Odds of flopping a straight or straight draw
How often do connectors flop a straight? The short answer is below, and under it the working: the formula with the numbers put in, and the count from dealing every possible card.
The working
JT makes a straight on the flop with four sets of ranks: AKQ, KQ9, Q98 and 987. Each rank has four cards, so each set can come 4 × 4 × 4 = 64 ways:
P(straight) = 4 × 4³ / C(50, 3) = 256 / 19,600 = 1.31% = 1 in 76.6
Draws have no tidy formula, so for every two-rank hand the build dealt all 19,600 flops, asked the engine whether the hand was already a straight, and if not tried all 47 turn cards to count the ranks that would make one. Two or more ranks is an 8-out draw (open-ended or a double gutshot); one rank is a gutshot. Hands are dealt offsuit so flushes do not muddy the count; suited, the straight numbers are the same and the flush ones are on their own page.
Gaps cost straights. Connectors from JT down to 54 are tied at the top, four straights each, because none of the ranks they need runs off the end of the deck. Each gap removes one straight. AK and A2 are connectors that can only go one way, so they flop a straight no more often than a three-gapper. The draw columns count every straight a turn card would make, including ones that use only one of your cards, which are weaker.
Connectors
| Hand | Straight | 8+ out draw | Gutshot | Any of these |
|---|---|---|---|---|
| AK | 0.33% | 0.00% | 11.35% | 11.7% |
| A2 | 0.33% | 0.00% | 11.35% | 11.7% |
| KQ | 0.65% | 3.02% | 12.73% | 16.4% |
| QJ | 0.98% | 6.37% | 14.78% | 22.1% |
| JT | 1.31% | 9.71% | 16.82% | 27.8% |
| T9 | 1.31% | 9.71% | 16.82% | 27.8% |
| 98 | 1.31% | 9.71% | 16.82% | 27.8% |
| 87 | 1.31% | 9.71% | 16.82% | 27.8% |
| 76 | 1.31% | 9.71% | 16.82% | 27.8% |
| 65 | 1.31% | 9.71% | 16.82% | 27.8% |
| 54 | 1.31% | 9.71% | 16.82% | 27.8% |
| 43 | 0.98% | 6.37% | 14.78% | 22.1% |
| 32 | 0.65% | 3.02% | 12.73% | 16.4% |
One-gappers
| Hand | Straight | 8+ out draw | Gutshot | Any of these |
|---|---|---|---|---|
| AQ | 0.33% | 0.65% | 11.35% | 12.3% |
| A3 | 0.33% | 0.65% | 11.35% | 12.3% |
| KJ | 0.65% | 3.67% | 12.73% | 17.1% |
| QT | 0.98% | 7.02% | 14.78% | 22.8% |
| J9 | 0.98% | 7.02% | 14.78% | 22.8% |
| T8 | 0.98% | 7.67% | 14.78% | 23.4% |
| 97 | 0.98% | 7.67% | 14.78% | 23.4% |
| 86 | 0.98% | 7.67% | 14.78% | 23.4% |
| 75 | 0.98% | 7.67% | 14.78% | 23.4% |
| 64 | 0.98% | 7.02% | 14.78% | 22.8% |
| 53 | 0.98% | 7.02% | 14.78% | 22.8% |
| 42 | 0.65% | 3.67% | 12.73% | 17.1% |
Two-gappers
| Hand | Straight | 8+ out draw | Gutshot | Any of these |
|---|---|---|---|---|
| AJ | 0.33% | 0.98% | 12.00% | 13.3% |
| A4 | 0.33% | 0.98% | 12.00% | 13.3% |
| KT | 0.65% | 4.00% | 13.39% | 18.0% |
| Q9 | 0.65% | 4.00% | 13.39% | 18.0% |
| J8 | 0.65% | 4.65% | 13.39% | 18.7% |
| T7 | 0.65% | 4.98% | 14.04% | 19.7% |
| 96 | 0.65% | 4.98% | 14.04% | 19.7% |
| 85 | 0.65% | 4.98% | 14.04% | 19.7% |
| 74 | 0.65% | 4.65% | 13.39% | 18.7% |
| 63 | 0.65% | 4.00% | 13.39% | 18.0% |
| 52 | 0.65% | 4.00% | 13.39% | 18.0% |
Three-gappers
| Hand | Straight | 8+ out draw | Gutshot | Any of these |
|---|---|---|---|---|
| AT | 0.33% | 1.31% | 12.65% | 14.3% |
| A5 | 0.33% | 1.31% | 12.65% | 14.3% |
| K9 | 0.33% | 1.31% | 11.35% | 13.0% |
| Q8 | 0.33% | 1.96% | 11.35% | 13.6% |
| J7 | 0.33% | 2.29% | 12.00% | 14.6% |
| T6 | 0.33% | 2.61% | 12.65% | 15.6% |
| 95 | 0.33% | 2.61% | 12.65% | 15.6% |
| 84 | 0.33% | 2.29% | 12.00% | 14.6% |
| 73 | 0.33% | 1.96% | 11.35% | 13.6% |
| 62 | 0.33% | 1.31% | 11.35% | 13.0% |
Hitting the draw later: open-ended, 31.5% and gutshot, 16.5% by the river.
More on the flop
- Flopping a set11.8%
- Flopping a flush or flush draw0.8%
- Flopping a pair or two pair32.4%
- An overcard to your pair41.4%
Other odds
- Counted, not quoted.
tools/build-odds.mjsdeals every possible flop, turn, river or starting hand and counts. Where a closed-form formula exists, the build refuses to publish unless the count matches it exactly. - Made hands come from the engine. Whether cards make a straight, a flush or a full house is decided by the same Rust/WebAssembly evaluator the trainer runs, not by hand-written rules.
- Odds are not equity. Hitting your hand is not winning the pot. For that, the matchup pages deal every board against a specific hand and the spot calculator works against a range.
- Raw data: odds.json.