Three-of-a-kind beats any two pair in poker and is ranked higher in the poker hand rankings, which apply in Texas Hold’em and most other standardized poker games.
Three-of-a-kind can be made with two hole cards and one community card or with one hole card and two community cards. In either case, the hand will beat any two pair.
The majority of the value of three-of-a-kind hands comes from the fact they beat two pairs and one pair hands that many players will overplay and often pay off big bets with.
Since three-of-a-kind is always a winner against two pairs, it is worth considering the odds of making these two hands and comparing them to find out just how often we will get into such spots at the table.
We explore the odds of making both hands, starting with random poker hands, and the logic behind those odds.
Why Does Three-of-a-Kind Beat Two Pair?
If you have ever seen a poker hands chart, you have surely noticed that two pairs is one of the weakest hands in poker, only outranking one pair and high card.
Three-of-a-kind is the very next hand on the chart, and it only outranks two pair by a bit because it is slightly more difficult to make.
While you will need to use four cards to make two pair and only three cards to make three-of-a-kind, two pair is still a bit more common, as making three-of-a-kind requires finding three cards of the exact same ranking.
If you want to understand exactly why three-of-a-kind outranks two pair, check out the table below that demonstrates the odds of making the two hands, and keep reading to learn more about the probability of making the two with various starting card combinations.
| Chances To | Three-of-a-Kind | Two Pair |
| Make it on the Flop | 1.35% – 10.8% | 2.02% |
| Make it on the Turn | 4.2% | 6.4% |
| Make it on the River | 4.3% | 6.5% |
How Often Will You Make Three-of-a-Kind?
Before you think about the odds of making three-of-a-kind, it is worth remembering that there are two major ways to make this hand in poker.
The first is by making a set, a three-of-a-kind combination made up of two hole cards and a single community card.
To make a set, you need to start with a pocket pair, which is a relatively rare occurrence to begin with. When you do have a pocket pair, you will flop a set about 10.8% of the time, which is quite favorable.
However, starting with two unpaired cards, which is usually the case, you will only make trips 1.35% of the time, which is much less frequent.
Furthermore, making a single pair on the flop will give you a 4.2% chance to make three-of-a-kind on the turn and another 4.3% on the river, for a grand total of 8.5%.
So, while your odds to make a set with a pocket pair are quite reasonable, the odds of making trips with two unpaired cards are significantly lower and not as attractive.
How Often Will You Make Two Pairs?
While flopped sets may be easier to make than flopped two pairs, it is significantly more likely you will flop two pairs with two unpaired cards than it is that you will flop trips with them.
Any two unpaired cards give you a 2.02% chance to make two pairs on the flop, compared to the 1.35% chance to flop trips.
What’s even more, making one pair on the flop gives you three outs to make two pairs on the turn or river, which is 50% more outs than you would have to make three-of-a-kind.
For that reason, your odds of improving to two pairs on the turn sit at 6.4%, and your odds of improving on the river sit at 6.5%, for a grand total of 12.9%.
With a much higher chance to improve to two pairs and a higher chance to flop two pairs than trips, two pairs are a significantly more common hand than three-of-a-kind.
If you play a few sessions of Texas Hold’em, you will notice that you hold two pairs on the river a lot more often than you hold three-of-a-kind, which is the main reason two pairs are ranked below three-of-a-kind in the poker hand rankings.