the rules and hand rankings.
We know it sounds obvious, but there are a lot of poker players that first start playing and then learn what beats what in poker.
While this might be okay if you are playing poker in home games with your friends if you decide to play for real money this approach can be pretty expensive.
In this article, we will answer the question does three of a kind beat a straight, or does a straight beat three of a kind, as this is one of the spots players get most confused when ranking hands in poker.
If you’re just looking for a straight up answer, it is no: three of a kind does not beat a straight in poker!
To find out why this is the case and why a straight always beats three of a kind in Texas Hold’em, keep on reading!
What Is a Three of a Kind In Poker?
In Texas Hold’em, a combination that consists of three cards of the same rank and two other cards (called kickers) that are both of different ranks is called three of a kind.
Examples of a three-of-a-kind hand:
- J♠J♦J♥2♣7♥ – Three of a kind, Jacks
- 10♠10♥10♣A♣9♦ – Three of a kind, Tens
In Texas Hold’em, there are different names for the three kind combinations depending on how many hole cards you use to put together this hand.
In situations where you are not using your hole cards or are using only one hole card to put together three of a kind, the three of a kind combination that you put together is called trips.
For example, if your hole cards are K♠J♦ and the board is J♠J♥J♠8♣7♦, the best 5-card hand you can make is J♠J♦J♥K♠8♣ – trip jacks (three of a kind, jacks)
Now, don’t be confused by the fact that you also used the Ks. This card is used as a kicker (because every hand in Texas Hold’em must have 5 cards), not as a part of the three of a kind.
The rule only applies to the hole cards that will be a part of the three of a kind.
If you are using both of your hole cards to put together a three of a kind combination, your combination is called a set.
For example, if your hole cards are 8♠8♦ and the board is 8♥10♠5♦4♣3♣, the best 5-card hand you can make is 8♠8♦8♥10♠5♦ – a set of eights (three of a kind, eights)
In this example, you used both of your hole cards to put together the three of a kind combination and this three of a kind combination is called a set.
The main reason, why different terms are used for these two ways of making three of a kind combinations is the fact that having a set is much less evident than having trips, making it easier to fool your opponents and extract value with a set than with trips.
The Number of Three of a Kind Combinations in Texas Hold’em
The standard 52-card deck used for Texas Hold’em has 4 different suits (hearts, diamonds, spades, and clubs) and 13 different card ranks (A, K, Q, J, T, 9, 8, 7, 6, 5, 4, 3, 2).
You can choose the rank of the three of a kind hand in 13 different ways, and you can choose which of the suits will not be included in 4 different ways.
This means that there are 858 distinct three of a kind ranks and 54,912 different three of a kind combinations in a standard deck.
How Three of a Kind Combinations Are Ranked
When it comes to ranking the three of a kind combinations, there are three rules that apply:
- The strength of the three of a kind hand depends on the rank of the three cards
- If the three main cards have the same rank, the first kicker is used to determine the winner
- If both the three main cards and the kicker are of the same rank, the second kicker is used to determine the winner
- 9♠9♦9♥A♠K♥ vs 8♠8♣8♦A♠K♥
This situation is pretty clear as three 9s are stronger than three 8s, which makes the first three of a kind combination stronger than the second.
- 10♠10♥10♦K♠Q♠ vs 10♠10♦10♣Q♠J♦
Both three of a kind combinations consist of cards of the same rank (T). In this situation we use the first kicker to determine which hand is stronger.
Because the kicker in the first combination (K♠) outranks the kicker in the second combination (Q♠), the first three of a kind combination outranks the second.
- J♠J♦J♥A♠7♦ vs J♠J♦J♣A♠10♦
In this example, both the rank of the three card combination (J) and the rank of the first kicker (A) are the same, so we will use the rule mentioned before and compare the second kicker.
In this scenario, the 2nd kicker in the first combination (7♦) is weaker than the 2nd kicker in the second combination (10♦), which makes the second combination stronger than the first.
What Is a Straight in Poker?
In Texas Hold’em, a 5-card combination that is made of five cards in consecutive order with at least one card being a different suit is called a straight combination.
Below are two examples of hands that contain a straight:
- 10♠9♣8♠7♣6♦ – a ten-high straight combination
- 5♥4♥3♥2♣A♣ – a five-high straight combination, also known as the “wheel”
If the straight combination contains five consecutive cards with the same suit it is called a straight flush.
Below are two examples of hands that contain a straight flush.
- Q♥J♥10♥9♥8♥ – a queen-high straight flush
- 7♠6♠5♠4♠3♠ – a seven-high straight flush
Finally, if the straight combination contains five consecutive cards of the same suit with the ace being the highest card and the ten being the lowest card in the combination, this combination is called the royal flush.
The strongest hand combination that contains a straight is the royal flush (although it is rarely referred to as a straight combination because it has its own name).
The second strongest combination that contains the straight is the straight flush combination. Finally, the “ordinary” straight is the weakest hand that contains a straight.
The strength of each individual straight is measured by the rank of the highest card in the straight combination.
This is why the royal flush is the strongest straight combination because the highest card in this combination is always the ace.
- Q♠J♠10♥9♥8♦ vs J♥10♥9♥8♦7♠ – queen-high straight vs jack-high straight
In this example, the first straight combination outranks the second straight combination because the highest card in the 1st combination (Q♠) outranks the highest card in the 2nd combination (J♥).
The same rule applies to straight flush combinations.
The Number of Straight Combinations in Texas Hold’em
When we take into consideration that there are 13 different card ranks and 4 different suits in the 52-card deck, we can calculate that there are
- 10,200 possible five-card straight combinations
- 36 possible five-card straight flush combinations (9 for each suit)
- 4 possible royal flush combinations (1 for each suit)
Does a Three of a Kind Beat a Straight in Poker?
In the table below, you can see all the possible hand combinations in Texas Hold’em, as well as the number of combinations and the probabilities of getting each individual hand.
|Four of a Kind||624||0.02401%||4,164-to-1|
|Three of a Kind||54,912||2.1128%||46-to-1|
As you can see by the number of combinations, probabilities and odds, each hand in poker is ranked based on how hard is to collect it.
The hands that are the easiest to collect, such as one pair and two pairs are the lowest ranked, while the hand that is the hardest to collect, the royal flush, has the highest ranking.
This is key to answering does a three of a kind beat a straight in poker.
If we look at the hand ranking for straight or three of a kind we can see that the numbers are as follows:
- There are 10,200 possible straight combinations and there is a 0.3925% chance of hitting this hand combination, which translates to 254-to-1
On the other hand
- There are 54,912 possible three of a kind combinations, and there is a 2.1128% chance for making this hand, which translates to 46-to-1
From the information above we can conclude that it is much harder to get a straight than to make three of a kind in Texas Hold’em, which means that the answer to the question: Does a three of a kind beat a straight is – No!
If the question was: does a straight beat three of a kind, the answer would be yes: a straight beats three of a kind in Hold’em every time.