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Poker Drawing Odds from Outs — result sheet
Calculate the chance of hitting at least one out by the next one or two cards from unseen-card count.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(hit by k cards) = 1 − ∏ᵢ₌₀ᵏ⁻¹(unseen − outs − i)/(unseen − i).
Poker drawing odds are a without-replacement probability problem. The calculator treats the entered outs as clean, mutually exclusive cards and reports the complement of missing all of them over the selected number of cards to come.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Known outs — cards; minimum 0; maximum 52
- Unseen cards — cards; minimum 1; maximum 52
- Cards to come — 2 choices
Worked example
| Input | Value |
|---|---|
| Known outs | 9 |
| Unseen cards | 47 |
| Cards to come | 2 |
Nine outs among 47 unseen cards give about a 34.97% chance to hit by two cards, under the clean-out assumption.
Assumptions and limits
- Every out is equally likely and improves the hand; dirty outs, opponent ranges, redraws, and exact hand-equity enumeration are not modeled.
- Unseen cards already excludes known hole cards, board cards, folded cards, or other cards the player chooses to remove from the sample space.
- This is probability arithmetic for a game decision, not financial advice or a promise of a result.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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