Three of a kind outranks two pair because it is rarer: 54,912 five-card combinations against 123,552. The hand rankings chart places them at ranks 7 and 8, and the probability column is the reason for that order.
Rarity sets the order
Poker hand rankings are an ordering by how often each hand occurs among all five-card combinations. A hand that appears less often beats a hand that appears more often. The table lists 2.112845% for three of a kind and 4.753902% for two pair, so the rarer hand is the one with the smaller share of all five-card hands.
Use the probability column rather than the combination column when comparing two ranks at a glance. Both columns encode the same ordering, but the percentage is the one that travels into any odds comparison; 2.112845% against 4.753902% is already a direct statement of how much less often the stronger hand appears.
Reading the two rows side by side
The table gives three of a kind 54,912 combinations, 2.112845% and a frequency of 1 in 47.33. Two pair gets 123,552 combinations, 4.753902% and 1 in 21.04. Read each row across rather than down: the combination count, the percentage and the frequency are three ways of stating the same rarity, and all three put the set ahead of two pair.
That is the number to use when the question is about rank rather than about a specific deal. A hand that is 1 in 47.33 is harder to make than one that is 1 in 21.04, and the ranking table encodes exactly that difference. Where a specific board is involved, the separate two pair against three of a kind page covers the matchup; this row describes the population of all hands.
Why a set is not a full house
Three of a kind and a full house are different ranks, not different names for the same hand. The table lists a full house at 3,744 combinations, 0.144058% and 1 in 694.2, well below the 54,912 combinations of three of a kind. A set made on the flop does not become a full house unless the board pairs, and a later street can also give a full house to another hand.
Use the rows separately: the 2.112845% figure describes a hand that is exactly three of a kind, and the 0.144058% figure describes a hand that is a full house. Neither is a probability that one turns into the other. Confusing the two ranks is the fastest way to misread why a set can be overtaken later in a hand.
Using the ranking table
| Rank | Hand | Five-Card Combinations | Probability | Frequency (1 in N) |
|---|---|---|---|---|
| 1 | Royal Flush | 4 | 0.000154% | 1 in 649,740 |
| 2 | Straight Flush | 36 | 0.001385% | 1 in 72,193 |
| 3 | Four of a Kind | 624 | 0.024010% | 1 in 4,165 |
| 4 | Full House | 3,744 | 0.144058% | 1 in 694.2 |
| 5 | Flush | 5,108 | 0.196540% | 1 in 508.8 |
| 6 | Straight | 10,200 | 0.392465% | 1 in 254.8 |
| 7 | Three of a Kind | 54,912 | 2.112845% | 1 in 47.33 |
| 8 | Two Pair | 123,552 | 4.753902% | 1 in 21.04 |
| 9 | One Pair | 1,098,240 | 42.256903% | 1 in 2.37 |
| 10 | High Card | 1,302,540 | 50.117739% | 1 in 2.00 |
The table orders all ten hand ranks by combination count, with the probability and frequency columns beside it. Use the rank column to settle which hand wins and the probability column to say how rare each one is. For the two rows in question, that means 54,912 and 2.112845% against 123,552 and 4.753902%.
The ordering is not a judgement about how a hand plays. It is a count of how many five-card combinations produce it, and the count is fixed before any cards are dealt. A reader who wants the probability behind a ranking reads the percentage; a reader who wants the raw count reads the combination column. Both point to the same conclusion: the rarer hand is ranked higher.