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AceHound
AceHound
AceHound
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June 26th, 2012 at 1:02:01 PM permalink
In Texas Hold'em what are the odds in getting four-of-a-kind provided that the player is holding a pocket pair?

1 in ????? hands

Thanks in advance
EdCollins
EdCollins
EdCollins
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June 26th, 2012 at 2:33:29 PM permalink
Assuming you're already holding a pair and stay until the River, I think it's approximately 1 in 123 hands.

Someone else should confirm.

This site says it's 1 in 119 hands: http://www.beatthefish.com/poker-strategy/texas-holdem-odds.html

But until I see the math, I'm going to go with 1 in 123.
JB
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JB
JB
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June 26th, 2012 at 2:36:42 PM permalink
I agree with EdCollins. A pocket pair will become quads once every 122.5 times on average.
jc2286
jc2286
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June 26th, 2012 at 2:38:42 PM permalink
I get 1 in 122.5 hands.

(2/50)*(1/49)*combin(5,2)
jc2286
jc2286
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June 26th, 2012 at 2:43:43 PM permalink
That site says you'll flop 4OAK 1 in 119 hands. I have no idea where that number is coming from.
EdCollins
EdCollins
EdCollins
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June 26th, 2012 at 3:24:07 PM permalink
Ah, you're correct. It does say "flop."

I don't know where that number is coming from either. That's way off. It's not nearly that often. I think you'll flop four of a kind, assuming you start with a pair, closer to once every 409 hands.
rdw4potus
rdw4potus
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June 26th, 2012 at 3:29:18 PM permalink
Quote: jc2286

That site says you'll flop 4OAK 1 in 119 hands. I have no idea where that number is coming from.



I don't think I can do the math, but I'd bet the the 1 in 119 also includes a singleton being hit by a 3OAK flop even though the site explicitly excludes that possibility in the prose.
"So as the clock ticked and the day passed, opportunity met preparation, and luck happened." - Maurice Clarett
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