Knowing all of the five card poker hands in order is crucial for newcomers to the game, which is probably why the question “does three of a kind beat two pair” is often asked by beginners.
Both three-of-a-kind and two pair are often winners in games that use the standard poker hand rankings (such as Texas Hold’em, Seven Card Stud, and Five Card Draw).
But does three-of-a-kind beat two pair?
The simple answer is: yes, three-of-a-kind-does beat two pair in poker.
Now that you have the answer, let me explain why three-of-a-kind beats two pair.
Why Does Three-of-a-Kind Beat Two Pair?
If we draw five random cards from a standard 52-card poker deck, three-of-a-kind occurs less often than two pair. So, because it’s mathematically harder to make three-of-a-kind, a three-of-a-kind hand wins against two pair.
The Math Behind Three-of-a-Kind
There are 858 distinct ways to make three-of-a-kind out of a 52-card deck. An example of a distinct three-of-a-kind hand includes KKK97.
Distinct hands refer to the cards in the hand without taking suits into account. The four suits (♠,♦,♣, and ♥), in different combinations, give us 64 possible ways to make KKK97.
(Note that the two extra cards in the hand have to be unpaired for this combination to qualify as three-of-a-kind. If they’re paired, like K♥ K♦ K♣ 9♣ 9♠, the hand ranks as a full house.)
With 858 distinct three-of-kind hands possible, multiplied by 64 possible suit combinations, a 52-card deck yields 54,912 possible ways to draw three-of-a-kind.
The Math Behind Two Pair
A standard poker deck produces 858 distinct ways to make two pair. That number is exactly the same as the distinct count of three-of-a-kind hands. Factoring in suits, however, makes two pair a more commonly occurring hand.
Let’s take a look at a hand that qualifies as two pair:
The above hand qualifies as two pair, tens and eights.
For example, our above example of TT886 can be drawn 144 different ways. The 144 different ways to make a two pair hand, multiplied by 858 distinct hands, gives us 123,552 possible ways to make two pair.
In Texas Hold’em, players have a 23.5% chance of making two pair with all five community cards on the board. Three-of-a-kind, with its 4.83% frequency, is a far less common hand.
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