In: Other
If someone playing Poker against you had a Full House, what are the odds you could win against them? (We’ll assume that their cards are ‘still in the deck’ when it comes to calculating your own odds)
a Full house is when someone has 3 cards of the same rank.
There are 13 distinct ranks:
A,2,3,4,5,6,7,8,9,10,J,Q,K
In Poker, 4 of a Kind, Straight flush and a Royal flush beats a Full House
4 of a kind means,
the player has 4 cards of identical rank.
Probability to get 4 cards of the same rank from a deck of 52 cards:
=
=
= 3.69 x 10-6
There are 13 ranks so the total probability would be the some of the 13 individual ranks:
13 x 3.69 x 10-6= 4.8 x 10-5
Straight flush is to obtain 5 cards , the player has to get 5 cards in a continuous order and all 5 cards have to be the same rank.
Possible combinations are:
(1,2,3,4,5) , ( 2,3,4,5,6) , (3,4,5,6,7) , ( 4,5,6,7,8) , ( 5,6,7,8,9) ,(6,7,8,9,10), (7,8,9,10,J) , ( 8,9,10,J,Q) , ( 9,10,J,Q,K)
The combination of ( 10,J,Q,K,A) is called a royal flush and is the highest card order in the game.
the probability to get ( 1,2,3,4,5):
= 1/ 25,98,960
This is for 1 suite,
there are 4 suites
Spades,Clubs, Diamonds and Hearts.
Therefore, there are 4 ways it can occur,
Total Probability= 1 / 649740 = 1.53 x 10-6
Therefore, the total probability to beat full house: 1.53 x 10-6 + 4.8 x 10-5 = 4.953 x 10-5 or 4.953 / 100000
approximately, 5 /100000 = 1 / 20000 or 1 in 20,000
Therefore, the probability to beat a full house is 1 in 20,000