This poker odds chart answers the question every drawing player asks: how often will the card come? The short answer for the most common draws is that a flush draw (9 outs) hits about 35% of the time from flop to river and about 20% with one card to come, and an open-ended straight draw (8 outs) hits about 31.5% and 17.4%. Every figure below was computed exactly rather than estimated, and the arithmetic is shown so a student can check it.
The outs chart
An “out” is an unseen card that improves a hand to a likely winner. After the flop a player has seen five cards (two hole cards, three on the board), so 47 are unseen. After the turn, 46 are unseen.
The formulas:
- One card to come (turn or river): outs ÷ unseen cards. On the turn, outs ÷ 46.
- Two cards to come (flop to river): 1 − (misses ÷ 47) × ((misses − 1) ÷ 46), where misses = 47 − outs. Equivalently, 1 − C(47 − outs, 2) ÷ C(47, 2).
Worked example for a flush draw on the flop: 9 outs, 38 misses. The chance of missing both cards is (38 ÷ 47) × (37 ÷ 46) = 1,406 ÷ 2,162 = 65.0%. So the chance of hitting by the river is 35.0%.
| Outs | Flop to turn (÷ 47) | Turn to river (÷ 46) | Flop to river (exact) | Rule of 4 | Error | Rule of 2 | Error |
|---|---|---|---|---|---|---|---|
| 1 | 2.1% | 2.2% | 4.3% | 4% | −0.3 | 2% | −0.2 |
| 2 | 4.3% | 4.3% | 8.4% | 8% | −0.4 | 4% | −0.3 |
| 3 | 6.4% | 6.5% | 12.5% | 12% | −0.5 | 6% | −0.5 |
| 4 | 8.5% | 8.7% | 16.5% | 16% | −0.5 | 8% | −0.7 |
| 5 | 10.6% | 10.9% | 20.4% | 20% | −0.4 | 10% | −0.9 |
| 6 | 12.8% | 13.0% | 24.1% | 24% | −0.1 | 12% | −1.0 |
| 7 | 14.9% | 15.2% | 27.8% | 28% | +0.2 | 14% | −1.2 |
| 8 | 17.0% | 17.4% | 31.5% | 32% | +0.5 | 16% | −1.4 |
| 9 | 19.1% | 19.6% | 35.0% | 36% | +1.0 | 18% | −1.6 |
| 10 | 21.3% | 21.7% | 38.4% | 40% | +1.6 | 20% | −1.7 |
| 11 | 23.4% | 23.9% | 41.7% | 44% | +2.3 | 22% | −1.9 |
| 12 | 25.5% | 26.1% | 45.0% | 48% | +3.0 | 24% | −2.1 |
| 13 | 27.7% | 28.3% | 48.1% | 52% | +3.9 | 26% | −2.3 |
| 14 | 29.8% | 30.4% | 51.2% | 56% | +4.8 | 28% | −2.4 |
| 15 | 31.9% | 32.6% | 54.1% | 60% | +5.9 | 30% | −2.6 |
| 16 | 34.0% | 34.8% | 57.0% | 64% | +7.0 | 32% | −2.8 |
| 17 | 36.2% | 37.0% | 59.8% | 68% | +8.2 | 34% | −3.0 |
| 18 | 38.3% | 39.1% | 62.4% | 72% | +9.6 | 36% | −3.1 |
| 19 | 40.4% | 41.3% | 65.0% | 76% | +11.0 | 38% | −3.3 |
| 20 | 42.6% | 43.5% | 67.5% | 80% | +12.5 | 40% | −3.5 |
Errors are in percentage points: the shortcut minus the exact figure.
The rule of 4 and 2, and where it breaks
The shortcut most players learn: multiply outs by 4 on the flop (two cards to come) and by 2 on the turn (one card to come). The table shows how good it is, and where it fails.
- Rule of 2 on the turn always runs a little low, by 0.2 to 3.5 points across 1 to 20 outs. The true multiplier is 100 ÷ 46, about 2.17. Being slightly conservative is a forgivable error.
- Rule of 4 on the flop is close up to about 9 outs, then overshoots badly. With 15 outs it says 60% when the truth is 54.1%. With 20 outs it says 80% against 67.5%.
A common fix for big draws: from 9 outs up, take 4 × outs and subtract (outs − 8). For 15 outs that gives 60 − 7 = 53%, close to the exact 54.1%. For 12 outs, 48 − 4 = 44%, against an exact 45.0%.
One more caution. The rule of 4 assumes the player sees both the turn and the river, which is only true when all the money is already in. Facing a flop bet with more betting to come, the honest number is the one-card figure. A flush draw is 35% to get there by the river, but only 19.1% to get there on the turn, and the turn is all a flop call guarantees.
Counting outs: common draws
| Draw | Example | Outs | Notes |
|---|---|---|---|
| Gutshot straight | 9♣ 8♦ on J♠ 7♥ 2♣ (needs a 10) | 4 | Inside straight draw |
| Two overcards | A♦ K♣ on 9♠ 6♥ 2♣ | 6 | Any ace or king, if a pair would win |
| Open-ended straight | 9♣ 8♦ on 7♥ 6♠ 2♣ | 8 | A 10 or a 5 |
| Flush draw | A♥ 5♥ on K♥ 9♥ 3♣ | 9 | 13 hearts minus the 4 seen |
| Flush + gutshot | Q♥ J♥ on 10♥ 8♥ 2♣ | 12 | 9 hearts + 3 non-heart 9s |
| Flush + open-ended | 8♥ 7♥ on 9♥ 6♥ 2♣ | 15 | 9 hearts + 3 non-heart 10s + 3 non-heart 5s |
| Pocket pair to a set | 5♠ 5♦ on K♣ 9♥ 2♠ | 2 | Usually not enough on its own |
Outs need to be honest. An out that also gives the opponent a better hand is not an out. With a straight draw on a two-flush board, the cards of that suit may complete an opponent’s flush, so careful players discount them. Not every out can be trusted, and a player who counts optimistically will call too often.
Preflop and flop odds
Some odds come up every session. All of these are exact.
| Event | Calculation | Probability |
|---|---|---|
| Dealt a pocket pair | 78 ÷ 1,326 | 5.88% (1 in 17) |
| Dealt a specific pair (such as AA) | 6 ÷ 1,326 | 0.45% (1 in 221) |
| Dealt AK (suited or not) | 16 ÷ 1,326 | 1.21% |
| Dealt suited cards | 312 ÷ 1,326 | 23.5% |
| Pocket pair flops a set or better | 1 − C(48,3) ÷ C(50,3) | 11.8% (about 7.5 to 1 against) |
| Pocket pair makes a set or better by the river | 1 − C(48,5) ÷ C(50,5) | 19.2% |
| Suited cards flop a flush | C(11,3) ÷ C(50,3) | 0.84% |
| Suited cards flop a flush draw (exactly 2 of the suit) | C(11,2) × 39 ÷ C(50,3) | 10.9% |
| Suited cards make a flush by the river | (3, 4 or 5 of 11 suited cards on board) | 6.4% |
| Unpaired hand fails to pair either card on the flop | C(44,3) ÷ C(50,3) | 67.6% |
The set-mining number is the one that matters for implied odds. A small pair flops a set about one time in 8.5. A player calling a raise to set-mine is paying for a ticket that loses roughly 7.5 times for every win, so the win needs to be large.
Classic preflop matchups (all in before the flop)
Exact figures from running all 1,712,304 possible five-card boards for each pair of hands. Suits matter a little, so they are listed.
| Hand | vs | Hand | Equity (first hand) |
|---|---|---|---|
| A♣ A♦ | vs | K♥ K♠ | 81.3% |
| A♥ A♣ | vs | 8♠ 7♠ | 77.0% |
| J♥ J♦ | vs | 10♠ 9♠ | 81.1% |
| Q♥ Q♦ | vs | A♠ K♠ | 53.8% |
| Q♥ Q♦ | vs | A♣ K♦ | 56.8% |
| 7♣ 7♦ | vs | A♥ K♦ | 55.0% |
| 2♥ 2♦ | vs | A♠ K♠ | 50.1% |
| A♥ K♣ | vs | J♦ 10♦ | 58.8% |
| A♥ K♦ | vs | A♣ Q♠ | 74.0% |
| K♥ Q♥ | vs | A♣ 2♦ | 46.1% |
The “coin flip” everyone talks about, a pair against two overcards, really is close to even: from 50.1% for deuces against suited AK to 56.8% for queens against offsuit AK. Domination (AK against AQ, sharing an ace) is much worse for the dominated hand, at about 26%. And suited connectors are not the miracle hands they look like on television: 8♠ 7♠ wins just 23% against aces.
How to use the chart at the table
- Count outs honestly, discounting any that might help the opponent.
- Use the one-card figure unless all the money is already in.
- Compare that figure with the pot odds. The pot odds explained note has the formula and a bet-size table, and pot odds vs equity shows how to reason against a range rather than one hand.
Tools referenced on this site. Every figure on this page can be checked with a combinatorics calculator or a short script. For full-range equity and strategy work, players use equity calculators and solvers; the poker solvers comparison covers the main options by published price and format.
Poker is for adults, 21+ (or 18+ where state law allows). If a session ever feels like chasing losses, help is free on call or text at 1-800-MY-RESET, and the responsible gambling page has more.