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does three of a kind beat two pair?

Why Does Three of a Kind Beat Two Pair?

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.

does three of a kind beat 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.

kh-hearts-new-cardsdoes three of a kind beat two pair?kc-clubs-new-cards9s-spades-new-cards7s-spades-new-cards

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 KKK♣ 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:

ts-spades-new-cardsDoes three-of-a-kind beat two pair?8h-hearts-hearts-new-cards8c-clubs-new-cards6d-diamonds-new-cards

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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About the Author

Geoffrey Fisk

Freelance writer and poker player based in San Diego, California.

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