--- title: "9 Outs on the Flop: Odds to Hit" url: "https://georgelipoker.com/outs/9-outs-flop.md" canonical_url: "https://georgelipoker.com/outs/9-outs-flop" last_updated: "2026-10-20" type: "reference" summary: "Exact odds for 9 outs on the flop: 34.97% by the river. Compare the rule of 4 figure, then see which bets you can call." related: ["https://georgelipoker.com/outs.md"] --- # 9 Outs on the Flop: Odds to Hit Exact odds for 9 outs on the flop: 34.97% by the river. Compare the rule of 4 figure, then see which bets you can call. With 9 outs on the flop, you complete your hand by the river 34.97% of the time. The page below gives the odds against, the error of the rule of thumb and the bets that chance can pay for. - Chance to hit by the river: 34.97% (9 outs, two cards to come) - Chance on the next card: 19.15% - Odds against by the river: 1.86 : 1 - Rule of 4 estimate: 36% (+1.03 points from the exact chance) ## The count behind 9 outs on the flop Between one chance in five and two in five, 34.97% is a draw worth playing when the bet is not oversized. - Unseen cards: 47 - Your outs: 9 - Cards that miss: 38 - Pairs of cards with no out: 703 - Pairs with at least one out: 378 - Chance by the river: 34.97% - Chance on the next card: 19.15% - Odds against hitting: 1.86 : 1 - Estimate from the rule of 4: 36% - Error of the rule of 4: +1.03 points - Adjusted rule 4k - (k - 8): 35% - Error of the adjusted rule: +0.03 points - Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cards - For 9 outs: 1 - C(38, 2) / C(47, 2) = 1 - 703 / 1,081 = 34.97% - Next card = 9 / 47 = 19.15% The draw fails only when the turn and the river both miss. That covers 703 of the 1,081 pairs, so it lands in the other 378, or 34.97%. The rule of 4 gives 36% against an exact 34.97%, a gap of +1.03 points. That is close enough to use at the table. The adjusted rule 4k - (k - 8) gives 35% for 9 outs, 0.03 points from the exact 34.97%. It trims the shortcut back toward the truth. ## Which holding has 9 outs? For a flush draw, the count is exactly 9. The chance you see here is the right one to use, as long as none of those cards help an opponent too. Use the effective count, not the raw one, when a rival could be drawing too. Losing 3 outs to overlap moves 34.97% down to 24.14%. 9 outs on the flop when some outs are shared with a better hand | Shared outs | Effective outs | Chance by the river | Chance given up | | --- | --- | --- | --- | | 0 | 9 | 34.97% | 0.00 points | | 1 | 8 | 31.45% | 3.52 points | | 2 | 7 | 27.84% | 7.12 points | | 3 | 6 | 24.14% | 10.82 points | ## The bets 9 outs can call on the flop Compare the columns: required equity on the left, margin in the middle, verdict at the end. With 9 outs you can call 7 of the 12 bet sizes. 9 outs on the flop against every bet size, with your chance by the river at 34.97% | Bet size | Equity a call needs | Margin over it | Verdict | | --- | --- | --- | --- | | 1/4 pot | 16.67% | +18.30 points | Call | | [1/3 pot](https://georgelipoker.com/call-or-fold/9-outs-flop-vs-third-pot.md) | 20.00% | +14.97 points | Call | | 2/5 pot | 22.22% | +12.75 points | Call | | [1/2 pot](https://georgelipoker.com/call-or-fold/9-outs-flop-vs-half-pot.md) | 25.00% | +9.97 points | Call | | [2/3 pot](https://georgelipoker.com/call-or-fold/9-outs-flop-vs-two-thirds-pot.md) | 28.57% | +6.40 points | Call | | [3/4 pot](https://georgelipoker.com/call-or-fold/9-outs-flop-vs-three-quarter-pot.md) | 30.00% | +4.97 points | Call | | [full pot](https://georgelipoker.com/call-or-fold/9-outs-flop-vs-pot-size.md) | 33.33% | +1.63 points | Call | | 1.25x pot | 35.71% | -0.75 points | Fold | | 1.5x pot | 37.50% | -2.53 points | Fold | | 2x pot | 40.00% | -5.03 points | Fold | | 3x pot | 42.86% | -7.89 points | Fold | | 4x pot | 44.44% | -9.48 points | Fold | The line between call and fold is a bet of 116.31% of the pot, or $116.31 on a $100 pot. Stay at or under it and the draw pays for itself. ## Nearby counts on both streets Neighboring counts help you judge a close draw. One out more or less shifts the chance by roughly 3.42 points on this street. Counts near 9: the chance by the river on the flop and on the turn | Outs | Flop, by the river | Turn, by the river | | --- | --- | --- | | [7](https://georgelipoker.com/outs/7-outs-flop.md) | 27.84% | 15.22% | | [8](https://georgelipoker.com/outs/8-outs-flop.md) | 31.45% | 17.39% | | 9 (this page) | 34.97% | 19.57% | | [10](https://georgelipoker.com/outs/10-outs-flop.md) | 38.39% | 21.74% | | [11](https://georgelipoker.com/outs/11-outs-flop.md) | 41.72% | 23.91% | - [9 outs on the turn](https://georgelipoker.com/outs/9-outs-turn.md): 19.57% on the river. - [8 outs on the flop](https://georgelipoker.com/outs/8-outs-flop.md): 31.45% by the river. - [10 outs on the flop](https://georgelipoker.com/outs/10-outs-flop.md): 38.39% by the river. ## When a bet buys only one card The by-the-river figure of 34.97% assumes you see both cards. If a turn bet follows, use 19.15%: against a half-pot price of 25.00%, that margin is -5.85 points and the verdict is Fold. 1 of 12 sizes survives the one-card test, where the two-card test passed 7. ## Questions ### What is the chance to hit with 9 outs on the flop? With 9 outs on the flop you hit by the river 34.97% of the time, about 35 of every 100 hands, and on the next card 19.15%. The odds against hitting by the river are 1.86 : 1, since 703 of 1,081 pairs of unseen cards hold no out. ### What is the error of the rule of 4 at 9 outs? The rule of 4 gives 36% for 9 outs against an exact 34.97%, an error of +1.03 points, so it runs a little high on the draw. The adjusted rule 4k - (k - 8) gives 35%, an error of +0.03 points, and is the closer figure. ### How many bet sizes can 9 outs on the flop pay for? At 34.97% by the river, you can call 7 of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of +9.97 points, so against half the pot the verdict is Call. The largest bet you can call is 116.31% of the pot, or $116.31 on a $100 pot. ### What if some of my 9 outs also help a better hand? Take them off the count first. With one shared out the chance by the river falls from 34.97% to 31.45%, and with 3 shared it falls to 24.14%, a loss of 10.82 points. The effective count is then 6 outs. ## How this is computed The chance to hit by the river from the flop is 1 - C(u - k, 2) / C(u, 2), where u = 47 unseen cards and k is your effective outs. For 9 outs that is 1 - 703 / 1,081 = 34.97%. The chance on the next card is k / 47, here 19.15%. The rule of 4 figure is 4 x k, here 36%, and its error is that figure minus the exact chance in percentage points, here +1.03 points. The adjusted rule 4k - (k - 8) gives 35%, an error of +0.03 points. Seen as a pure card count, the 47 unseen cards are all equally likely and an opponent's hand removes none of them. Prices use a $100 pot and a call equal to the bet, so the equity needed is the bet over the pot plus two bets. Computed from the closed form by the GeorgeLiPoker math library. ## Related pages - [Outs calculator](https://georgelipoker.com/tools/outs-calculator.md): Enter your own count and street. - [Pot odds calculator](https://georgelipoker.com/tools/pot-odds-calculator.md): Enter a pot and a bet to see the equity a call needs. - [Outs and odds to hit](https://georgelipoker.com/outs.md): The chance to hit for every count on both streets. - [9 outs on the turn](https://georgelipoker.com/outs/9-outs-turn.md): The same count with one card to come. - [Pot odds for a 2x-pot bet](https://georgelipoker.com/pot-odds/2x-pot.md): The equity a 2x-pot call needs. - [Pot odds for a two-fifths-pot bet](https://georgelipoker.com/pot-odds/two-fifths-pot.md): The equity a two-fifths-pot call needs. - [Hand equity](https://georgelipoker.com/equity.md): Your chance to win against a named hand. ## Related - [Outs and Odds to Hit by Street](https://georgelipoker.com/outs.md)