Flush Draw

A flush draw has nine outs, and by the river those nine outs produce 34.97%, not 19.15% counted twice. The two numbers belong to different questions, and the pot-odds formula is where a single figure has to be chosen between them. Where the nine outs come from Thirteen cards of one suit exist. Two are in the hand and two are on the board, which leaves nine unseen cards of that suit. That is the whole source of the count: it is fixed by the suit’s size and the four cards already known, so a flush draw on the flop always starts at nine outs. ...

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. ...

Short answer for this exact matchup: the flush draw (Qh Jh) wins about 38.6% of all runouts, the top pair (Kd 9s) wins about 61.4%, and ties are impossible. One player has two hearts in the hand and the flop adds two more; the other has paired the highest card on the board. The matchup Flush draw: Qh Jh, giving four hearts together with the board. Top pair: Kd 9s, pairing the king on the flop with a nine kicker. Flop: Kh 7h 4d. The Qh Jh heart draw needs one more heart to make the flush, but a heart is not a guaranteed winner: some heart runouts give the top pair a full house. The pair of kings is ahead on the flop and only needs to survive, although it improves on some runouts too. ...