AK vs. AA or KK

[jacki]

I hold AK
Board reads AK2, suits unimportant.
What is the likelihood my opponent holds AA or KK, assuming the following range of hands:

88-AA
AKs-A8s
AKo-AJo
Suited connectors KQs-T9s

[Mark1808]

I'll take a stab. First off, suits do matter in the number of ways to make AK suited. If the 2 A's and K's out are all differant suits there are no ways to make AK suited, if the A&K's known are only 2 suits (AsAhKhKs) then there are 2 ways to make AKs. I will assume 2 ways on AKs. So, the number of ways to make each hand given cards obsereved is as follows:

Pair 8's 6
Pair 9's 6
Pair 10's 6
pair J's 6
Pair Q's 6
Pair K's 1
Pair Aces 1
AK s 2
AQ s 2
AJ s 2
A10 s 2
A9 s 2
A8 s 2
AK o 4
AQ o 8
AJ o 8
KQ s 2
QJ s 4
J10 s 4
10 9 s 4

Total 78

AA 1.3% 77 to 1
KK 1.3% 77 to 1

[uuDevil]

[ QUOTE ]
I hold AK
Board reads AK2, suits unimportant.
What is the likelihood my opponent holds AA or KK, assuming the following range of hands:

88-AA
AKs-A8s
AKo-AJo
Suited connectors KQs-T9s

[/ QUOTE ]
I get the following:

88-QQ, 5 prs x 6 ways to hold each= 30
KK-AA, 2 prs x 1 way (only 2 A's, 2 K's left)= 2
AQs-A8s, 5 hands x 2 ways (only 2 A's)= 10
AK (suited or unsuited), 1 hand x 4 ways= 4
AQo-AJo, 2 hands x 8 ways= 16
KQs, 1 hand x 2 ways (only 2 K's)= 2
QJs-T9s, 3 hands x 4 ways= 12

Total ways to hold these hands= 76
Total ways to hold AA or KK= 2

P(AA or KK)= 2/76= .02632 or odds of 74:2, i.e. 37:1 against.

[Mark1808]

I get the following:

88-QQ, 5 prs x 6 ways to hold each= 30
KK-AA, 2 prs x 1 way (only 2 A's, 2 K's left)= 2
AQs-A8s, 5 hands x 2 ways (only 2 A's)= 10
AK (suited or unsuited), 1 hand x 4 ways= 4
AQo-AJo, 2 hands x 8 ways= 16
KQs, 1 hand x 2 ways (only 2 K's)= 2
QJs-T9s, 3 hands x 4 ways= 12

Total ways to hold these hands= 76
Total ways to hold AA or KK= 2

P(AA or KK)= 2/76= .02632 or odds of 74:2, i.e. 37:1 against.

[/ QUOTE ]

You are correct I counted 6 AK's but there can be only 4. so 37 to 1 your opponent holds either AA or KK.