In a standard 5-card poker hand for 1 deck:
Calculate P(Royal Flush)
Royal Flush Hands
Calculate Total 5 Card hands
| Total Hands = | 52! |
| (52-5)! * 5! |
| Total Hands = | 52! |
| 47! * 5! |
| Total Hands = | (52 * 51 * 50 * 49 * 48) * 47! |
| 47! * (5 * 4 * 3 * 2 * 1) |
Cancelling the 47!, we get:
| Total Hands = | 311,875,200 |
| 120 |
Total Hands = 2,598,960
Build Probability
Possible Royal Flushes = Possible ways to get 10,J,Q,K,A all suited
Possible Royal Flushes = 1 way * 4 possible suits (Spade,Heart,Diamond,Club) = 4
| P(Royal Flush) = | Royal Flushes |
| Total Hands |
| P(Royal Flush) = | 4 |
| 649,740 |
Reduce top and bottom by 4
GCF = Greatest Common Factor
| P(Royal Flush) = | 4 |
| 2,598,960 |
| P(Royal Flush) = | 1 |
| 649,740 |
Final Answer
Decimal probability = 1.5391E-6
You have 1 free calculations remaining
What is the Answer?
Decimal probability = 1.5391E-6
How does the 5 Card Poker Hand Calculator work?
Free 5 Card Poker Hand Calculator - Calculates and details probabilities of the 10 different types of poker hands given 1 player and 1 deck of cards.
This calculator has 1 input.
What 1 formula is used for the 5 Card Poker Hand Calculator?
Total Possible 5 Card Hands = 2,598,960
For more math formulas, check out our Formula Dossier
What 4 concepts are covered in the 5 Card Poker Hand Calculator?
- 5 card poker hand
- combination
- a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter
nPr = n!/r!(n - r)! - factorial
- The product of an integer and all the integers below it
- probability
- the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
