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Magister8Ludi
Joined: 16 Sep 2006
Posts: 3
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 Posted: Sat Sep 16, 2006 10:20 pm Post subject: Formula please???? |
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I have just purchased Matthew's "Odds and Probabilites. I know the odds for getting AA and KK are both 220-1, but could someone send me the formula for AA and KK appearing in the same hand? As well as, AA, KK and QQ appearing in the same hand? Does it matter if there are ten players, nine, eight...etc.
Thanks in advance,
Ludi |
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Bugsbunny
Wascally
Joined: 07 Apr 2004
Posts: 7626
Location: Drinking Carrot juice
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| Posted: Sun Sep 17, 2006 4:15 am Post subject: |
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I'm going to do this the easy way  This post should probably get stickied in the probability forum. If you have any questions after reading this, and following the links, let me know and I'll try to answer them Post followup questions in the probability forum - I don't check this one anywhere near as often.
http://forumserver.twoplustwo.com/showthreaded.php?Number=3446464
(also check out AA vs KK )
| Quote: | | Quote: | Anyone know where I can find the answers to the following:
I read that the odds of running into AA if I hold KK is about 24/1...how would I calculate that? Better yet, how do I calculate the odds of running into AA if I hold KK at a 10-h table...and at a 6-h table?
Now if I hold QQ, how would I determine the odds of running into KK or AA...again, 10-h...and 6-h?
Last, if I hold KK or AA...what's the probability of running into AK...again, 10-h and 6-h?
Thanks in advance for any guidance. I apologize, too, if it's been posted elsewhere in the forum.
J |
AA vs. KK gets asked so often that people are taking over/under bets on when it will be asked next, so prepare for abuse about using the search function.  Many of these posts reside in the recent archives which must be searched separately. At least this post provides an opportunity to put several important ones in one place. Some of these have not appeared before.
Also, you asked for the odds of running into AK when you hold AA or KK. You may have meant that you hold the AK, and want the odds of running into AA or KK. Anyway, I computed both. In each case, the second hand listed is your hand.
The following expressions all give the exact answers to as many decimal points as you care to compute. From the inclusion-exclusion principle:
AA vs. KK (10 handed):
9*6/C(50,2) - C(9,2)/C(50,4) =~ 21.8-to-1
AA vs KK (6 handed):
5*6/C(50,2) - C(5,2)/C(50,4) =~ 39.9-to-1
AA or KK vs. QQ (10 handed):
9*12/C(50,2) –
C(9,2)*12*7/C(50,2)/C(48,2) +
C(9,3)*12*(6*2 + 1*6)/C(50,2)/C(48,2)/C(46,2) –
C(9,4)*12*(6*2*1 + 1*6*1)/C(50,2)/C(48,2)/C(46,2)/C(44,2)
=~ 10.6-to-1
AA or KK vs. QQ (6 handed):
5*12/C(50,2) –
C(5,2)*12*7/C(50,2)/C(48,2) +
C(5,3)*12*(6*2 + 1*6)/C(50,2)/C(48,2)/C(46,2) –
C(5,4)*12*(6*2*1 + 1*6*1)/C(50,2)/C(48,2)/C(46,2)/C(44,2)
=~ 19.7-to-1
AK (opponent) vs. AA or KK (10 handed):
9*8/C(50,2) - C(9,2)*8*3/C(50,2)/C(48,2) =~ 16.2-to-1
AK (opponent) vs. AA or KK (6 handed):
5*8/C(50,2) - C(5,2)*8*3/C(50,2)/C(48,2) =~ 29.8-to-1
AA or KK (opponent) vs. AK (10 handed):
9*6/C(50,2) – C(9,2)*6*3/C(50,2)/C(48,2) =~ 21.9-to-1
AA or KK (opponent) vs. AK (6 handed):
5*6/C(50,2) - C(5,2)*6*3/C(50,2)/C(48,2) =~ 40.1-to-1
You can find numbers for some other hands for 9 handed and 4 handed in this thread. |
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