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.

Exact enumeration results

The numbers below come from exact enumeration, not from a simulation. Seven cards are known (both hole cards plus the flop), so 45 cards remain unseen. Dealing the turn and river from those 45 cards gives C(45,2) = 990 equally likely two-card combinations. Counting every one:

Outcome Runouts Percentage
Flush draw (Qh Jh) wins 382 38.6%
Top pair (Kd 9s) wins 608 61.4%
Tie 0 0.0%

Where the flush draw’s equity comes from

Most of the flush draw’s equity is the flush itself. Four hearts are already visible among the seven known cards, so 9 hearts and 36 non-hearts remain among the 45 unseen cards. At least one heart arrives in 1 − (36/45 × 35/44) = 36.36% of runouts.

This is a completion chance, not a win probability. Hitting a heart does not always win: if the turn and river bring 4c and 4h, the top pair makes a full house, fours full of kings, and beats the flush. Out of the 990 runouts, 360 bring at least one heart and 8 of those still lose, so the flush draw wins with a flush or a straight flush in 352/990 = 35.56% of all runouts.

The other 30 winning runouts are non-flush wins: 15 straights, 9 two-pair wins and 6 three-of-a-kind wins. For example, 9c and Tc give Qh Jh a king-high straight that beats the pair of kings, and Jc Jd makes three jacks. This is why 38.6% sits above the 35.56% flush-only figure.

Why the top pair is still a solid favorite

At about 61.4%, top pair wins 608 of the 990 runouts. It keeps that edge because the draw must improve to win, while the pair only needs to survive. The pair also improves sometimes, and the type of improvement depends on which card arrives. A later king makes three of a kind. Two running sevens, or two running fours, give the opponent a full house rather than a second pair, because the board itself then carries trips that combine with the king. When the board pairs once with a seven or a four, the top pair does pick up a second pair of its own, but a heart that pairs the board completes the flush instead, so that improvement goes to the draw.

Across the 990 runouts, that help is not the main reason the top pair is ahead. It wins most of its 608 runouts simply by avoiding the flush: in 630 of the 990 runouts no heart arrives at all, which is 63.6% of all runouts.

Still, winning about three in five is not winning always. A hand that wins 38.6% of the time is far from dead, and treating every missed flush draw as a hand with no other way to win is one of the classic beginner leaks. The check is not whether the flush arrived; it is whether you have compared every winning path, including pairs on the board, straights and two pair.

How to use this number

The equity comparison only works with stated premises. Here they are: you are heads-up against this exact hand, all other players are out of the pot, the bet you face on this flop is an all-in so you are guaranteed to see both remaining cards, there is no rake, and outcomes are measured in chips. Under those premises, a call is profitable whenever your required equity is below 38.6%. If any premise fails, for example because there can be more betting on later streets, the situation changes: you might face another decision with more money to put in, so the simple comparison no longer applies and must be redone with the new price.

In other words, 38.6% is the answer to a precise question, not a universal green light. The question is: what price am I paying, and will I really get to see both cards?

FAQ

Is a flush draw always about 38.6% against top pair?

No. This number is specific to these exact cards and this exact flop. Other flush draws have overcards, lower pairs or backdoor possibilities, and each variation moves the equity.

Why does the heart completion chance differ from the classic 9-out formula?

The classic formula 1 − (38/47 × 37/46) ≈ 35% assumes only your two hole cards and the flop are known, leaving 47 unseen cards. Here the opponent’s cards are known too, so 45 cards remain and the chance of at least one heart is 1 − (36/45 × 35/44) = 36.36%. Neither number is a win probability on its own.

Can the flush draw win without making the flush?

Yes. Non-flush wins account for 30 of the 382 winning runouts: 15 straights (for example, 9c and Tc complete a king-high straight), 9 two-pair wins and 6 three-of-a-kind wins (for example, Jc Jd makes three jacks).

What equity do I need to call a bet with this draw?

You need the bet’s price, not this table alone. Required equity equals your call divided by the pot after your call. Compare that number with your hand’s equity for the exact situation; the 38.6% figure applies only to this matchup under the premises listed above.

Run your own matchups in the poker odds calculator and check which made hands rank where in the poker hand rankings chart.

Sources

  • Known cards: Qh Jh (flush draw), Kd 9s (top pair), flop Kh 7h 4d; seven distinct cards, none repeated.
  • Method: exact enumeration of all C(45,2) = 990 turn-and-river combinations from the 45 unseen cards of a standard 52-card deck.
  • Results: flush draw wins 382/990 = 38.6%; top pair wins 608/990 = 61.4%; ties 0. Flush-or-better wins 352/990 = 35.6%; non-flush wins 30 (15 straights, 9 two pairs, 6 three of a kinds).
  • Equity definition: expected share of the pot at showdown, including the fraction of ties; ties cannot occur in this matchup.
  • The 9-out formula 1 − (38/47 × 37/46) ≈ 35% belongs to the 47-card model, where only your hole cards and the flop are known.