Poker Equity & OddsHow often does set over set happen?
Short answer
When two players each hold a pocket pair, both flop a set on 1.04% of flops, about one in 96. Counted per hand instead, two players heads up get dealt pairs and both flop a set about once in 27,792 hands. At a nine-handed table where every pocket pair sees the flop, it is about once in 782 hands. Those are different questions, which is why the figures you find online disagree so much. Each count below says what it counts.
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Three numbers that get mixed up
| Question | Chance | About one in |
|---|---|---|
| Two players hold pocket pairs. How often do both flop a set? | 1.04% | 96 flops |
| Any hand heads up: both players dealt a pair and both flop a set | 0.0036% | 27,792 hands |
| Six players, every pocket pair sees the flop | 0.0537% ±0.0014 | 1,861 hands |
| Nine players, every pocket pair sees the flop | 0.1279% ±0.0022 | 782 hands |
The first row is the one that matters once you are in the hand. 8♠ 8♥ against Q♣ Q♦: each pair has two cards of its rank left among the cards you can't see, and 180 of the 17,296 flops have at least one of each. The per-hand rows are much smaller because both players first have to be dealt a pair. More players means more pairs at the table, so the nine-handed figure is far above the heads-up one.
You flopped a set: is someone on a bigger one?
Only an opponent holding a pocket pair that matches a higher board card has you beaten. Each higher board card leaves 3 such combos out of the 1,081 hands an opponent can hold. With 8♠ 8♥:
You put me on queens? Good luck.
| Flop | Cards above your set | 1 opponent | 2 | 5 | 8 |
|---|---|---|---|---|---|
| Q♥ 8♦ 3♣ | one | 0.28% | 0.56% | 1.39% | 2.22% |
| K♥ Q♦ 8♣ | two | 0.56% | 1.11% | 2.76% | 4.39% |
| 8♦ 5♣ 3♥ | none, top set | 0.00% | 0.00% | 0.00% | 0.00% |
Even against eight random hands with two higher cards on the flop it is 4.39%, about one time in 23. Real opponents are not random: the players still in the hand on a K♥ Q♦ 8♣ flop hold kings and queens more often than a random hand does, so the true figure can be higher. It still doesn't come close to a reason to fold a set on the flop.
Set under set on the flop
On Q♥ 8♦ 3♣, every one of the 990 turns and rivers counted. The Outs & Odds tool gives the eights 7 outs to a full house, because it does not know what the other player holds. Against queens most of them are not outs: two of the queens are in the other player's hand, and the last queen or a three gives the queens the bigger hand. That leaves the last eight, and even then the last queen as the other card gives the queens quads.
What it means for set mining
Set mining works because you flop a set or better one time in 8.5 (the set odds guide has the exact count), and a set is usually the best hand on the flop. Set over set is part of that price, but a small part: it needs another player with a pair that also hits, on the same flop. When it happens, the lower set is close to drawing dead, so the chips go in and there is nothing to do about it. What decides whether set mining pays is how much you win when you hit, which is the implied odds guide.
Put your set against their range
Tap in your set and a range for the other player, and the calculator counts how often the bigger sets in that range beat you. It runs on the phone, so it works offline.
Questions
How often does set over set happen?
It depends on what you count. When two players each hold a pocket pair, both flop a set on 1.04% of flops, about one in 96. Per hand heads up it is about one in 27,792, and at a nine-handed table where every pocket pair sees the flop, about one in 782 hands.
What are the odds of set over set when both players have a pocket pair?
1.04%: 180 of the 17,296 flops give both pairs a set or better. The pairs' ranks don't change it, as long as they are different.
How often is there set over set at a full table?
About one hand in 782 at nine players, 0.1279% ±0.0022, if every pocket pair sees the flop. That is sampled over 10,000,000 deals. Six players: about one in 1,861.
Can the lower set still win?
Rarely. 8♠ 8♥ against Q♣ Q♦ on Q♥ 8♦ 3♣ has 4.3%. It needs the last eight, and even then the last queen as the other card gives the queens quads.
Where the numbers come from. Every figure on this page comes from the Poker Equity & Odds engine and exact counting. The flop counts go through every flop, the bigger-set table is an exact count over the hands your opponents can hold, and the lower set's equity counts all 990 turns and rivers. The six- and nine-player rows are sampled: 10,000,000 random deals each, with the 95% margin printed next to the number. Engine build 482550e8. More worked numbers: odds of flopping a set and the flop equity cheat sheet.
