--- title: "13 Outs on the Flop: Odds to Hit" url: "https://georgelipoker.com/outs/13-outs-flop.md" canonical_url: "https://georgelipoker.com/outs/13-outs-flop" last_updated: "2026-10-20" type: "reference" summary: "13 outs on the flop: a 48.10% chance by the river, 1.08 : 1 against. See the rule of 4 error and the bets you can call." related: ["https://georgelipoker.com/outs.md"] --- # 13 Outs on the Flop: Odds to Hit 13 outs on the flop: a 48.10% chance by the river, 1.08 : 1 against. See the rule of 4 error and the bets you can call. With 13 outs on the flop, you complete your hand by the river 48.10% 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: 48.10% (13 outs, two cards to come) - Chance on the next card: 27.66% - Odds against by the river: 1.08 : 1 - Rule of 4 estimate: 52% (+3.90 points from the exact chance) ## The count behind 13 outs on the flop A 48.10% chance is the territory of big draws. The miss is 51.90%, so even a bet the size of the pot can be a call. - Unseen cards: 47 - Your outs: 13 - Cards that miss: 34 - Pairs of cards with no out: 561 - Pairs with at least one out: 520 - Chance by the river: 48.10% - Chance on the next card: 27.66% - Odds against hitting: 1.08 : 1 - Estimate from the rule of 4: 52% - Error of the rule of 4: +3.90 points - Adjusted rule 4k - (k - 8): 47% - Error of the adjusted rule: -1.10 points - Chance by the river = 1 - C(u - k, 2) / C(u, 2), with u = 47 unseen cards - For 13 outs: 1 - C(34, 2) / C(47, 2) = 1 - 561 / 1,081 = 48.10% - Next card = 13 / 47 = 27.66% Here is the arithmetic for 13 outs. Both cards must miss for the draw to fail: that is 561 pairs out of 1,081. The remaining 520 pairs give you 48.10%. 52% from the rule of 4 sits 3.90 points over the true 48.10%. The larger the count of outs on the flop, the further the shortcut drifts. Subtracting the 5 outs beyond 8 gives 47%. That lands 1.10 points from 48.10%, so it is the shortcut to prefer here. ## Which holding has 13 outs? There is no stock draw with exactly 13 outs. The number comes from your own count of helpful cards, with overlaps removed. A shared out has a price: 3.15 points for the first, and 9.71 points in all with 3 shared. Subtract any shared outs before you compare with a bet. 13 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 | 13 | 48.10% | 0.00 points | | 1 | 12 | 44.96% | 3.15 points | | 2 | 11 | 41.72% | 6.38 points | | 3 | 10 | 38.39% | 9.71 points | ## The bets 13 outs can call on the flop Draw the line at 48.10%: any bet that needs less equity than that is a call. Here that covers all 12 bet sizes. 13 outs on the flop against every bet size, with your chance by the river at 48.10% | Bet size | Equity a call needs | Margin over it | Verdict | | --- | --- | --- | --- | | 1/4 pot | 16.67% | +31.44 points | Call | | [1/3 pot](https://georgelipoker.com/call-or-fold/13-outs-flop-vs-third-pot.md) | 20.00% | +28.10 points | Call | | 2/5 pot | 22.22% | +25.88 points | Call | | [1/2 pot](https://georgelipoker.com/call-or-fold/13-outs-flop-vs-half-pot.md) | 25.00% | +23.10 points | Call | | [2/3 pot](https://georgelipoker.com/call-or-fold/13-outs-flop-vs-two-thirds-pot.md) | 28.57% | +19.53 points | Call | | [3/4 pot](https://georgelipoker.com/call-or-fold/13-outs-flop-vs-three-quarter-pot.md) | 30.00% | +18.10 points | Call | | [full pot](https://georgelipoker.com/call-or-fold/13-outs-flop-vs-pot-size.md) | 33.33% | +14.77 points | Call | | 1.25x pot | 35.71% | +12.39 points | Call | | 1.5x pot | 37.50% | +10.60 points | Call | | 2x pot | 40.00% | +8.10 points | Call | | 3x pot | 42.86% | +5.25 points | Call | | 4x pot | 44.44% | +3.66 points | Call | Anything above $1,268.29 on a $100 pot, which is 1,268.29% of the pot, asks for more equity than this draw holds. ## Nearby counts on both streets Adding or losing one out moves the chance by about 3.05 points on the flop. Here are the counts next to 13, with the other street alongside. Counts near 13: the chance by the river on the flop and on the turn | Outs | Flop, by the river | Turn, by the river | | --- | --- | --- | | [11](https://georgelipoker.com/outs/11-outs-flop.md) | 41.72% | 23.91% | | [12](https://georgelipoker.com/outs/12-outs-flop.md) | 44.96% | 26.09% | | 13 (this page) | 48.10% | 28.26% | | [14](https://georgelipoker.com/outs/14-outs-flop.md) | 51.16% | 30.43% | | [15](https://georgelipoker.com/outs/15-outs-flop.md) | 54.12% | 32.61% | - [13 outs on the turn](https://georgelipoker.com/outs/13-outs-turn.md): 28.26% on the river. - [12 outs on the flop](https://georgelipoker.com/outs/12-outs-flop.md): 44.96% by the river. - [14 outs on the flop](https://georgelipoker.com/outs/14-outs-flop.md): 51.16% by the river. ## When a bet buys only one card Check the one-card case before you call a flop bet. 27.66% against 25.00% is +2.66 points for 13 outs, and that is Call against a half-pot bet. The one-card view cuts the bet sizes you can call to 4, from 12 in the table above. ## Questions ### How should I read the hit chance for 13 outs on the flop? With 13 outs on the flop you hit by the river 48.10% of the time, about 48 of every 100 hands, and on the next card 27.66%. The odds against hitting by the river are 1.08 : 1, since 561 of 1,081 pairs of unseen cards hold no out. ### How accurate is the rule of 4 for 13 outs? The rule of 4 gives 52% for 13 outs against an exact 48.10%, an error of +3.90 points, so it overstates the draw. The adjusted rule 4k - (k - 8) gives 47%, an error of -1.10 points, and is the closer figure. ### Are 13 outs on the flop enough to call a half-pot bet? At 48.10% by the river, you can call all 12 bet sizes. A half-pot bet needs 25.00%, a margin of +23.10 points, so against half the pot the verdict is Call. The largest bet you can call is 1,268.29% of the pot, or $1,268.29 on a $100 pot. ### Should I count every out when a rival could be drawing too, with 13 outs? Take them off the count first. With one shared out the chance by the river falls from 48.10% to 44.96%, and with 3 shared it falls to 38.39%, a loss of 9.71 points. The effective count is then 10 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 13 outs that is 1 - 561 / 1,081 = 48.10%. The chance on the next card is k / 47, here 27.66%. The rule of 4 figure is 4 x k, here 52%, and its error is that figure minus the exact chance in percentage points, here +3.90 points. The adjusted rule 4k - (k - 8) gives 47%, an error of -1.10 points. The model gives every one of the 47 unseen cards the same chance and removes nothing for what a rival holds. It measures hitting an out, not winning the hand. Bets are priced on a $100 pot, and a call adds one bet to the pot. 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. - [13 outs on the turn](https://georgelipoker.com/outs/13-outs-turn.md): The same count with one card to come. - [Pot odds for a third-pot bet](https://georgelipoker.com/pot-odds/third-pot.md): The equity a third-pot call needs. - [Pot odds for a pot-size bet](https://georgelipoker.com/pot-odds/pot-size.md): The equity a pot-size 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)