Courchevel Question - Gambling and Probability

Two Plus Two Forums Other Topics Probability

Courchevel Question

Post Reply Subscribe

...

09-19-2018 , 10:33 PM

ScotchOnDaRocks

Carpal \'Tunnel

Join Date: May 2015 Posts: 7,200

This is 5 card omaha where one of the community cards are exposed before preflop betting.

In a six handed game what is probability someone has a set? Thanks

Quote

09-20-2018 , 01:29 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,731

I think you are asking what is the prob someone has a set using only the "spit" card (first community card, dealt face up "pre-flop"), but you could be asking something else.

Could you clarify your question?

Quote

09-20-2018 , 01:56 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,731

Guessing that is what you mean, here is what I got:

Clearly only 1 player can make a set using the "Spit" card and two of the same rank from their 5 hole cards. So P6=6*P1 in this case.

P1 = [C(3,2)*C(48,3) + C(3,3)*C(48,2)] / C(51,5)

= 53,016 / 2,349,060

= 2.2569%

So P6

= 6 * 53,016 / 2,349,060

= 318,096 / 2,349,060

= 13.5414%

If that is the question you were asking, someone will probably confirm or deny this answer.

If you are not asking that question, let us know what you are asking.

Quote

09-20-2018 , 06:19 PM

ScotchOnDaRocks

Carpal \'Tunnel

Join Date: May 2015 Posts: 7,200

Yes thanks just using the spit card

Wow that seems higher than I would have thought.

Although it seems to make sense. Without removal everyone has 3.25% to have any of the pairs. But the removal makes it harder, so number seems reasonable.

Quote

09-20-2018 , 07:54 PM

heehaww

Pooh-Bah

Join Date: Aug 2011 Posts: 5,081

Using PIE: 6[C(5,2)*3/C(51,2) - 2*C(5,3)/C(51,3)] = same answer

Quote

09-21-2018 , 12:55 AM

ScotchOnDaRocks

Carpal \'Tunnel

Join Date: May 2015 Posts: 7,200

Thanks gents!

Quote

09-21-2018 , 01:37 AM

David Sklansky

Administrator

Join Date: Aug 2002 Posts: 17,075

[(3/51 x 2/50 x 48/49 x 47/48 x 46/47 x 10) + (3/51 x 2/50 x 1/49 x 48/48 x 47/47 x 10)] x 6

Quote

Post Reply Subscribe

...