Poker Combinatorics: Compare pot odds with what?

Question

I'm getting a little confused studying Poker Combinatorics.

(a) Some suggests comparing Pot Odds with [Combinations you beat - calling this equity%].

(b) Some suggest comparing Pot Odds with [Hero's hand vs Range - call this equity%].

Example of (a)

Pot odds: 2:1 = 33% Total combinations = 42 Combinations you beat = 33 (79%) Combinations you don’t beat = 9 (21%) Seeing as you have the best hand 79% of the time (or 79% "equity") and the pot odds indicate that you only need to have the best hand 38% of the time, it makes it +EV to call.

Example of (b)

Will be too long to post. Basically find equity vs range of hand and then calculate average equity using combinations.

So.. uhm which one is it?

Answer 1

The way I understand your question, it seems like b and a are the same thing.

in your example of (a) you mention that the total combinations come out to 42. this number is not arbitrary, it has to come from somewhere. If you were up against a random hand, then there would be a lot more than 42 total combinations. I am assuming that this 42 total combinations represents the 42 possible combinations that the opponent has in their range.

When you calculate pot odds and compare them to your equity in the hand, you want to calculate your equity by doing the following:

1. construct a range for your opponent
2. find the % of hands in that range that you beat
3. compare that % to your pot odds

In that sense, it is both a and b. hopefully I was able to help you clarify.