Poker Outs Calculator

Exact poker draw odds from outs, for the turn and both streets.

What it does

Outs turn poker draws into numbers. After the flop you know five cards, your two plus the three on the board, which leaves 47 unseen for the turn and 46 for the river. Count the cards that complete your hand, divide by what remains, and the call or fold decision gets a price.

The tool above prices any draw. Enter the out count and it prints the exact turn probability, the exact turn-or-river probability, and the 2/4 rule pair beside them. The default flush draw at 9 outs lands 19.1 % on the turn and 35.0 % across both streets, against rule estimates of 18 and 36.

Courses frame the same counting. MIT OpenCourseWare poker and probability courses walk through combinatorial hand analysis and the count of target outcomes over equally likely totals, while the University of Alberta poker research group studies the game at a university level. The American Mathematical Society publishes probability essays in the same spirit.

Rules of thumb need the exact beside them. The 2x turn estimate stays close, but the 4x two street estimate runs high past about 12 outs: 60 % against 54.1 % at 15 outs. Tainted outs need discounting too, since paired boards and better redraws steal part of the deck.

How to use

Count your clean outs after the flop.
Enter the out count.
Read the exact turn line first.
Read the turn-or-river line for the full decision.
Check the 2/4 rule pair beside the exact pair.
Discount tainted outs and recount before calling.

Formula

Turn % = outs / 47 x 100. Turn-or-river % = (1 minus (47 minus outs)(46 minus outs) / 2162) x 100. Rules: outs x 2, outs x 4.

outs: Cards that complete the hand, 1 to 21.
47: Unseen cards on the turn: 52 minus 5 known.
46: Unseen cards on the river after the turn.
2162: 47 x 46, the two street denominator.

A 52 card deck with your 2 hole cards and 3 flop cards known leaves 47 unseen for the turn and 46 for the river, so 47 x 46 = 2162. Outs range is 1 to 21.

Worked example

Example: 9 outs on the flop

Defaults: 9 outs (a flush draw) with turn and river to come.

Inputs: 9 outs with a flush draw after the flop.
Turn: 9 / 47 = 19.1 %.
Miss both: 38 x 37 / 2162 = 0.6503.
Turn or river: 1 minus 0.6503 = 35.0 %.
Rule check: 9 x 2 = 18 vs 19.1; 9 x 4 = 36 vs 35.0. Tool shows 19.1 %, 35.0 %, the 2/4 pair.

Reference table

Exact draw odds
Outs	Turn	Turn or river
1	2.1 %	4.3 %
2	4.3 %	8.4 %
4 gutshot	8.5 %	16.5 %
8 open-ender	17.0 %	31.5 %
9 flush	19.1 %	35.0 %
12	25.5 %	45.0 %
15 combo	31.9 %	54.1 %
20	42.6 %	67.5 %

Limits

Clean outs assumed. Tainted and redrawn outs need discounting.
Flop decisions only. Turn play uses 46 card math.
Ignores pot odds, position, and opponent ranges.
Exact cards unknown assumes a full unseen deck.

Common mistakes

Counting tainted outs at full value.
Using the 4x rule at high out counts.
Forgetting the deck shrinks from 47 to 46 on the river.
Mixing turn-only odds into two street calls.
Counting outs twice across overlapping draws.

Try it yourself

Quick checks. Answers sit tucked under each question.

4 outs (gutshot)?

Turn 4 / 47 = 8.5 %. Miss 43 x 42 / 2162 = 0.8353, so both streets 16.5 %.

15 outs (straight plus flush)?

Turn 15 / 47 = 31.9 %. Miss 32 x 31 / 2162 = 0.4588, so both streets 54.1 %.

Questions

What are outs?

Unseen cards that complete your hand. A flush draw has 9, an open ended straight has 8, a gutshot has 4.

How is turn probability figured?

Outs divided by 47 unseen cards. With 9 outs that is 19.1 %.

How is turn-or-river figured?

One minus the chance of missing both streets: 1 minus (47 minus outs)(46 minus outs) / 2162. With 9 outs that is 35.0 %.

What is the 2/4 rule?

Multiply outs by 2 for the turn and by 4 for both streets. With 9 outs: about 18 % and 36 %, near the exact 19.1 and 35.0.

When does the rule overstate?

It runs high past about 12 outs. With 15 outs it says 60 % against an exact 54.1 %, so trust the exact line there.

Do all outs count full value?

No. Outs assume clean cards; paired boards and better draws redraw against you, so discount tainted outs first.

Sources

How this page was checked. The formula above was matched against the cited sources, and the worked example was run through the tool on this page before publishing. If you spot an error, contact us so we can fix it and note the correction.