Probability of 3 of a kind
In a standard 5-card poker hand for 1 deck:
Calculate P(3 of a kind)
3 of a kind 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 3 of a kinds = 13 cards to choose * 4 ways to draw that card = 52
Possible 3 of a kinds = 52 ways to draw the 3 of a kind * 48 4th cards = 2,496
Possible 3 of a kinds = 2,496 * 44 5th cards not matching the 4th card = 109,824
Possible 3 of a kinds = 109,824 possibilities/2 ways to draw cards 4 & 5
Possible 3 of a kinds = 109,824/2
Possible 3 of a kinds = 54912
| Probability of a 3 of a kind = | Possible 3 of a kind hands |
| Total Hands |
Reduce top and bottom by 624
GCF = Greatest Common Factor
| P(3 of a kind) = | 54,912 |
| 2,598,960 |
GCF for 88 and 4165 = 624
| P(3 of a kind) = | 88 |
| 4,165 |
Final Answer
Decimal probability = 0.0211284514
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What is the Answer?
Decimal probability = 0.0211284514
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 handcombinationa mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matternPr = n!/r!(n - r)!factorialThe product of an integer and all the integers below itprobabilitythe 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
Example calculations for the 5 Card Poker Hand Calculator
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