In a standard 5-card poker hand for 1 deck:
Calculate P(Full House)
Full House 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 full houses = Possible ways to get 3 of a kind and a pair in one hand.
Possible 3 of a kind portion for full houses = 13 cards * 4 ways to choose 3 of a kind = 52 ways
Possible 1 pair portion for full houses = 12 possible choices <> 3 of a kind * 6 possible pairs = 72 ways
Total Possible full house combos (3 of a kind & 1 pair) = 52 * 72 = 3,744 ways
| Probability of a full house = | Possible full houses |
| Total Hands |
Reduce top and bottom by 624
GCF = Greatest Common Factor
| P(Full House) = | 3,744 |
| 2,598,960 |
GCF for 6 and 4165 = 624
| P(Full House) = | 6 |
| 4,165 |
Final Answer
Decimal probability = 0.0014405762
What is the Answer?
Decimal probability = 0.0014405762
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 = 2,598,960For 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
