PDA

View Full Version : Probability question

djoyce003
11-07-2005, 11:51 AM
hey guys...wondering if someone could tell me the probability of QQ KK and AA all being out in the same hand at a 6max table. Also I'd like to know how the calculation works. Saw this happen last night so i'm curious. Also what is the probability of say 3 of the top 5 pairs being out on one hand...3 of TT-AA in any one hand at 6max?
11-07-2005, 12:10 PM
Not an exact answer but these should keep you going until the Z-meister returns.

Some odds for encountering AA vs KK, AA vs QQ, etc (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=3446464&page=&view=&s b=5&o=&vc=1)
Inclusion Exclusion Principle with examples (http://archiveserver.twoplustwo.com/showthreaded.php?Cat=&Board=&Number=417383&page=&v iew=&sb=5&o=&fpart=)
BruceZ
11-07-2005, 12:30 PM
[ QUOTE ]
hey guys...wondering if someone could tell me the probability of QQ KK and AA all being out in the same hand at a 6max table. Also I'd like to know how the calculation works. Saw this happen last night so i'm curious.

[/ QUOTE ]

Here is the solution for 10-handed (http://archiveserver.twoplustwo.com/showflat.php?Cat=&Board=probability&Number=309687& Forum=f11&Words=irchans&Searchpage=0&Limit=25&Main =303032&Search=true&where=bodysub&Name=&daterange= 1&newerval=3&newertype=y&olderval=&oldertype=&body prev=#Post309687). For 6-handed, change this:

P(AA,KK,QQ out with 10 players) =
C(10,3)*P3 - C(10,4)*P4 + C(10,5)*P5 - C(10,6)*P6

to this:

P(AA,KK,QQ out with 6 players) =
C(6,3)*P3 - C(6,4)*P4 + C(6,5)*P5 - C(6,6)*P6


[ QUOTE ]
Also what is the probability of say 3 of the top 5 pairs being out on one hand...3 of TT-AA in any one hand at 6max?

[/ QUOTE ]

For 3 pairs out of 5, it will be awfully close to C(5,3) times the above result, since it is very unlikely that there will be more than 3.
djoyce003
11-07-2005, 03:15 PM
what does C(6,3) mean?
BruceZ
11-07-2005, 05:39 PM
[ QUOTE ]
what does C(6,3) mean?

[/ QUOTE ]

Number of combinations of 3 things that can be chosen out of 6 things. C(6,3) = 6!/3!/(6-3)! = 6*5*4/(3*2*1) = 20. This can be evaluated by typing 6choose3 (http://www.google.com/search?hl=en&q=6choose3) into google, or by using the =COMBIN function in Excel, or with some calculators.