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Someone run some math on a hand for me?

  
 
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euphoricism
Old 12-19-2006, 02:44 AM     Post subject: Someone run some math on a hand for me? #1 (permalink)  
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I suck way too much at math for this, but I just HAVE to know how often we expect this to happen...

Three way to the flop. All three of us have pocket pairs. All three of us flop sets. One guy (the one who flopped top set, so it doesnt really matter) turns quads and so we have quads over boat over boat.

That has to be insanely rare.

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ensign_lee
Old 12-19-2006, 03:09 AM #2 (permalink)  
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thenonsequitur
Old 12-19-2006, 02:21 PM     Post subject: Re: Someone run some math on a hand for me? #3 (permalink)  
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Quote:
Originally Posted by euphoricism
Three way to the flop.
The probability of the whole hand happening like this depends on the number of players being dealt in (more players makes it more likely for there to be pocket pairs out there, and thus the whole probability increases). So I am going to calculate for the game being 5-handed.

Quote:
Originally Posted by euphoricism
All three of us have pocket pairs.
The chance of getting dealt a pocket pair of a specific rank is equal to the chance of being dealt any card of that rank and then another card of that rank: P(pp) = 4/52 * 3/51 = 1/221 (= 220:1).

Lets calculate the probability of three specific people each being dealt a pocket pair, P(tsp).

The first guy has 13 ranks to choose from, so the probability that he gets dealt a pocket pair is 13*P(pp).

The second guy has a different pocket pair, so he has only 12 ranks to choose from, so the probability is 12*P(pp).

The third guy has only 11 ranks to choose from, or 11*P(pp).

So the chance of three different pocket pairs is P(3sp) = 13*12*11*P(pp)^3 = 132/830297 (~ 6289:1).

With 5 people playing though, there are a number of possibly ways to choose 3 specific people. 5 choose 3 = 5!/(3!)(5-3)! = 10 ways.

So the probability that any 3 people out of the 5 each get dealt a different pocket pair is P(3ap) = 10*P(3sp) = 10 * 132/830297 = 1320/830297 (~ 628:1).

Quote:
Originally Posted by euphoricism
All three of us flop sets.
First lets figure out the probability that the first player hit his set on the first card of the flop, second player on the second card, and third player on the third card.

The probability that the first player hit on the first card is 2/46.
Second player's probability is 2/45.
Third player's probability is 2/44.

So the probability that the sets hit in that particular order is P(3ss) = 2^3/44*45*46 = 1/11385 (= 11384:1).

But the sets can happen in any order. With three cards the number of possible orders is 6 (123,132,213,231,312,321). So the probability of 3 sets being flopped (where order doesn't matter) is P(3as) = 6 * P(3ss) = 2/3795 (~ 1897 : 1).

So the probability of 3 people out of 5 each having a pocket pair and each flopping a set is P(3ap)*P(3as) = 1320/830297 * 2/3795 = 16/19096831 (~ 1193551 : 1).

Quote:
Originally Posted by euphoricism
One guy (the one who flopped top set, so it doesnt really matter) turns quads
This is easy. It's the chance that one specific player (the one with top set) hits his last card of rank. This is 1/43.

So the chance of the whole sequence is 16/19096831 * 1/43 = 16/821163733 (~ 51322732 : 1).

Quote:
Originally Posted by euphoricism
And so we have quads over boat over boat. That has to be insanely rare.
More rare than fifty million to 1.
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gabe
Old 12-19-2006, 04:48 PM #4 (permalink)  
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you make it look easy
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Harry
Old 12-19-2006, 08:38 PM #5 (permalink)  
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euphoricism
Old 12-19-2006, 09:30 PM #6 (permalink)  
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Holy shit Seq. You are THE MAN.
PM me your stars account, for your free $10 hidden bonus
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Margin Of Error
Old 12-19-2006, 10:50 PM     Post subject: Re: Someone run some math on a hand for me? #7 (permalink)  
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Quote:
Originally Posted by thenonsequitur
More rare than fifty million to 1.

I'm so bad at math thats the only part I can understand.
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thenonsequitur
Old 12-20-2006, 12:17 AM #8 (permalink)  
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Quote:
Originally Posted by euphoricism
Holy shit Seq. You are THE MAN.
PM me your stars account, for your free $10 hidden bonus
I kind of wanted to figure it out for my own sake too, just to know, so a bonus isn't really necessary. But if you want to send me $10, I won't turn down the offer . My Stars name is JujuJuice.
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Genitruc
Old 01-27-2007, 01:42 AM #9 (permalink)  
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 anybody read the thread on 2p2 (boosted J trip report I think from PCA) where 3-way flop everyone flops a set and goes bananas. Dood with bottom set (777 on 7-q-j board) folds face up (twincaracas from pokerstars 25-50) after push-call in front of him.


Turn is a 7 obv
when the vpip's are high and the value bets are like razors, who can be safe?
 
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Pay4myCad!!
Old 01-27-2007, 07:18 AM #10 (permalink)  
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Quote:
Originally Posted by gabe
you make it look easy
ditto that, thx non
Of course I have bad days...
Sometimes I'll go a whole day without quads.
 
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Old 01-27-2007, 10:48 AM #11 (permalink)  
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Quote:
Originally Posted by Genitruc
anybody read the thread on 2p2 (boosted J trip report I think from PCA) where 3-way flop everyone flops a set and goes bananas. Dood with bottom set (777 on 7-q-j board) folds face up (twincaracas from pokerstars 25-50) after push-call in front of him.


Turn is a 7 obv
talk about the right play at the wrong time...

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