Combinations question(C(x,y))

[Vannek]

Simple question here that been bugging me, lets say you hold KK and your opponent moves all-in preflop, you have reasons to believe he has KK/AA, is it the number of ways he could be holding AA C(4,2) and KK C(2,2)?If so then its 6x more likely he has aces than kings?That number seems a bit high for me

[Lost Wages]

Yes, that is correct. There are six ways that he can have aces and only one way he can have kings. So if you thought that he would play either hand exactly the same way (and no other) then it's 6:1 that he aces.

Lost Wages

[Vannek]

Thanks for the answer.
Ok, lets say that you think he has AA/KK/AK, by my math here the chances he has AK when you have KK is 4(As) * 2(Ks) = 8 ways, so its the same as AA.
So the final answer would be 8+8+1 = 17 and the chances would be 47% for AA 47% for AK and 6% for KK?

[Lost Wages]

AK is 8 ways, but remember, AA is 6 ways.

Lost Wages