Calculate the probability of a Royal Flush: First calculate the total number of possible hands in a 52 card deck: From a deck of 52 cards, we want the number of possible unique ways we can
choose 5 cards.
Using the combinations formula 52 choose 5 shown
here, we get:
Total Possible 5 Card Hands = | 52! |
| (52-5)! * 5! |
Total Possible 5 Card Hands = | 52! |
| 47! * 5! |
Total Possible 5 Card Hands = | (52 * 51 * 50 * 49 * 48) * 47! |
| 47! * (5 * 4 * 3 * 2 * 1) |
Cancelling the 47! on top and bottom we get:
Total Possible 5 Card Hands = | 311,875,200 |
| 120 |
Total Possible 5 Card Hands = 2,598,960
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
Probability(Royal Flush) = | Possible Royal Flushes |
| Total Possible 5 Card Hands |
Probability(Royal Flush) = | 4 |
| 2,598,960 |
Using our
GCF Calculator, we see that 4 and 2598960 can be reduced by 4
Reducing top and bottom by 4, we get:Probability(Royal Flush) = | 1 |
| 649,740 |
In decimal format, this probability is equal to approximately 1.5391E-6
What is the Answer?
In decimal format, this probability is equal to approximately 1.5391E-6
How does the 5 Card Poker Hand Calculator work?
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
What are some example calculations for the 5 Card Poker Hand Calculator?
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