--- title: "4 Outs on the Flop: Odds to Hit" url: "https://georgelipoker.com/outs/4-outs-flop.md" canonical_url: "https://georgelipoker.com/outs/4-outs-flop" last_updated: "2026-10-22" type: "reference" summary: "16.47% by the river with 4 outs on the flop. The exact figure, the odds against and which pot-fraction bets are worth calling." related: ["https://georgelipoker.com/outs.md"] --- # 4 Outs on the Flop: Odds to Hit 16.47% by the river with 4 outs on the flop. The exact figure, the odds against and which pot-fraction bets are worth calling. A count of 4 on the flop is worth 16.47% by the river. Use this page to read that as odds against, to see how the rule of 4 copes with it and to check which bets earn a call. - Chance to hit by the river: 16.47% (4 outs, two cards to come) - Chance on the next card: 8.51% - Odds against by the river: 5.07 : 1 - Rule of 4 estimate: 16% (-0.47 points from the exact chance) ## The count behind 4 outs on the flop Think of 16.47% as a long shot that pays when the price is right. At 5.07 : 1 against, you need the pot to be laying a generous price. - Unseen cards: 47 - Your outs: 4 - Cards that miss: 43 - Pairs of cards with no out: 903 - Pairs with at least one out: 178 - Chance by the river: 16.47% - Chance on the next card: 8.51% - Odds against hitting: 5.07 : 1 - Estimate from the rule of 4: 16% - Error of the rule of 4: -0.47 points - Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cards - For 4 outs: 1 - C(43, 2) / C(47, 2) = 1 - 903 / 1,081 = 16.47% - Next card = 4 / 47 = 8.51% The draw fails only when the turn and the river both miss. That covers 903 of the 1,081 pairs, so it lands in the other 178, or 16.47%. The quick estimate of 16% and the exact 16.47% nearly agree, separated by 0.47 points. Leave the adjusted rule for bigger flop draws. With 4 outs on the flop, the plain rule of 4 figure is 16%. ## Which holding has 4 outs? One standard source of this count is a gutshot straight draw. Count the cards carefully at the table, because outs that also help a rival do not count in full. Not every out is clean. Here is the chance once shared outs are removed: from 16.47% down to 4.26% when 3 are shared. 4 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 | 4 | 16.47% | 0.00 points | | 1 | 3 | 12.49% | 3.98 points | | 2 | 2 | 8.42% | 8.05 points | | 3 | 1 | 4.26% | 12.21 points | ## The bets 4 outs can call on the flop Here is the price list. For each bet size it shows the equity a call needs, your margin over it and the verdict, and no verdict is Call. 4 outs on the flop against every bet size, with your chance by the river at 16.47% | Bet size | Equity a call needs | Margin over it | Verdict | | --- | --- | --- | --- | | 1/4 pot | 16.67% | -0.20 points | Fold | | [1/3 pot](https://georgelipoker.com/call-or-fold/4-outs-flop-vs-third-pot.md) | 20.00% | -3.53 points | Fold | | 2/5 pot | 22.22% | -5.76 points | Fold | | [1/2 pot](https://georgelipoker.com/call-or-fold/4-outs-flop-vs-half-pot.md) | 25.00% | -8.53 points | Fold | | [2/3 pot](https://georgelipoker.com/call-or-fold/4-outs-flop-vs-two-thirds-pot.md) | 28.57% | -12.11 points | Fold | | [3/4 pot](https://georgelipoker.com/call-or-fold/4-outs-flop-vs-three-quarter-pot.md) | 30.00% | -13.53 points | Fold | | [full pot](https://georgelipoker.com/call-or-fold/4-outs-flop-vs-pot-size.md) | 33.33% | -16.87 points | Fold | | 1.25x pot | 35.71% | -19.25 points | Fold | | 1.5x pot | 37.50% | -21.03 points | Fold | | 2x pot | 40.00% | -23.53 points | Fold | | 3x pot | 42.86% | -26.39 points | Fold | | 4x pot | 44.44% | -27.98 points | Fold | Past 24.55% of the pot, the price beats your 16.47%. On a $100 pot that line is $24.55. ## Nearby counts on both streets Neighboring counts help you judge a close draw. One out more or less shifts the chance by roughly 3.89 points on this street. Counts near 4: the chance by the river on the flop and on the turn | Outs | Flop, by the river | Turn, by the river | | --- | --- | --- | | [2](https://georgelipoker.com/outs/2-outs-flop.md) | 8.42% | 4.35% | | [3](https://georgelipoker.com/outs/3-outs-flop.md) | 12.49% | 6.52% | | 4 (this page) | 16.47% | 8.70% | | [5](https://georgelipoker.com/outs/5-outs-flop.md) | 20.35% | 10.87% | | [6](https://georgelipoker.com/outs/6-outs-flop.md) | 24.14% | 13.04% | - [4 outs on the turn](https://georgelipoker.com/outs/4-outs-turn.md): 8.70% on the river. - [3 outs on the flop](https://georgelipoker.com/outs/3-outs-flop.md): 12.49% by the river. - [5 outs on the flop](https://georgelipoker.com/outs/5-outs-flop.md): 20.35% by the river. ## When a bet buys only one card Price the flop call on one card. With 4 outs, that is 8.51%, and a half-pot bet asks for 25.00%. The margin of -16.49 points gives the verdict Fold. No row flips when you drop to the next card. The count of calls stays 0 of 12. ## Questions ### What is the chance to hit with 4 outs on the flop? With 4 outs on the flop you hit by the river 16.47% of the time, about 16 of every 100 hands, and on the next card 8.51%. The odds against hitting by the river are 5.07 : 1, since 903 of 1,081 pairs of unseen cards hold no out. ### Can I trust the shortcut for 4 outs on the flop? The rule of 4 gives 16% for 4 outs against an exact 16.47%, an error of -0.47 points. That is close enough to use at the table. ### Do 4 outs on the flop justify a call, and against which bets? At 16.47% by the river, you can call none of the 12 bet sizes. A half-pot bet needs 25.00%, a margin of -8.53 points, so against half the pot the verdict is Fold. The largest bet you can call is 24.55% of the pot, or $24.55 on a $100 pot. ### What if some of my 4 outs also help a better hand? Take them off the count first. With one shared out the chance by the river falls from 16.47% to 12.49%, and with 3 shared it falls to 4.26%, a loss of 12.21 points. The effective count is then 1 out. ## 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 4 outs that is 1 - 903 / 1,081 = 16.47%. The chance on the next card is k / 47, here 8.51%. The rule of 4 figure is 4 x k, here 16%, and its error is that figure minus the exact chance in percentage points, here -0.47 points. Model notes: every unseen card among the 47 has the same chance of coming, no rival hand is removed, and each bet is matched by one call on a $100 pot, which is the whole amount a hit wins. 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. - [4 outs on the turn](https://georgelipoker.com/outs/4-outs-turn.md): The same count with one card to come. - [Pot odds for a two-thirds-pot bet](https://georgelipoker.com/pot-odds/two-thirds-pot.md): The equity a two-thirds-pot call needs. - [Pot odds for a 2x-pot bet](https://georgelipoker.com/pot-odds/2x-pot.md): The equity a 2x-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)