Texas Hold'em: Probability of Full House

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around calculating the probability of obtaining a full house in Texas Hold'em poker, specifically when both hole cards must be used in forming the full house. The scope includes mathematical reasoning and probability calculations related to poker hands.

Discussion Character

  • Mathematical reasoning, Debate/contested

Main Points Raised

  • One participant seeks clarification on the probability of achieving a full house when both hole cards must contribute to the hand.
  • Another participant suggests consulting Wikipedia for probability information related to poker.
  • A participant expresses skepticism about relying on Wikipedia and emphasizes the need for a specific calculation method when both hole cards are involved.
  • One participant outlines the combinations of hole cards (specifically A and K) and calculates the probability of having a qualifying starting hand, but expresses confusion about the subsequent calculations for the community cards.
  • The same participant questions whether the calculation for the board cards should involve multiplying the probabilities of drawing specific cards from the remaining deck.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the correct method for calculating the probability, and there is ongoing confusion regarding the calculations involved.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the starting hands and the specific calculations for the community cards, which remain unresolved.

c1gipe
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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
 
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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
 
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?
 

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