Overview
Use the tabs below to switch between the 5-card hand probability table, outs hit rates, and Hold'em distributions. Results update with shareable URLs and CSV exports so you can reuse examples in study notes or lessons.
Start with the hand odds table, then jump to outs, Hold'em hand distributions, or equity simulation versus random opponents.
| Hand | Count | Probability | 1 in N |
|---|
Based on 5-card hands from a 52-card deck (no jokers).
Use this first tab for unconditional 5-card hand frequencies. Switch to Outs when you are counting draw cards, or to Equity when opponents matter.
Result meaning: these are unconditional odds across all possible 5-card hands.
Hit probability
Result meaning: this is the probability of hitting at least once within the remaining cards.
Cards
- Select 2 hole cards and up to 5 board cards.
- Choose exact or simulation mode (auto is recommended).
- Read the distribution and copy a shareable link.
All calculations run locally in your browser.
Distribution
Result meaning: this distribution ignores opponents and shows only your final hand categories.
Simulation settings
- Set opponent count and trials.
- Run the simulation (seed optional).
- Read win/tie/lose estimates.
Opponents are modeled as fully random hands.
Results
Result meaning: equity is an estimate against random opponents, not a range-vs-range analysis. Effective win rate is win rate plus half of tie rate.
Examples
- Flush draw (9 outs) from the flop: hit by the river is about 34.97%.
- Open-ended straight draw (8 outs) from the flop: about 31.45% by the river.
- Pocket pair hitting a set on the flop: about 11.76%.
Interpretation & quick tips
Outs: exact hit probability
If there are outs cards that help you, and you have k cards to come, the “hit at least once” probability is:
P(hit) = 1 − C(remaining − outs, k) / C(remaining, k)
In Hold’em from the flop, remaining = 47 and k = 2 (turn + river).
Pot odds (break-even threshold)
If the pot is P and you must call C to continue, the break-even win probability (ignoring future betting) is C / (P + C). This is just a math threshold, not a strategy recommendation.
Common pitfalls
- Double-counting outs: some cards complete multiple draws; the “outs” count should be the number of distinct helpful cards.
- Dirty outs: an out that improves you may also improve an opponent (e.g., pairing the board).
- Equity mode: this tool simulates against random opponents, so results can differ from range-vs-range equity.
References
How to use poker odds results
Use the tabs for different questions: exact 5-card hand frequencies, outs hit rates, Hold'em hand distributions, and equity simulation versus random opponents.
Exact odds vs simulation
Hand tables and outs use combinatorics when the card states are simple enough to enumerate exactly. Equity against random opponents uses simulation for heavier scenarios, so increase trials for close spots and keep the seed fixed when you need a reproducible comparison.
Reading outs and equity
Outs are distinct unseen cards that improve to the selected target. Equity is win plus a share of ties against random hands; it is not a range-vs-range solver or strategy recommendation.
Common mistakes to avoid
- Counting dirty outs that also improve an opponent.
- Comparing unseeded simulations as if the random stream were identical.
- Treating pot odds or equity thresholds as betting advice without stack, position, and range context.
- Mixing exact 5-card hand odds with Hold'em board-runout equity without checking the known cards.
See also
FAQ
What are the odds of each poker hand?
The table lists exact 5-card hand counts and probabilities from a 52-card deck, plus the reciprocal frequency (1 in N).
What is the hit rate for a 9-out flush draw?
From the flop (known=5), the exact chance to hit by the river is 1 - C(38,2)/C(47,2) ≈ 34.97%.
How are hand distributions different from equity?
Distributions ignore opponents and show only your final hand category. Equity simulates win/tie/lose odds against random opponents.
Why use a simulation seed?
A seed keeps the random stream fixed so results are reproducible across runs and shared URLs.
How many simulation trials should I run?
Use a small trial count for quick exploration, then increase trials when comparing close equity spots. Keep the same seed when you want two runs to be reproducible.
Related
- nCr/nPr calculator Use combinations for card probabilities.
- Hypergeometric calculator Model outs and draw probabilities.
- Birthday paradox Another classic probability tool.
How it's calculated
- 5-card hand odds use exact counts from C(52,5) = 2,598,960.
- Outs hit rate uses the complement: 1 - C(U-outs, toCome) / C(U, toCome).
- Hold'em distributions enumerate remaining boards when fast, or simulate with a seeded PRNG.