Pocket Pair vs Pocket Pair: How Often the Bigger Pair Wins
Before the flop, a bigger pocket pair beats a smaller one about 80% of the time: Q♠Q♥ against 7♦7♣ has 80.3%, A♠A♥ against 2♦2♣ has 81.5%. The gap between the two pairs barely matters, because the smaller pair wins mostly by making a set; the suits shift the result by up to 1.3 points. It is a 4-to-1 favorite, not a coin flip.
Compute a matchup
Pair against pair, computed exactly
| Matchup | Bigger pair's equity |
|---|---|
| A♠A♥ vs 2♦2♣ | 81.5% |
| K♠K♥ vs Q♦Q♣ | 81.2% |
| J♠J♥ vs 2♦2♣ | 81.2% |
| 9♠9♥ vs 8♦8♣ | 81.2% |
| Q♠Q♥ vs 7♦7♣, no suit shared | 80.3% |
| Q♠Q♥ vs 7♠7♦, one suit shared | 80.9% |
| Q♠Q♥ vs 7♠7♥, both suits shared | 81.6% |
Each line is an exact count over all 1,712,304 boards. Q♠Q♥ against 7♦7♣ is also a little lower than aces against deuces because sevens make more straights. The suits explain the rest: when the two pairs share suits, the smaller pair's flushes run into a bigger flush of the same suit.
Why it is close to 4 to 1
The smaller pair has two cards left of its rank. At least one of them comes on 19.9% of the boards: 341,550 of the 1,712,304. A set accounts for about four in five of its wins (81.3%); flushes and straights make up the rest, and the bigger pair's own sets take some back. In the end, 7♦7♣ has 19.7% against Q♠Q♥.
Compare with a pair against two higher cards, which is close to a coin flip: 9♠9♣ against A♥K♦ has 55.7% (pair vs overcards). Against a bigger pair, a pocket pair is in a far worse spot than against overcards.
What it changes in a decision
- Calling an all‑in with a medium pair. Against a range full of bigger pairs, you are a 4-to-1 underdog; against two overcards, you have about 55%. Count which part of the range you face before you call: see calling all‑ins.
- Shoving with a small pair. A short stack shoves small pairs because every fold wins the blinds, and against the overcards that call it is still about even: see the push/fold chart.
Keep going
- What equity means: poker equity.
- When the smaller pair hits: set vs trips.
- The pairs in between: how to play middle pairs.
- A pocket pair below every board card: the underpair in poker.
Sources
- Equities enumerated exactly over every board; boards holding at least one of the two cards counted by enumeration.