# Some help with mathematics please

• Bronze
Joined: 23.05.2006
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?

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)
• 3 replies
• Black
Joined: 21.02.2006
You can simplify this calculations by just using Pokerstove (google for it, its freeware) and you will get the same result of 1:2,4 on winning the hand (If treated as Preflop All-In).
So I assume you did everything right, even though I didn't recalculate it myself right now.

Of course we totally ignore the postflop play here, and in no-limit most of the time Preflop Equity discussions are not as important as in fixed limit for example.
This is of course only true for the bigstackplay, as you are able to extract a lot of money postflop, with the shortstack Preflop Equity-Calculations get much more important!