In a standard 5-card poker hand for 1 deck:
Calculate P(Choose Your Hand)
Choose Your Hand Hands
Calculate the probability of drawing a AKKQJ
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
Calculate the probabilty of each card
Calculate the probability of drawing Ace
There are 4 A cards in the deck
There are 52 total cards in the deck
| Probability of drawing A = | 4 |
| 52 |
Calculate the probabilty of each card
Calculate the probability of drawing King
There are 4 K cards in the deck
There are 51 total cards in the deck
| Probability of drawing K = | 4 |
| 51 |
Calculate the probabilty of each card
Calculate the probability of drawing King
There are 3 K cards in the deck
There are 50 total cards in the deck
| Probability of drawing K = | 3 |
| 50 |
Calculate the probabilty of each card
Calculate the probability of drawing Queen
There are 4 Q cards in the deck
There are 49 total cards in the deck
| Probability of drawing Q = | 4 |
| 49 |
Calculate the probabilty of each card
Calculate the probability of drawing Jack
There are 4 J cards in the deck
There are 48 total cards in the deck
| Probability of drawing J = | 4 |
| 48 |
Calculate final probability:
Since each card draw is independent
Multiply each of our 5 card draws
| P(AKKQJ) = | 4 x 4 x 3 x 4 x 4 |
| 52 x 51 x 50 x 49 x 48 |
| P(AKKQJ) = | 768 |
| 311875200 |
Reduce top and bottom by 384
GCF = Greatest Common Factor
| P(Choose Your Hand) = | 768 |
| 311,875,200 |
GCF for 2 and 812175 = 384
| P(Choose Your Hand) = | 2 |
| 812,175 |
Final Answer
What is the Answer?
How does the 5 Card Poker Hand Calculator work?
This calculator has 1 input.
What 1 formula is used for the 5 Card Poker Hand Calculator?
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
