--- title: "3 Outs on the Flop: Odds to Hit" url: "https://georgelipoker.com/outs/3-outs-flop.md" canonical_url: "https://georgelipoker.com/outs/3-outs-flop" last_updated: "2026-10-20" type: "reference" summary: "3 outs, flop: you hit by the river 12.49% of the time, 7.01 : 1 against, with the rule of 4 checked and every bet size priced." related: ["https://georgelipoker.com/outs.md"] --- # 3 Outs on the Flop: Odds to Hit 3 outs, flop: you hit by the river 12.49% of the time, 7.01 : 1 against, with the rule of 4 checked and every bet size priced. On the flop, two cards are still to come. With 3 outs, the chance that an out lands by the river is 12.49%, and the sections below price that chance against a bet. - Chance to hit by the river: 12.49% (3 outs, two cards to come) - Chance on the next card: 6.38% - Odds against by the river: 7.01 : 1 - Rule of 4 estimate: 12% (-0.49 points from the exact chance) ## The count behind 3 outs on the flop This count leaves you empty-handed 87.51% of the time. A 12.49% chance can still be worth chasing, but only when the bet you face is a small fraction of the pot. - Unseen cards: 47 - Your outs: 3 - Cards that miss: 44 - Pairs of cards with no out: 946 - Pairs with at least one out: 135 - Chance by the river: 12.49% - Chance on the next card: 6.38% - Odds against hitting: 7.01 : 1 - Estimate from the rule of 4: 12% - Error of the rule of 4: -0.49 points - Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cards - For 3 outs: 1 - C(44, 2) / C(47, 2) = 1 - 946 / 1,081 = 12.49% - Next card = 3 / 47 = 6.38% Think in pairs. The 47 unseen cards form 1,081 pairs, and only 946 avoid every out. Subtract and you land on 135 helpful pairs, a 12.49% chance. The quick estimate of 12% and the exact 12.49% nearly agree, separated by 0.49 points. No adjustment is needed on the flop with 3 outs. The plain rule of 4 gives 4 x 3 = 12%. ## Which holding has 3 outs? One overcard to top pair fits this count exactly, with 3 outs. Memorizing counts like this lets you read the chance straight from the table on this page. A shared out has a price: 4.07 points for the first, and 12.49 points in all with 3 shared. Subtract any shared outs before you compare with a bet. 3 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 | 3 | 12.49% | 0.00 points | | 1 | 2 | 8.42% | 4.07 points | | 2 | 1 | 4.26% | 8.23 points | | 3 | 0 | 0.00% | 12.49 points | ## The bets 3 outs can call on the flop The table prices every bet against 12.49%. Margin is your chance minus the equity a call needs, and no bet size is a call. 3 outs on the flop against every bet size, with your chance by the river at 12.49% | Bet size | Equity a call needs | Margin over it | Verdict | | --- | --- | --- | --- | | 1/4 pot | 16.67% | -4.18 points | Fold | | [1/3 pot](https://georgelipoker.com/call-or-fold/3-outs-flop-vs-third-pot.md) | 20.00% | -7.51 points | Fold | | 2/5 pot | 22.22% | -9.73 points | Fold | | [1/2 pot](https://georgelipoker.com/call-or-fold/3-outs-flop-vs-half-pot.md) | 25.00% | -12.51 points | Fold | | [2/3 pot](https://georgelipoker.com/call-or-fold/3-outs-flop-vs-two-thirds-pot.md) | 28.57% | -16.08 points | Fold | | [3/4 pot](https://georgelipoker.com/call-or-fold/3-outs-flop-vs-three-quarter-pot.md) | 30.00% | -17.51 points | Fold | | [full pot](https://georgelipoker.com/call-or-fold/3-outs-flop-vs-pot-size.md) | 33.33% | -20.84 points | Fold | | 1.25x pot | 35.71% | -23.23 points | Fold | | 1.5x pot | 37.50% | -25.01 points | Fold | | 2x pot | 40.00% | -27.51 points | Fold | | 3x pot | 42.86% | -30.37 points | Fold | | 4x pot | 44.44% | -31.96 points | Fold | Past 16.65% of the pot, the price beats your 12.49%. On a $100 pot that line is $16.65. ## Nearby counts on both streets Neighboring counts help you judge a close draw. One out more or less shifts the chance by roughly 3.98 points on this street. Counts near 3: the chance by the river on the flop and on the turn | Outs | Flop, by the river | Turn, by the river | | --- | --- | --- | | [1](https://georgelipoker.com/outs/1-outs-flop.md) | 4.26% | 2.17% | | [2](https://georgelipoker.com/outs/2-outs-flop.md) | 8.42% | 4.35% | | 3 (this page) | 12.49% | 6.52% | | [4](https://georgelipoker.com/outs/4-outs-flop.md) | 16.47% | 8.70% | | [5](https://georgelipoker.com/outs/5-outs-flop.md) | 20.35% | 10.87% | - [3 outs on the turn](https://georgelipoker.com/outs/3-outs-turn.md): 6.52% on the river. - [2 outs on the flop](https://georgelipoker.com/outs/2-outs-flop.md): 8.42% by the river. - [4 outs on the flop](https://georgelipoker.com/outs/4-outs-flop.md): 16.47% by the river. ## When a bet buys only one card When more betting is still to come, the fair test is the next card alone. 6.38% against the 25.00% that a half-pot call needs is -18.62 points, which reads Fold. Whether you count one card or two, 3 outs clear none of the 12 bet sizes. ## Questions ### What are the odds of hitting with 3 outs on the flop? With 3 outs on the flop you hit by the river 12.49% of the time, about 12 of every 100 hands, and on the next card 6.38%. The odds against hitting by the river are 7.01 : 1, since 946 of 1,081 pairs of unseen cards hold no out. ### What does the rule of 4 say for a count of 3? The rule of 4 gives 12% for 3 outs against an exact 12.49%, an error of -0.49 points. That is close enough to use at the table. ### How many bet sizes can 3 outs on the flop pay for? At 12.49% by the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -12.51 points, so against half the pot the verdict is Fold. The largest bet you can call is 16.65% of the pot, or $16.65 on a $100 pot. ### Should I count every out when a rival could be drawing too, with 3 outs? Take them off the count first. With one shared out the chance by the river falls from 12.49% to 8.42%, and with 3 shared it falls to 0.00%, a loss of 12.49 points. The effective count is then 0 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 3 outs that is 1 - 946 / 1,081 = 12.49%. The chance on the next card is k / 47, here 6.38%. The rule of 4 figure is 4 x k, here 12%, and its error is that figure minus the exact chance in percentage points, here -0.49 points. Two assumptions sit behind the page. First, all 47 unseen cards are equally likely, with no cards taken out for an opponent. Second, each bet is called in full on a $100 pot, so you pay one bet to play for a pot that holds the pot and both 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. - [3 outs on the turn](https://georgelipoker.com/outs/3-outs-turn.md): The same count with one card to come. - [Pot odds for a half-pot bet](https://georgelipoker.com/pot-odds/half-pot.md): The equity a half-pot call needs. - [Pot odds for a 1.5x-pot bet](https://georgelipoker.com/pot-odds/1-5x-pot.md): The equity a 1.5x-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)