Hello Everyone,
No rush on answering my question - I am just hoping that some mathematical genius might be able to figure this out very easily, since it's been a while since I studied Probability. If any math whizzes happen to be poker players, this is a player's worst nightmare. I having difficulty determining what is relevant and what is not.
I am a poker player, and last night I lost with Quad Jacks against Quad Kings (Quads are 4 of a Kind, ie. KKKK) in the game of Texas Hold Em. The basics of the game are that each player is dealt 2 cards Face Down (out of a standard deck of 52 cards) - the 2 Face down cards are obviously your only known cards until the community board cards are put up after each round of betting (Flop - 1st 3 cards, Turn/4th street - 4th card, and River/5th street - 5th card) to make the best 5 card poker hand.
Here's what happened and what I know (at least I think my line of math thinking is correct):
So in a 10 Handed game, I was dealt JJ - the probability of being dealt any pocket pair (2 cards that are dealt face down) is 3/51 - since the first card does not matter 1 in 17 or about 5.88% of the time. The odds of being dealt specifically any given pocket pair - in our case Pocket Jacks is 4/52 x 3/51 or 0.452% or ~220 to 1 odds. I figured the probability that someone has a higher Pocket pair - either 2 Queens, 2 Kings, or 2 Aces is 12/50 x 3/49 or 1.47% or ~68 to 1
So basically, I have pocket Jacks - my opponent has pocket Kings
The flop (or first 3 cards come) Jack, Jack, King
If 4 out of 52 cards are known, the probability that I flop 4 of a kind is what? Essentially, each card is a separate "Draw" - the First draw is 2/48 - if I hit a Jack on the first draw, the 2nd draw is 1/47 if not, it's 2/47 - the 3rd draw would also be determined upon the first and 2nd draws since we are taking away a card without replacement.
I am interested in knowing what the odds or probability of this event occurring is. I understand that after the flop I am a 96% favorite to win the hand.
Basically what are the odds that I would lose with 4 of a kind Jacks to a higher 4 of a kind - given the fact that I have flopped Quads, and 2 draws remain. My opponent needs to hold exactly QQ, KK, or AA and hit exactly the 2 remaining cards in essentially 3 draws.
Thanks for any help you guys can offer!
-RvrKrd
No rush on answering my question - I am just hoping that some mathematical genius might be able to figure this out very easily, since it's been a while since I studied Probability. If any math whizzes happen to be poker players, this is a player's worst nightmare. I having difficulty determining what is relevant and what is not.
I am a poker player, and last night I lost with Quad Jacks against Quad Kings (Quads are 4 of a Kind, ie. KKKK) in the game of Texas Hold Em. The basics of the game are that each player is dealt 2 cards Face Down (out of a standard deck of 52 cards) - the 2 Face down cards are obviously your only known cards until the community board cards are put up after each round of betting (Flop - 1st 3 cards, Turn/4th street - 4th card, and River/5th street - 5th card) to make the best 5 card poker hand.
Here's what happened and what I know (at least I think my line of math thinking is correct):
So in a 10 Handed game, I was dealt JJ - the probability of being dealt any pocket pair (2 cards that are dealt face down) is 3/51 - since the first card does not matter 1 in 17 or about 5.88% of the time. The odds of being dealt specifically any given pocket pair - in our case Pocket Jacks is 4/52 x 3/51 or 0.452% or ~220 to 1 odds. I figured the probability that someone has a higher Pocket pair - either 2 Queens, 2 Kings, or 2 Aces is 12/50 x 3/49 or 1.47% or ~68 to 1
So basically, I have pocket Jacks - my opponent has pocket Kings
The flop (or first 3 cards come) Jack, Jack, King
If 4 out of 52 cards are known, the probability that I flop 4 of a kind is what? Essentially, each card is a separate "Draw" - the First draw is 2/48 - if I hit a Jack on the first draw, the 2nd draw is 1/47 if not, it's 2/47 - the 3rd draw would also be determined upon the first and 2nd draws since we are taking away a card without replacement.
I am interested in knowing what the odds or probability of this event occurring is. I understand that after the flop I am a 96% favorite to win the hand.
Basically what are the odds that I would lose with 4 of a kind Jacks to a higher 4 of a kind - given the fact that I have flopped Quads, and 2 draws remain. My opponent needs to hold exactly QQ, KK, or AA and hit exactly the 2 remaining cards in essentially 3 draws.
Thanks for any help you guys can offer!
-RvrKrd