Card Hand Probability
C(52, 5) = 2,598,960 hands. Free online Card Hand Probability. Calculate card hand probability online — fast, accurate, mobile-friendly, no signup needed.
Derivation
- ├── 01Given
hand = flush - ├── 02Formula
{royal:4,straight_flush:36,four:624,full:3744,flush:5108,straight:10200}[e.hand] / 2598960 × 100 - ├── 03Substitute
{royal:4,straight_flush:36,four:624,full:3744,flush:5108,straight:10200}[e.'flush'] / 2598960 × 100 - └── 04Compute Probability0.19654
Probability theory traces to the Pascal–Fermat letters (1654) about a gambling dispute over how to fairly split a prize if a game is interrupted.
Understanding the Card Hand Probability
The Card Hand Probability computes Probability from 1 input: hand. C(52, 5) = 2,598,960 hands.
Games and puzzles mix math with pattern-spotting. Whether it’s a lottery combination, a dice probability, or a game-theory decision, the numbers behind the fun are worth running properly. The Card Hand Probability sits in that toolkit — it C(52, 5) = 2,598,960 hands. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.
How it’s calculated
Where
- hand
- Hand — one of: Royal flush, Straight flush, Four of a kind, Full house, Flush, Straight
Step-by-step walkthrough
Apply the formula to a realistic set of inputs: Hand = flush.
- 01Start by noting the input — Hand: flush (a category, not a number).
- 02Substitute these values into the formula: {royal:4,straight_flush:36,four:624,full:3744,flush:5108,straight:10200}[e.hand] / 2598960 × 100
- 03Compute Probability: the calculator returns 0.19654.
- 04Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
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