Poker Probability Methodology
Our probability references use exact card-count arithmetic where the deck state is simple enough to model directly. We show the denominator, assumptions and situations where “outs” can mislead.
The calculations on this page are derived from a standard 52-card deck. They are not estimates from simulation.
Unknown-card counts in Hold’em
After the flop, you know your two hole cards plus three board cards, leaving 47 unseen cards. After the turn, six cards are known, leaving 46 unseen cards.
One card to come
With nine clean outs after the turn: 9 ÷ 46 ≈ 19.57%.
From flop to river
For nine clean outs on the flop: 1 − (38/47 × 37/46) ≈ 34.97%.
What makes an out “clean”?
An out is only clean if hitting it produces the outcome you are modeling without simultaneously creating a material chance that the opponent improves to a stronger hand. Counterfeit outs, dominated draws, paired-board complications and unknown opponent ranges can make raw out counts optimistic.
What this method does not calculate
- Equity against an opponent’s range.
- Backdoor combinations unless explicitly modeled.
- Future betting or implied odds.
- Tournament money value or ICM.
Verification resources
Use the Poker Outs Probability Calculator for individual calculations or the reference table for 1–15 outs.
Last updated: August 26, 2026 · Publisher: Double Up Poker