Calculator Inputs
Plotly Probability Graph
The chart changes with your selected mode and graph settings.
Example Data Table
| Scenario | Hand Type | Exact Probability | Expected Occurrences per 1,000 Hands |
|---|---|---|---|
| 5-card deal | One Pair | 0.42256903 (42.256903%) | 422.5690 |
| 5-card deal | Straight | 0.00392465 (0.392465%) | 3.9246 |
| 7-card best hand | Full House | 0.02596102 (2.596102%) | 25.9610 |
| 7-card best hand | Royal Flush | 0.00003232 (0.003232%) | 0.0323 |
Formula Used
1) Exact probability
Probability = Favorable combinations ÷ Total combinations
2) Total hands
Total hands = C(52, n), where n is 5 or 7.
3) Session expectation
Expected count = Number of observed hands × Probability
4) At least one target hand
P(at least one) = 1 − (1 − p)N, where p is hand probability and N is observed hands.
5) Odds against
Odds against = (1 − p) ÷ p
Exact 5-card counting examples
In 7-card mode, the calculator uses exact best-hand frequency totals for final 7-card evaluations rather than simple 5-card formulas.
How to Use This Calculator
- Select 5-Card Deal for classic 5-card probabilities or 7-Card Best Hand for best-hand evaluation from seven cards.
- Choose the target category, such as one pair, straight, or royal flush.
- Enter the number of hands you want to study. This drives expected count and at-least-one calculations.
- Set decimal places to control display precision.
- Pick a graph mode. Distribution shows all categories. Comparison shows your chosen category in both 5-card and 7-card models.
- Click Calculate Probability to display results above the form.
- Use Download CSV to save the summary and table. Use Download PDF to export a printable report.
Frequently Asked Questions
1) What is the difference between 5-card and 7-card mode?
5-card mode analyzes one dealt 5-card hand. 7-card mode evaluates seven cards and classifies the strongest possible 5-card poker hand from them.
2) Is a royal flush counted separately?
Yes. Royal flush is separated from straight flush. That keeps the categories mutually exclusive and makes the table easier to interpret.
3) Why is one pair so common?
There are many rank and kicker combinations that create exactly one pair. Rare hands need much tighter structure, so their counts stay very small.
4) What does “1 in hands” mean?
It converts probability into an intuitive frequency. For example, 1 in 693 means you would expect that result about once every 693 equally likely hands.
5) What does “at least one in session” show?
It estimates the chance of seeing your selected hand at least once over the number of hands you entered, using repeated independent-hand probability.
6) Are these probabilities exact or simulated?
They are exact combinatorial probabilities based on full counting results. No Monte Carlo sampling is required for the displayed values.
7) Can I use this for Texas Hold’em reasoning?
Yes for final 7-card best-hand odds. It does not model partial streets, blockers, or opponent ranges. It focuses on final category frequencies.
8) Why use logarithmic scale on the chart?
Rare hands can become visually tiny on a linear axis. Log scale reveals both common and rare categories more clearly in one graph.