Set versus flush draw is the classic “made hand against draw” flop battle, and this version has a detail most players miss: one of the flush outs is already used up. Here is the full picture.
| Matchup | Set wins | Flush draw wins | Ties |
|---|---|---|---|
| 7h 7d vs Ah Kh on 7c 2h 9h | 75.3% | 24.7% | 0.0% |
The matchup, defined
A set is three of a kind made with a pocket pair plus one board card. A flush draw here means two suited hole cards plus two suited board cards, four of the suit in total across hand and board, waiting for a fifth to complete the flush.
- The set holds 7h 7d, which makes three sevens with the 7c on the board.
- The flush draw holds Ah Kh, with the 2h and 9h on the board giving four hearts.
- The flop comes 7c 2h 9h.
The result, with the blocked-outs detail
Simulated 200,000 runouts with a standard 52-card deck (single model, named here): the set wins 75.3%, the flush draw wins 24.7%, ties 0.0%.
Now the detail. Five hearts are already visible: Ah and Kh in the flush draw’s hand, 2h and 9h on the board, and 7h in the set’s hand. Thirteen hearts exist in the deck, so only 8 hearts remain unseen, not 9. The set’s 7h BLOCKS one heart out. With both hands known, 45 cards are unseen in total, and the flush completes in 1 - (37/45 x 36/44) of all runouts, about 32.7%.
Why does the draw win less than that flush rate? Because some heart runouts still lose. If the board pairs on a later street, the set improves to a full house (sevens full), which beats any flush; and if the case seven arrives, the set even makes four of a kind. Those improved-set runouts come straight out of the draw’s win column.
One more boundary worth knowing: the flush draw’s only winning path is the flush. An ace or king pairing gives it one pair, which loses to three sevens, and the board offers it no straight. So its entire 24.7% is hearts, minus the runouts where the set fills up.
How to use the number
Keep the premises attached. If the flush draw faces an all-in on this flop, calling needs less than 24.7% equity to be profitable in this simplified model, where the all-in ends the betting and both cards come for free. If another bet is possible on the turn, the caller can be forced to fold some of its equity, and the comparison must be redone with the new price.
From the set’s side, 75.3% is a big favorite but not immunity: roughly one time in four the flush arrives and holds. The blocking detail softens the draw only slightly; it does not turn the matchup around.
FAQ
Why only 8 flush outs instead of 9?
A normal flush draw has 9 outs because 13 minus the 4 visible suited cards leaves 9. Here 5 hearts are visible (two in the flush draw’s hand, two on the board, one in the set’s hand), so 13 - 5 = 8 hearts remain unseen. The set’s 7h is the blocker.
Can the flush draw win without a heart?
In this specific matchup, no. Pairing the ace or king gives one pair, which loses to three sevens, and no straight is possible for Ah Kh on a 7c 2h 9h flop. Only the flush wins.
Can a flush lose to a set?
Yes, when the board pairs and the set becomes a full house, or when the case seven gives four of a kind. Both beat any flush. That is why the draw’s win rate (24.7%) is below its raw flush completion rate (about 32.7%).
Where can I verify numbers like this?
Enter both hands and the flop into a poker odds calculator and run a large simulation. The hand rankings chart is a good companion for checking which made hand category each improvement lands in.
Numbers are most useful when their model is stated: this page used a 200,000-run simulation with both hands known, and every claim above belongs to that model.