Odds two stud players rolled up in same hand
 

Saw this thread from the RGP 'golden days'. Agree/disagree with the math on this?

Re: Odds two stud players rolled up in same hand
 

C(8,2)*P(13,2)*4^2/C(52,3)/C(49,3) –
C(8,3)*P(13,3)*4^3/C(52,3)/C(49,3)/C(46,3) +
C(8,4)*P(13,4)*4^4/C(52,3)/C(49,3)/C(46,3)/C(43,3) -
C(8,5)*P(13,5)*4^5/C(52,3)/C(49,3)/C(46,3)/C(43,3)/C(40,3) +
C(8,6)*P(13,6)*4^6/C(52,3)/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3) -
C(8,7)*P(13,7)*4^7/C(52,3)/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3)/C(34,3) +
C(8,8)*P(13,8)*4^8/C(52,3)/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3)/C(34,3)/C(31,3)
= 1 in 5860

Some of the other posters were close, but mine is exact for the odds of 2-8 players being rolled up, by the inclusion-exclusion principle.

Re: Odds two stud players rolled up in same hand
 

Thanks Bruce. I'll consider that 'no chance' for playing purposes.

Re: Odds two stud players rolled up in same hand
 

I disagree, since for playing purposes, the interesting probability is the conditional probability that someone else is rolled up given that you are, which is much more likely.

Re: Odds two stud players rolled up in same hand
 

That's like the guy who always carries his own bomb aboard an airplane, since the chance of 2 people bringing a bomb are miniscule.

Once you are rolled up, it becomes over 100 times more likely that 2 players will be rolled up.

Here is the exact probability of 1 or more players being rolled up with you when you are rolled up:

C(7,1)*P(12,1)*4^1/C(49,3) –
C(7,2)*P(12,2)*4^2/C(49,3)/C(46,3) +
C(7,3)*P(12,3)*4^3/C(49,3)/C(46,3)/C(43,3) -
C(7,4)*P(12,4)*4^4/C(49,3)/C(46,3)/C(43,3)/C(40,3) +
C(7,5)*P(12,5)*4^5/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3) -
C(7,6)*P(12,6)*4^6/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3)/C(34,3) +
C(7,7)*P(12,7)*4^7/C(49,3)/C(46,3)/C(43,3)/C(40,3)/C(37,3)/C(34,3)/C(31,3)

= 1 in 55.3

It isn't necessary to go through all this to get close, you can just use the first term or two:

7*12*4/C(49,3) = 1 in 54.8

Re: Odds two stud players rolled up in same hand
 

Thanks, that's an interesting point. I get bogged down in the math but that's why I majored in business [img]/images/graemlins/crazy.gif[/img]

But still. I'm not going to risk playing weak/tight when rolled up because I'm afraid of a 1:55 shot. I'd rather get pounded that one time.

Re: Odds two stud players rolled up in same hand
 

It won't happen early in the hand, but there will come a point when you realize that he started rolled up provided you are decent and he is playing at least ok. That is, each play he makes changes the chance (increases, usu.) that he started rolled up in a Bayesian sense.

Craig