can anyone tell me the odds of 3 players flopping a set?? - Gambling and Probability

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can anyone tell me the odds of 3 players flopping a set??

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08-06-2008 , 05:02 AM

pipedown3

enthusiast

Join Date: Apr 2006 Posts: 61

in a live 3/6 game the cutoff made it 6 and the sb & bb called. the came 24K.

the pot was hotly contested. as it turned out, the cut off had KK, the sb had 22 and the bb had 44.

i'd like to know what the odds are of 3 players each flopping a set?

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08-06-2008 , 05:14 AM

Abbaddabba

Pooh-Bah

Join Date: Jul 2005 Posts: 5,807

knowing only that 3 players have unique pairs and that all see the flop,

6/46*4/45*2/44

= 48/91080, or approximately 1/1900.

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08-07-2008 , 08:18 AM

juggler97531

journeyman

Join Date: May 2005 Posts: 377

i took it from the other side:
Assumption that they all started with pairs is quite optimistic.

I made calculations assuming every player plays top 20% of his hands inc. all pairs(probably still too tight):

Player1 has a set with ppb 3.93%.

When player1 has a set
Player2 has a set with ppb 2.57%

When both player1 and 2 have a set
Player3 has a set with ppb 1.29

So the ppb they all
0.0013%
it is about 1/75000

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08-07-2008 , 09:14 AM

Siihphilis

stranger

Join Date: Jul 2008 Posts: 11

Quote:

Originally Posted by Abbaddabba

knowing only that 3 players have unique pairs and that all see the flop,

6/46*4/45*2/44

= 48/91080, or approximately 1/1900.

this is correct imo

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08-07-2008 , 09:59 AM

jay_shark

Pooh-Bah

Join Date: Sep 2006 Posts: 3,655

Quote:

Originally Posted by pipedown3

If we make the assumption that players with pocket pairs will see the flop, then the probability of this occurring at a 6-handed table is

6C3*78/52C2*72/50C2*66/48C2*2^3/46C3 ~ 0.00000213221

or odds against of about 468,995.9562:1

This computes the probability before the deal begins; that is, the event that 3 players will be dealt distinct pocket pairs and then go on to flop sets.

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