MATH QUESTION(intersting live hand)

[johnsy]

Was a hand i saw go down at HollywoodPark in a $500NL game.
1 limper, Button rasies jj, sb call 1010, BB call 33, limper calls 88
Flop 10 8 3r, Button bets, SB Rasies, BB calls, Limper Calls, Button Folds
Turn j ......all the money goes in 3 way to river
River 3 ..WTF????
What r the odds this hand goes down this exact way?

[mostsmooth]

1:1

[KJL]

The odds that four opponent are dealt four different pocket pairs is:
C(4,2)/C(52,2)*C(4,2)/C(50,2)*C(4,2)/C(48,2)*C(4,2)/C(46,2)=~.00000000066
The odds that three of those pocket pairs turn into sets and one becomes quads is:
C(2,1)*C(2,1)*C(2,1)*C(2,2)/C(44,5)=~.0000008
The odds of this all happening is the product of the two probabilties, which is: ~.0000000000000005

These odds assume that order dosen't matter, if it did the odds would be even smaller.

[AaronBrown]

You've figured the probability of the four specific pocket pairs (J, T, 8 and 3) rather than just four different pocket pairs. I'm not sure which one was meant by the question. Second, you've figured the probability that one specific one is quads (the 3 in this case) rather than just that one gets quads. Third, you have to multiply by 2/5 to get the probability that the quad shows up on the river.

But the trouble with calculations like this is any had is wildly unlikely after it is dealt. I admit this is an unusual hand, but it's not as unusual as the numbers seem to indicate. If you watch a few thousand poker hands, you will see one with four players with strong hands and an innocent looking board.

[ohnonotthat]

[ QUOTE ]

But the trouble with calculations like this is any hand is wildly unlikely after it is dealt. I admit this is an unusual hand, but it's not as unusual as the numbers seem to indicate. If you watch a few thousand poker hands, you will see one with four players with strong hands and an innocent looking board.

[/ QUOTE ]

Aaron,

Allow me, strictly for the sake of illuminating the OP, to point out the hair in the egg.

Any hand is [sic] "WILDLY unlikely after it's been dealt out" is an indisbutably true statement, as is . . .

ALL hands are EQUALLY [wildly] unlikely after they've been dealt out.

I'll bet we all remember the last time we saw all 5 parts to a Royal ON BOARD.

Quick - - -

Who remembers the last time they saw a final board of:

Kc Ts 8h 6d 3c ?



Nobody ?



Amazing - especially since the exact hand I asked about is four times less likely to show than a Royal. (There are 4 ways to make a Royal but this hand is distinct).