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General Gambling >> Probability

Pages: 1
gary1523
newbie

Reged: 11/08/05
Posts: 48
AA vs KK probability??
#7138477 - 09/01/06 11:20 AM

does anyone have the answer as to how often AA vs KK or basically any two identical hole cards should run into each other at a 10 seat holdem game????????

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BruceZ
Carpal \'Tunnel

Reged: 09/03/02
Posts: 4078
Re: AA vs KK probability?? [Re: gary1523]
#7139394 - 09/01/06 01:00 PM

Quote:

does anyone have the answer as to how often AA vs KK or basically any two identical hole cards should run into each other at a 10 seat holdem game????????

AA vs. KK:

By the inclusion-exclusion principle:

C(10,2)*12*6/C(52,2)/C(50,2) -
C(10,3)*6*1*6*3*2/C(52,2)/C(50,2)/C(48,2) +
C(10,4)*6*1*6*1*C(4,2)/C(52,2)/C(50,2)/C(48,2)/C(46,2)

=~ 1 in 502 hands.

AA vs. AA (or any specific identical pairs XX vs. XX):

C(10,2)*1/C(52,4) =~ 1 in 6016 hands.

Note that this is different from the odds that someone else holds AA when you hold AA, as that probability would be simply 9*1/C(50,2) = 9/1225. The first question is different from the odds that someone holds AA when you hold KK. For these and other similar odds, see this post.

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gary1523
newbie

Reged: 11/08/05
Posts: 48
Re: AA vs KK probability?? [Re: BruceZ]
#7139500 - 09/01/06 01:10 PM

thanks much
gary

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nuts
old hand

Reged: 12/29/05
Posts: 842
Loc: UK
Re: AA vs KK probability?? [Re: BruceZ]
#7152984 - 09/02/06 10:56 PM

Quote:

Quote:

does anyone have the answer as to how often AA vs KK or basically any two identical hole cards should run into each other at a 10 seat holdem game????????

AA vs. KK:

By the inclusion-exclusion principle:

C(10,2)*12*6/C(52,2)/C(50,2) -
C(10,3)*6*1*6*3*2/C(52,2)/C(50,2)/C(48,2) +
C(10,4)*6*1*6*1*C(4,2)/C(52,2)/C(50,2)/C(48,2)/C(46,2)

=~ 1 in 502 hands.

AA vs. AA (or any specific identical pairs XX vs. XX):

C(10,2)*1/C(52,4) =~ 1 in 6016 hands.

Note that this is different from the odds that someone else holds AA when you hold AA, as that probability would be simply 9*1/C(50,2) = 9/1225. The first question is different from the odds that someone holds AA when you hold KK. For these and other similar odds, see this post.

so the odds of getting AA is 1-~220, does this mean that i'm going to see Kk just less than half the time?

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BruceZ
Carpal \'Tunnel

Reged: 09/03/02
Posts: 4078
Re: AA vs KK probability?? [Re: nuts]
#7155001 - 09/03/06 04:26 AM

Quote:

Quote:

Quote:

does anyone have the answer as to how often AA vs KK or basically any two identical hole cards should run into each other at a 10 seat holdem game????????

AA vs. KK:

By the inclusion-exclusion principle:

C(10,2)*12*6/C(52,2)/C(50,2) -
C(10,3)*6*1*6*3*2/C(52,2)/C(50,2)/C(48,2) +
C(10,4)*6*1*6*1*C(4,2)/C(52,2)/C(50,2)/C(48,2)/C(46,2)

=~ 1 in 502 hands.

AA vs. AA (or any specific identical pairs XX vs. XX):

C(10,2)*1/C(52,4) =~ 1 in 6016 hands.

Note that this is different from the odds that someone else holds AA when you hold AA, as that probability would be simply 9*1/C(50,2) = 9/1225. The first question is different from the odds that someone holds AA when you hold KK. For these and other similar odds, see this post.

so the odds of getting AA is 1-~220, does this mean that i'm going to see Kk just less than half the time?

No, the chance of seeing KK when you have AA is the same as the chance of seeing AA when you have KK, or 1 in 22.8 at a 10-handed table. I assume you are getting half the time by dividing 502 by 221, but the correct way to do this is to note that someone at the table gets AA once in about 22 hands, and 502/22 =~ 22.8.

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medinpok
stranger

Reged: 07/20/06
Posts: 8
Re: AA vs KK probability?? [Re: BruceZ]
#9762867 - 03/29/07 09:52 PM

The link to the inclusion-exclusion principle thread is not working and I have been unable to find it using the search function. Does anyone know where the thread is?

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BruceZ
Carpal \'Tunnel

Reged: 09/03/02
Posts: 4078
Re: AA vs KK probability?? [Re: medinpok]
#9786050 - 03/31/07 06:32 PM

Quote:

The link to the inclusion-exclusion principle thread is not working and I have been unable to find it using the search function. Does anyone know where the thread is?

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