Two Four of a Kind in a Row
February 18th, 2010 at 9:53:56 AM
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What is the probability of getting 4 of a kind twice in a row. 8 handed. With being dealt pocket cards both times.
February 18th, 2010 at 1:18:01 PM
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Quote: mobeusWhat is the probability of getting 4 of a kind twice in a row. 8 handed. With being dealt pocket cards both times.
Getting dealt a pair and then having that same pair on the board to get quads is:
p = (1/17)*combin(48,3)/combin(50,5) = 0.000480192076830732, or about 1 in 2082.
Having it happen twice in a row is p^2 = 0.000000230584430651, or about 1 in 4336806.
Lunch break, hope I did that right.
Someone else can do the math for 8 players ...
I saw my first natural royal flush ever playing NL last week (player had AK spades, board came down QJT spades, in order -- too bad no one had the 98 spades).
--Dorothy
"Who would have thought a good little girl like you could destroy my beautiful wickedness!"
February 18th, 2010 at 1:57:12 PM
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I assume you're talking about Hold 'Em.
The number of players is irrelevant.
The cards needed could have been in the other player's hands, or they could have been further in the deck. Or they could have hit the board as they did in your case.
The important thing to calculate is the odds that you are holding a pair, and the odds that, out of the 50 cards you haven't seen, the cards you need hit the board.
I.E. Let's say you go heads-up all-in pre-flop. You have pocket tens, and the other guy has pocket jacks. You're behind. The chance of a ten hitting is 2 / 48. 48 is the number of cards you haven't seen. Even if another player had a ten, those odds do not change unless the other player tells you he folded that ten.
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It reminds me of the time I had K2 suited, on the button. EVERYONE limped in, so I limped too. The flop was 222. People were betting and raising before it got to me.
After the hand was over, I said: "What were you thinking? That nobody would hold a 2? But ALL TEN PLAYERS held their cards. That's 18 cards out of the 47 you haven't seen. Any of them could have been a deuce. Sure, less than 50%, but not much less. Thanks for building the pot for me."
The number of players is irrelevant.
The cards needed could have been in the other player's hands, or they could have been further in the deck. Or they could have hit the board as they did in your case.
The important thing to calculate is the odds that you are holding a pair, and the odds that, out of the 50 cards you haven't seen, the cards you need hit the board.
I.E. Let's say you go heads-up all-in pre-flop. You have pocket tens, and the other guy has pocket jacks. You're behind. The chance of a ten hitting is 2 / 48. 48 is the number of cards you haven't seen. Even if another player had a ten, those odds do not change unless the other player tells you he folded that ten.
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It reminds me of the time I had K2 suited, on the button. EVERYONE limped in, so I limped too. The flop was 222. People were betting and raising before it got to me.
After the hand was over, I said: "What were you thinking? That nobody would hold a 2? But ALL TEN PLAYERS held their cards. That's 18 cards out of the 47 you haven't seen. Any of them could have been a deuce. Sure, less than 50%, but not much less. Thanks for building the pot for me."
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
