KEY TAKEAWAYS
With two suited hole cards, the odds of flopping a flush are 0.84%, or about 1 in 119 (roughly 117.8 to 1 against). The exact count is 165 winning flops out of 19,600 possible flops. With offsuit hole cards the chance is 0%, because three board cards of one suit cannot make a flush when the hole cards do not share a suit. Averaged over every starting hand a player can be dealt, the figure falls to about 0.20%, or 1 in 505.
A made flush on the flop is rare, but the neighbors of that number matter more in real hands. The same suited hand flops a flush draw 10.9% of the time and a backdoor draw 41.6% of the time, and the draw is where most flush value is decided. This article shows how each figure is counted, walks through a full example with real cards, lists the mistakes that distort these numbers, and explains what the percentages do and do not mean at a table.
Everything here assumes Texas Hold’em and a standard 52-card deck. Readers who want the same style of calculation for a pocket pair can compare it with the odds of flopping a set.
What Counts as a Flopped Flush
A flush is five cards of the same suit. In Hold’em the five cards come from two hole cards and five board cards, so a flopped flush means the hand is already complete after only three board cards. That is only possible when both hole cards share a suit and all three flop cards match it. A flush also needs no help from the turn or river, which is why it is such a clean event to count.
Three related events sound alike but are different calculations. A made flush is three suited flop cards with two suited hole cards. A flush draw is four cards of one suit after the flop, which happens with exactly two suited flop cards. A backdoor flush draw is three cards of one suit after the flop, which happens with exactly one suited flop card and needs both the turn and the river to complete.
Each event is mutually exclusive on a given flop, so their probabilities add up to 100%. Because the hole cards fix the suit, the question is always the same: of the 50 unseen cards, how many belong to that suit, and how many flops contain exactly 3, 2, 1 or 0 of them? Readers new to the term can review what outs are in poker before continuing, because the flush draw numbers below use the same counting idea.
How the 0.84% Is Calculated
The calculation starts from what the player can see. A standard deck has 52 cards and the player holds two, so 50 cards are unseen. A flop uses three of them, giving C(50,3) = 19,600 equally likely flops. A suit has 13 cards, and two are in the player’s hand, so 11 cards of that suit remain unseen, while the other 39 unseen cards belong to the other three suits.
Counting a made flush
A made flush needs all three flop cards from the 11 remaining suited cards, so the number of ways is C(11,3) = 165. The probability is 165 ÷ 19,600 = 0.8418%, which rounds to 0.84%. As odds against, (19,600 − 165) ÷ 165 = 117.8 to 1.
Counting the other flop types
A flush draw needs exactly two suited flop cards and one card from the other 39. The count is C(11,2) × 39 = 55 × 39 = 2,145, so the probability is 2,145 ÷ 19,600 = 10.94%. A backdoor draw needs exactly one suited card and two from the other 39: 11 × C(39,2) = 11 × 741 = 8,151, or 41.59%. No suited cards at all is C(39,3) = 9,139, or 46.63%. The four counts add up to 19,600, which confirms that every flop has been counted once.
| Flop type (suited hole cards) | Flops out of 19,600 | Probability | About 1 in |
|---|---|---|---|
| Three suited cards (made flush) | 165 | 0.84% | 119 |
| Exactly two suited cards (flush draw) | 2,145 | 10.94% | 9.1 |
| Exactly one suited card (backdoor draw) | 8,151 | 41.59% | 2.4 |
| No suited cards | 9,139 | 46.63% | 2.1 |
The table shows that nearly half of all flops give no help at all to a suited hand, and a made flush is the thinnest slice. The calculation can also be done as a chain of fractions: (11 ÷ 50) × (10 ÷ 49) × (9 ÷ 48) = 990 ÷ 117,600 = 0.8418%, which matches the combination method exactly.
Worked Example: A♥ 9♥ on the Flop
Suppose a player holds A♥ 9♥. Two hearts are in the hand, so 11 hearts remain among 50 unseen cards. The chance that the flop is all hearts is 0.84%, the same 165 ÷ 19,600 shown above.
Now suppose the flop comes K♥ 7♥ 2♣. The player has four hearts and needs one more. Nine hearts are unseen, and the unseen pool is now 52 − 2 − 3 = 47 cards. The chance of a heart on the turn is 9 ÷ 47 = 19.1%. If the turn misses, 46 cards remain, so the river chance is 9 ÷ 46 = 19.6%. The chance of finishing by the river is 1 − (38 ÷ 47) × (37 ÷ 46) = 35.0%.
A shortcut of simply adding 19.1% and 19.6% would give 38.7%, which overstates the result because a heart on the turn removes the need for the river. The correct two-card figure is 35.0%, and the miss chance is 65.0% (38 ÷ 47 × 37 ÷ 46). The opponents’ unknown hole cards are not removed from the count, because the player cannot see them.
Reading the Number at the Table
A useful way to hold these figures is by what the flop shows. Three suited flop cards with suited hole cards is a 1-in-119 event, so it is rare enough that most suited hands never see it. Two suited flop cards is the common good case at about 1 in 9, and it carries a 35.0% chance of a flush by the river. One suited flop card leaves only a 4.2% backdoor chance, which comes from C(10,2) ÷ C(47,2) = 45 ÷ 1,081.
| Flop type | Chance of a flush by the river | Weight in all flops |
|---|---|---|
| Three suited cards | 100% (already made) | 0.84% |
| Exactly two suited cards | 35.0% | 10.94% |
| Exactly one suited card | 4.2% | 41.59% |
| No suited cards | 0% | 46.63% |
Weighting each row gives the overall figure: 0.84% + 10.94% × 35.0% + 41.59% × 4.2% = about 6.4%. A direct count agrees, because 135,597 of the 2,118,760 possible five-card boards contain at least three of the 11 suited cards, which is 6.40%. Suited hole cards end with a flush about once in 15.6 hands, but the vast majority of those flushes arrive on the turn or river rather than the flop.
The numbers describe frequency over a very large number of hands, not a schedule. A player dealt 1,000 suited hands would expect to flop about 8 flushes, yet a stretch with none or with several is entirely normal.
Common Calculation Mistakes
Adding the turn and river chances is the most frequent error. Adding 19.1% and 19.6% gives 38.7%, but the correct combined figure for nine outs is 35.0%, because the two chances overlap. The rule of 2 and 4 would give 36% here, which is why it is treated as an approximation, as covered in the article on the rule of 2 and 4.
Using 52 cards instead of the unseen cards distorts every figure. After two hole cards the deck holds 50 unseen cards, and after the flop it holds 47. Dividing by 52 understates the chance every time.
Mixing up the event is another trap. The 10.9% figure is the chance of flopping a flush draw, while 35.0% is the chance of completing it afterwards. Quoting 35% as the chance to flop a flush, or 0.84% as the chance to make a flush by the river, answers a different question from the one asked.
Assuming offsuit hands can flop a flush is also wrong. Two offsuit hole cards contribute at most one card of any suit, so a flush on the flop is impossible, and only a draw is possible.
Where the Number Matters in Practice
The 0.84% figure explains why suited cards add only a small amount of value to a starting hand: suitedness lifts the chance of ending with a flush by the river to about 6.4% of hands, and the equity effect is real but modest. About 23.5% of dealt hands are suited (312 of 1,326 combinations), so a random hand flops a flush 23.5% × 0.84% = 0.20% of the time, or about 1 in 505.
The figure also helps with the other side of the table. A random flop contains three cards of one suit about 5.2% of the time (4 × C(13,3) ÷ C(52,3) = 1,144 ÷ 22,100), so a monotone board is uncommon and most flops leave flush questions open for later streets. Calculators and charts report these same values, and they match the hand-counted results above.
Because every figure here is a long-run frequency, none of it predicts the next flop. A player can flop a flush twice in a session or never in a month without anything unusual happening. Real-money poker also carries financial risk, and legal age and legality vary by state and venue.
Related Concepts and the Next Step
The flop is only the first of three decision points for a draw. Once a flush draw appears, the next question is how to compare its price with its chance, which the guide on how to calculate pot odds explains step by step. A complete hand-by-hand comparison of a flush draw against a made hand is in set vs. flush draw, street by street. For the dealing side of the same math, see the odds of being dealt pocket aces.
Frequently Asked Questions
