Hey Guys,

I'm currently working on some mathematical hand evaluation, unfortunatly, as some of you probably know, I am a mathematical nitwit

so I could use some input.

The following situation and calculation is completely hypothetical, in a real situation the ranges will probably be different however it's the method and not the specifics which are important to me. (For those interested, it's a hand from Harrington on Hold'em vol. I)

8 - handed table

Hero is BB with 76o

Villian is UTG+1 big stack, known to be loose and aggressive raises 2x BB.

Everybody else folds. Hero gets 3.5-1 direct pot odds to call but what are his average odds against the Villains hand range?

As I said it's about the method, not the specifics so I've taken quite some liberty in the villains ranges for simplification.

22+ AT+ KT+

So basically we have:

4 lower pairs or 24 handcombinations against which we are roughly 1.2-1

7 higher pairs or 42 handcombinations against which we are roughly 5-1

7 high card holdings or 112 handcomb. against which we are rough 1.7-1

(For simplification I've removed the holdings 77 and 66 for 2 reasons, first: both only add 3 handcombinations to the whole, second: I don't have the odds for these types of domination around (being stuck far away from home). They obviously influence the results, but not the method.)

What are the Hero's average odds against the villains holdings?

This is were my math knowledge starts to break down however, basically I can say that:

lower pairs count for 13% of the average

higher pairs count for 24% of the average

high cards count for 63% of the average

What I tried:

24 x 1.2 = 28.8

42 x 5 = 210

112 x 1.7 = 190.4

24 + 42 + 112 = 178

28.8 + 210 + 190.4 = 429.2

429.2 /178 = 2.4-1 average odds

But I have the feeling this method is both cumbersome and not completely correct. Can anybody lend a head?

Thanks in advance,

Anakha

PS. For any serious mathwizzes here: sorry for my horrible, horrible formula layout, I'm simply reinventing the wheel since, well, I never had much tutoring in the subject. (practically none at all)