Does Three of a Kind Beat Two Pair in Poker & Why?
Does three of a king beat two pair or does two pair beat three of a king in poker?, these are some of the dilemmas, new poker players struggle with the most when starting with Texas Holdem.
The straightforward answer is yes, three of a kind beats two pair in poker.
If you are interested in finding out why three of a kind beats two pair as well as some of the rules you can use to answer similar questions without having to Google each answer, stay with us.
Does Three of a Kind Beat Two Pair in Poker?
In Texas Holdem poker, as in life, the main rule used to determine the value of something is its frequency.
With this said, the value of the hand combination in poker is determined by the number of possible combinations and the odds of being dealt the combination.
If you check the table below, you will see that the hand with the lowest number of combinations (the rarest hand), royal flush, is the hand that has the biggest value in poker.
|Four of a Kind||624||0.02401%||4,164-to-1|
|Three of a Kind||54,912||2.1128%||46-to-1|
Likewise, the paired hand with the largest number of combinations, one pair, is the hand that has the lowest value in Texas Hold’em.
The value of all other hand combinations is somewhere between these two in the table.
We can see that the hands which interest us the most, three of a kind and two pair are towards the bottom of the table, meaning they have less value than most other hands.
Furthermore, the table shows us that there are 123,552 possible combinations of a two pair hand which means you have a 4.75% or 20-to-1 chance of collecting this hand when you play.
On the other hand, there are 54,912 possible combinations of a three of a kind hand, which translates to a 2.11% or 46-to-1 chance of getting this hand combination.
So, by using math and the rules for poker hand rankings, we can answer the question is 3 of a kind better than 2 pair.
Not only that, but we can use this method to answer all similar questions about what beats what in Texas Hold’em.
So, if you ever find yourself in a situation where you are not sure what hand combination is stronger, just ask yourself the question: which hand are you less likely to get. Whichever is the answer, that hand is stronger
What Is a Three of a Kind in Poker?
Okay, now that we have resolved the dilemma of two pair vs. three of a kind, it is time to explain further each one of these combinations including what they consist of and how they are ranked.
As the name suggests, in poker, three of a kind refers to a 5-card hand combination that consists of three cards of the same rank and two additional unrelated cards called kickers.
- A♠A♣A♦7♠2♣ – three of a kind, aces
- 2♥2♦2♠J♣5♣ – three of a kind, deuces
In Texas Holdem, three of a kind is a term used to describe this combination in general. However, in most cases, players use more specific terms to describe their three of a kind hand based on the way it is formed.
The first way, in which you can collect a three of a kind combination is by using a pocket pair and combining it with the board. In these situations, the three of a kind combination is called a set.
Imagine a situation in which you are holding 5♠5♣ and the board runs out 5♦Q♣A♣8♠9♠.
The best hand that you can make in this situation is 5♠5♣5♦A♣Q♣ – a set of 5s with an ace and a queen kicker.
The second way to collect a three of a kind hand in poker is to use one of your hole cards (as a part of the main combination) and two cards from the board. This hand combination is called trips.
For example, if your hole cards are 8♣7♠ and the board is 7♣7♦A♣5♣2♥, your best hand combination in this situation is 7♠7♣7♦A♣8♣ – trip 7s with an ace and an eight kicker.
If you compare the board in the first example and the board in the second example, you can see that in the second example, it is much more obvious that someone can be holding a hand combination that contains three of a kind.
For this reason, players use different terms for three of a kind combos to additionally explain the transparency of their hand.
Holding a set is much better than holding trips as your opponent is less likely to put you on three of a kind.
The Number of Three of a Kind Combinations in Texas Hold’em
The deck of cards used for Texas Hold’em consists of 52 different cards that are split into four 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.
This means that one three of a kind hand can have 13 different ranks (deuces to aces) and 3 of the 4 suits.
If we do the math, we can confirm that there are 54,912 different three of a kind combinations that can result from a standard 52-card deck.
Remember, each time you use three cards of the same rank to make the calculation, you need to add two different kickers. The combinations of kickers are what adds significantly to the total number of possible hands.
How Are Three of a Kind Combinations Ranked?
Sometimes when you play poker, you will find yourself in situations where both you and your opponent have a three of a kind hand, and you need to know how your hand stands in relation to theirs.
To help you with this, we will explain which rules are used to rank three of a kind hands in Texas Hold’em.
There are three main rules that will help you determine if your three of a kind hand is a winning one or not:
- The first thing you need to consider is the rank of three of a kind cards.
- If the rank of the three of a kind cards is the same in both hands, the next thing that you should look at is the rank of the higher kicker.
- If both the three main cards and the higher kicker are of the same value, you need to consider the strength of the lower kicker.
These rules might seem confusing at first, but they are very easy to apply once you get a hang of it. We have prepared a few examples so you can see how these rules are applied in practice.
- 6♠6♦6♥K♠Q♥ vs. 4♠4♣4♦K♠Q♥
In this situation, the ranks of the three cards are different and we can use them to determine which three of a kind hand is stronger. The first hand is stronger than the second because a 6 outranks a 4 in Hold’em.
- Q♠Q♦Q♥A♠6♣ Q♣Q♦Q♥J♥6♦
In this example, the rank of the three of a kind hands is the same, so we need to look at the rank of the higher kicker, which means that the first hand beats the second one, since an ace is stronger than a jack.
- 5♥5♣5♠A♥7♠ vs. 5♦5♣5♠A♥3♠
Finally, in this example, the three card combination (5s) and the rank of the higher kicker (A) are of the same rank in both hands, so we need to consider the rank of the lower kicker.
This means that the first hand beats the second because the lower kicker in the first hand (7) outranks the lower kicker in the second hand (3).
What Is Two Pair in Poker?
A two pair combination in poker consists of two cards of one rank + two cards of another rank + a kicker. For example:
- J♠J♦4♠4♦9♣ – two pair, jacks and fours
- 10♣10♦8♣8♥7♠ – two pair, tens and eights
There are several ways in which you can get a two pair hand in Texas Hold’em.
Firstly, you can pair both of your hole cards with the cards on the board. For example, if you are holding A♠K♣ and the board is A♦K♦5♠4♣2♣, you have paired your hole cards with the board, and you have a two pair, aces and kings (and a 5 kicker).
Secondly, you can have a pocket pair in your hand, and the board can pair up. If you have 7♠7♣ and the board is 8♠8♦A♠J♣Q♠, your 5-card combination is 8♠8♦7♠7♣A♠ – two pair, eights and sevens (and an A kicker).
Next, you can pair one of your hole cards with the board, and the board can contain two cards of the same rank.
For example, if you are holding Q♠10♦ and the board is Q♦6♠6♣4♦2♦, your final 5-card combination is Q♠Q♦6♠6♣10♦ – two pair, queens and sevens (and a T kicker).
Finally, you can have a two pair combination by playing the board, i.e. your hand is A♠7♦ and the board reads J♠J♦9♠9♦4♣. Your final hand here is J♠J♦9♠9♦A♠ – two pair, jacks and nines (and an A kicker).
The Number of Two Pair Combinations in Texas Hold’em
As we’ve mentioned in the beginning, there are 123,552 possible two pair combinations in Texas Hold’em.
This means that, on average, your chances of collecting a 5-card combination that has a two pair in it is around 20-to-1.
This makes two pair the second most common paired hand in poker.
These odds shift significantly based on your hole cards. If you are holding a pocket pair, you have a 16.7% of hitting two pair on the flop.
This is followed by a 19.15% chance on the turn and a 19.57% chance of hitting two pair on the river.
How Two Pair Combinations Are Ranked
Just like with three of a kind there are three main rules when it comes to tanking two pair combinations:
- Two pair combinations are first ranked by the rank of its higher pair.
- If the rank of the higher pair is the same in both combinations, combinations are then ranked by their lower ranking pairs.
- If both the higher and the lower ranking pair have the same rank, the combinations are then ranked by the rank of the kicker.
Just like before, let’s look at how these rules are used in practice.
- A♠A♦2♠2♦7♠ vs. Q♠Q♦J♠J♦7♠
In this example, the first hand outranks the second hand because the highest pair in the first combination (A♠A♦) outranks the highest pair in the second combination (Q♠Q♦).
- K♠K♦8♠8♥A♦ vs. K♣K♦6♣6♥A♦
Here, the rank of the highest pair in both combinations is the same and so the rank of the lower pair comes into play.
The first combination beats the second combination because the lower pair in the first combination (8♠8♥) outranks the lower pair in the second combination (6♣6♥).
- Q♠Q♦J♠J♦9♠ vs. Q♠Q♦J♠J♦10♥
Lastly, if the ranks of both the higher and the lower pair a two pair combination are the same, the kicker comes into play.
In the example above, the second combination outranks the first because the kicker in the second combination (10♥) outranks the kicker in the first (9♠).
And there you have it – now you know not just that three of a kind beats two pair in poker but also understand why this is the case so you can explain it to your poker buddies!