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Poker Hand Odds Calculator

Work out poker hand odds instantly with clear inputs, formula shown and shareable results.

About Poker Hand Odds Calculator

With two cards to come the exact chance is one minus the product of the two miss probabilities over 47 and 46 unseen cards; the rule of 4 and 2 multiplies outs by four or two as a mental shortcut. The shortcut overstates a nine-out flush draw by about a point and a half, which matters when a pot odds decision is close.

Formulas

Two cards to come

P(hit) = 1 - (47 - outs)/47 x (46 - outs)/46

Rule of 4 and 2

approximate % = outs x 4 with two cards to come, outs x 2 with one

Worked example

With the default values below, Poker Hand Odds Calculator returns Chance of hitting of 34.968%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of outsaccepts 1–47
9
Cards still to comeone of Turn and river (two cards), River only (one card)
Turn and river (two cards)

Results

Chance of hitting
34.968%
Odds against, to one
1.860
Rule of 4 and 2 estimate
36 %
How far the shortcut is out
1.032 %

Step by step

  1. 1Values used
  2. 2Two cards to come
  3. 3Rule of 4 and 2
  4. 4Chance of hitting= 34.968
  5. 5Odds against, to one= 1.860
  6. 6Rule of 4 and 2 estimate= 36 %
  7. 7How far the shortcut is out= 1.032 %

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Poker Hand Odds figure worked out?

P(hit) = 1 - (47 - outs)/47 x (46 - outs)/46. With two cards to come the exact chance is one minus the product of the two miss probabilities over 47 and 46 unseen cards; the rule of 4 and 2 multiplies outs by four or two as a mental shortcut.

Why does this matter?

The shortcut overstates a nine-out flush draw by about a point and a half, which matters when a pot odds decision is close.

What do I need to enter?

Enter number of outs, cards still to come. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.

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