Two Plus Two Older Archives AA v KK v QQ at a five handed table
 FAQ Members List Calendar Search Today's Posts Mark Forums Read

 Thread Tools Display Modes
#1
08-24-2005, 02:00 PM
 Guest Posts: n/a
AA v KK v QQ at a five handed table

I played at a home game last night, and the following hand came up with five players at the table.

P1 AA, P2 KK, P3 QQ, P4-xx, P5-xx

I read that the chances of hitting pocket aces are about 1/221? Does this mean that the odds of this particular combination are roughly as follows?

(5/221) * (4/221) * (3/221)

Thanks
#2
08-25-2005, 04:49 AM
 mtrubo Junior Member Join Date: Jan 2007 Posts: 0
Re: AA v KK v QQ at a five handed table

1 in 221 are the odds of hitting a pocket pair of a specific rank, so the odds of getting AA, KK or QQ all have 1 in 221 odds.

so the odds are 221*221*221 = 221^3

However, there are C(10,2) ways of arranging starting hands for 5 players.

so the odds are 221^3/C(10,2) = 221^3/45 = 239863.6
1 in 239863.6

(someone please correct me if i'm wrong)
#3
08-25-2005, 08:44 AM
 LetYouDown Senior Member Join Date: Mar 2005 Location: Sharing a smoke w/negativity Posts: 524
Re: AA v KK v QQ at a five handed table

You need the inclusion/exclusion principle for this to get an exact answer. Do a search, you should find it instantly.
#4
08-25-2005, 12:59 PM
 aloiz Junior Member Join Date: Feb 2004 Posts: 4
Re: AA v KK v QQ at a five handed table

If you want the odds that you have AA v KK v QQ v XX v XX where XX does not include QQ-AA then the following will work:

I split the equation up into two halves. P(3 players have AA, KK, QQ) * P(remaining 2 don't have AA, KK, QQ|first 3 do)

5*C(4,2) * 4*C(4,2) * 3*C(4,2) / C(52,2)/C(50,2)/C(48,2)
Choose what player has AA, and which suits. Choose what player has KK and which suits. Choose what player has QQ and which suits.

P(2 remaing players don't have AA,KK,QQ|first three do) = 1 - P(either or both players have AA,KK,QQ|first three have AA,KK,QQ). So we have two cases. The first being that only one of the two has QQ-AA, the second being that both have QQ-AA.

First case:
2*3*(C(44,2)-2) / C(46,2)/C(44,2)
Choose what player has QQ-AA, choose QQ, KK, or AA. Choose hand for second player.

Second case:
C(3,2)*2 / C(46,2)/C(44,2)
Choose the two pairs, then the division of those pairs between the two players.

So we get:
5*C(4,2) * 4*C(4,2) * 3*C(4,2) / C(52,2)/C(50,2)/C(48,2) *
(1 - 2*3*(C(44,2)-2)/C(46,2)/C(44,2) + C(3,2)*2/C(46,2)/C(44,2)) =~ 7.032 * 10^-06 or about 142201:1

If you want to include the possiblity that the other two players could have QQ-AA then you need to use inclusion exclusion principle, and the problem becomes pretty difficult. I'd actually be surprised if an exact answer has been given before on this forum.

aloiz
#5
08-25-2005, 06:13 PM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 1,636
Re: AA v KK v QQ at a five handed table

[ QUOTE ]
If you want to include the possiblity that the other two players could have QQ-AA then you need to use inclusion exclusion principle, and the problem becomes pretty difficult. I'd actually be surprised if an exact answer has been given before on this forum.

[/ QUOTE ]

I solved this for a 10-handed table here. Regular inclusion-exclusion won't do it. You need a generalization of inclusion-exclusion. Also see some of the other posts in that thread for an explanation.

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Two Plus Two     Two Plus Two Internet Magazine     About the Forums     MOD DISCUSSION     ISOP General Poker Discussion     Texas Hold'em     Beginners Questions     Books and Publications     Televised Poker     News, Views, and Gossip     Brick and Mortar     Home Poker     Poker Beats, Brags, and Variance     Poker Theory Limit Texas Hold'em     Mid- and High-Stakes Hold'em     Medium Stakes Hold'em     Small Stakes Hold'em     Micro-Limits     Mid-High Stakes Shorthanded     Small Stakes Shorthanded PL/NL Texas Hold'em     Mid-, High-Stakes Pot- and No-Limit Hold'em     Medium-Stakes Pot-, No-Limit Hold'em     Small Stakes Pot-, No-Limit Hold'em Tournament Poker     Multi-table Tournaments     One-table Tournaments Other Poker     Omaha/8     Omaha High     Stud     Other Poker Games General Gambling     Probability     Psychology     Sports Betting     Other Gambling Games     Rake Back     Computer Technical Help Internet Gambling     Internet Gambling     Internet Bonuses     Software 2+2 Communities     Other Other Topics Other Topics     Sporting Events     Politics     Science, Math, and Philosophy     The Stock Market

All times are GMT -4. The time now is 05:24 AM.

 Contact Us - www.twoplustwo.com - Archive - Top