Outs and drawing odds calculator

Enter how many cards would complete your hand and which street you are on. You get the exact probability and, next to it, what the rule of 2 and 4 would have told you.

Chance of hitting by the river

35.0%

9 outs from 47 unseen cards: 19.1% on the turn alone (4.2 : 1 against), 35.0% over the turn and river together (1.9 : 1 against).

Method	Estimate	Error
Exact, next card	19.1%	—
Rule of 2 (next card)	18%	-1.1 pts
Exact, by the river	35.0%	—
Rule of 4	36%	+1.0 pts
Rule of 4, corrected	35%	+0.0 pts

How to count your outs

An out is an unseen card that would give you the best hand. Count them by asking what you need and how many of those cards you cannot see. A flush draw has four cards of a suit between your hand and the board, so nine of the thirteen remain. An open-ended straight draw, such as 9-8 on a 7-6-2 board, is completed by any 5 or any 10: eight cards. A gutshot needs one rank, so four.

When two draws overlap, do not count the shared cards twice. A flush draw plus an open-ended straight draw is 9 + 8 − 2 = 15, because the two straight cards in your suit are already among the nine flush cards. Then be honest about outs that might not win (see discounted outs in the questions below) and enter the number you are left with.

The exact formula

After the flop you have seen five cards: your two and the three on the board. That leaves 47 unseen. After the turn, 46. Every unseen card is equally likely to come next, whether it is in the deck or in an opponent's hand, because you cannot see either.

Next card from the flop: outs / 47
Next card from the turn: outs / 46
By the river from the flop: 1 − ((47 − outs) × (46 − outs)) / (47 × 46) — one minus the chance of missing twice in a row
Odds against: (1 − p) / p to 1

The rule of 2 and 4, and where it drifts

The shortcut multiplies outs by 2 for one card and by 4 for two. For one card it is always slightly low, because each card is really 1/47 = 2.13% or 1/46 = 2.17%, not 2%. For two cards it is within half a point up to about eight outs and increasingly too high after that, because simply doubling counts the boards where you hit on both the turn and the river twice. At 15 outs the rule of 4 says 60% when the truth is 54.1%.

The usual correction subtracts one percentage point for each out above eight: 4 × outs − (outs − 8). That brings 15 outs to 53%, within about a point of the truth across the range where it matters. The table below shows all three side by side so you can see the error for yourself.

Worked example

You hold A♥ 5♥ on a K♥ 9♥ 2♣ flop: nine flush outs. The exact chance of a heart on the turn is 9/47 = 19.1%. If you miss the turn, the river is 9/46 = 19.6%. Seeing both cards for free, the chance of at least one heart is 1 − (38 × 37)/(47 × 46) = 1 − 1406/2162 = 35.0%. The rule of 4 says 36% and the rule of 2 says 18%, both close. Facing a bet on the flop, compare 19.1% with the equity the pot odds calculator says the call needs, not 35%, unless the bettor is all-in.

Outs table, 1 to 20

Exact probabilities compared with the shortcuts. "Turn card" is from the flop with 47 unseen; "river card" is from the turn with 46 unseen.

Outs	Turn card	River card	Flop to river	Odds against	Rule of 4	Corrected
1	2.1%	2.2%	4.3%	22.5 : 1	4%	4%
2	4.3%	4.3%	8.4%	10.9 : 1	8%	8%
3	6.4%	6.5%	12.5%	7.0 : 1	12%	12%
4	8.5%	8.7%	16.5%	5.1 : 1	16%	16%
5	10.6%	10.9%	20.4%	3.9 : 1	20%	20%
6	12.8%	13.0%	24.1%	3.1 : 1	24%	24%
7	14.9%	15.2%	27.8%	2.6 : 1	28%	28%
8	17.0%	17.4%	31.5%	2.2 : 1	32%	32%
9	19.1%	19.6%	35.0%	1.9 : 1	36%	35%
10	21.3%	21.7%	38.4%	1.6 : 1	40%	38%
11	23.4%	23.9%	41.7%	1.4 : 1	44%	41%
12	25.5%	26.1%	45.0%	1.2 : 1	48%	44%
13	27.7%	28.3%	48.1%	1.1 : 1	52%	47%
14	29.8%	30.4%	51.2%	1 : 1.0 (odds on)	56%	50%
15	31.9%	32.6%	54.1%	1 : 1.2 (odds on)	60%	53%
16	34.0%	34.8%	57.0%	1 : 1.3 (odds on)	64%	56%
17	36.2%	37.0%	59.8%	1 : 1.5 (odds on)	68%	59%
18	38.3%	39.1%	62.4%	1 : 1.7 (odds on)	72%	62%
19	40.4%	41.3%	65.0%	1 : 1.9 (odds on)	76%	65%
20	42.6%	43.5%	67.5%	1 : 2.1 (odds on)	80%	68%

Common draws and their outs

Clean outs for typical flop situations, before any discounting.

Draw	Example	Outs	Next card	By river
Flush draw plus open-ended straight draw	9♥ 8♥ on 7♥ 6♣ 2♥	15	31.9%	54.1%
Flush draw plus gutshot	9♥ 8♥ on J♥ 7♣ 2♥	12	25.5%	45.0%
Flush draw	A♥ 5♥ on K♥ 9♥ 2♣	9	19.1%	35.0%
Open-ended straight draw	9♠ 8♦ on 7♣ 6♥ 2♠	8	17.0%	31.5%
Double gutshot	9♠ 7♦ on J♣ 8♥ 5♠	8	17.0%	31.5%
Set to a full house or quads	5♣ 5♦ on 5♥ K♠ 9♣	7	14.9%	27.8%
Two overcards to the board	A♣ K♦ on 9♥ 6♠ 2♣	6	12.8%	24.1%
Gutshot (inside straight draw)	9♠ 8♦ on J♣ 7♥ 2♠	4	8.5%	16.5%
Pocket pair to a set	6♣ 6♦ on K♥ 9♠ 3♣	2	4.3%	8.4%

Where outs counting stops being reliable

Outs assume you know which cards win and that nothing else matters. Both are approximations. An out can be dead if an opponent holds a better draw to the same card, and hands you did not count can win, such as runner-runner draws: two consecutive cards that together make a straight or flush, worth roughly one to one and a half extra outs. Outs also ignore that your opponent may improve when you do.

When you know the exact cards involved, the equity calculator enumerates every turn and river and settles the question precisely. This page is for the quick estimate at the table and for learning why the shortcut works.

Common questions

What are the odds of hitting a flush draw?

With nine outs on the flop, 19.1% on the turn alone, 19.6% on the river alone once the turn has missed, and 35.0% by the river if you see both cards. As odds against, that is about 4.2 to 1 on the next card and 1.9 to 1 over two cards.

What is the rule of 2 and 4?

A mental shortcut: multiply your outs by 4 on the flop to estimate your chance of hitting by the river, or by 2 for a single card. It works because each unseen card is roughly 2% of the deck (1/47 is 2.13%). It is close for small numbers of outs and increasingly too high above about eight, because it ignores the chance of hitting on both cards.

Why does the calculator use 47 and 46 unseen cards when other players hold cards too?

Because you cannot see their cards, they are no more likely to be your outs than any other unseen card. From your seat, all 47 cards you have not seen after the flop are equally likely to come next. Opponents' hands only change the answer if you know, or can reasonably guess, what they hold.

Should I use the chance by the river or the chance on the next card?

Use the next-card figure when you face a bet now and could face another on the turn. The two-card figure assumes you will see the river without paying any more, which is only true when someone is all-in. Using the by-river number to justify a flop call against an opponent who will bet again is the most common mistake with outs.

What are discounted outs?

Outs that improve your hand but may not win. A heart that completes your flush while pairing the board could give an opponent a full house, and an ace that pairs your ace may also give a player holding ace-king a better pair. Experienced players count those as half an out or less. The calculator takes whatever number you give it, so enter the discounted count if you have one.