Combinatorics basic question

Lets say villain open raises from UTG in 6max NLHE game, and lets say his range is 66+, ATs+ AJo+, KJs+ and KQ. There are 8*6 = 48 combos of pairs in his range, 4*4=16 As, 3*12 = 36 Ao, 2*4=8 Ks, and 12 KQo for a total of 48 + 16 + 36 + 8 + 12 = 120 combos. If hero is for some reasone all-in 3bet holding AKo and villain is folding everything except AA and KK, how percent his hand is he folding? Do we need consider fact that hero is holding one A and one K?
6 combos of AA + 6 combos of KK = 12 /120 = 10% time he will call or there are 3 combos of AA and 3 combos of KK = 6 / 120 = 5%? But if hero is holding AK do we need to reduce number of total combinations(120) because there are also most made of A and K combos?

Reduce the combos based on everything known.

That mean exclude one A and one K from 120 combos of his range too.

Yes.

JamesJS said:

That mean exclude one A and one K from 120 combos of his range too.

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If you have AK, then villain can not have 12- possibilities of AA and KK combined he can only have 3 of each for 6 total. The rest of his range that does not contain an ace or K, remains the same. The part of his range that does contain an A or K (but not both) is diminished by 25%.

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I think this is a trick question.

If Hero is AIPF it doesn't matter what combo's villain has. Time for that thinking has passed. But this is Sunday, and Praying he doesn't is valid I guess.

JamesJS said:

That mean exclude one A and one K from 120 combos of his range too.

Click to expand...

yea so with that range it's just 6/105 *100 once you've excluded all combos that you have blockers for.