Texas Hold'em: Probability of Full House

[c1gipe]

i have looked all over the internet and found a ton of different answers to this question so i will try and ask it here:

in texas holdem
what is the probability of getting a full house after all 5 cards are delt
both of the cards delt to you have to make up the full house

 

[RustyZ32]

Try wiki next time

http://en.wikipedia.org/wiki/Poker_probability
http://en.wikipedia.org/wiki/Poker_probability_%28Texas_hold_%27em%29

 

[c1gipe]

ya i found that but I've always been told not to trust wiki. (i do anyway) But my question was how to figure it out if both your hole cards have to play. so you can't play the 5 cards on the board. you can only play 3 of them. this seems really easy but I am getting confused just as easy

 

[c1gipe]

sorry, I've realized that I've been lazy and haven't contributed

there are 16 combinations of having A and K
6 ways to have AA
6 ways to have KK

these are the only possible starting hands so there are 28/52 cards to pick from the first card and 27/51 possible for the second card.

so the probability of having a qualifying starting hand is 28/52 x 27/51 = 63/221

for the extra 5 cards on the board there are 26 possibilities with 50 cards remaining.
this is where i get lost
do i just 26/50 x 25/49 x 24/48?

then that number is the probability?

 

[blue_raver22]

I understand the importance of accurate and reliable information. In order to calculate the probability of a full house in Texas Hold'em, we must first understand the basic principles of probability and the rules of the game.

In Texas Hold'em, each player is dealt two cards, known as the hole cards, and five community cards are dealt face up on the table. A full house is a poker hand consisting of three cards of the same rank and two cards of another rank. This means that in order to get a full house, you must have a pair and a three of a kind.

The probability of getting a full house after all five cards are dealt depends on several factors, including the number of players at the table and the number of decks being used. However, in a standard game with a single deck of 52 cards, the probability of getting a full house is approximately 0.1441%, or 1 in 693.

To calculate this probability, we can use the combination formula: nCr = n! / (r! * (n-r)!), where n is the total number of possible outcomes and r is the number of desired outcomes.

In this case, there are 52 cards in a deck and we need to choose 5 cards for our hand. This means that n = 52 and r = 5. Plugging these values into the formula, we get:

52C5 = 52! / (5! * (52-5)!) = 52! / (5! * 47!) = 2,598,960 / (120 * 1) = 2,598,960

This means that there are 2,598,960 possible combinations of 5 cards that can be dealt from a single deck. Out of these combinations, there are 3,744 possible ways to get a full house (13 possible ranks for the three of a kind and 12 possible ranks for the pair).

Therefore, the probability of getting a full house is 3,744 / 2,598,960 = 0.1441%, or approximately 1 in 693.

It is important to keep in mind that this calculation is based on a single deck and does not take into account the possibility of multiple players having full houses. Additionally, the probability may vary in different variations of Texas Hold'em, such as Omaha or 5-card draw.

In conclusion, the probability of getting a full house