Calculating equity of ranges

Question

I want to calculate the equity of a range against another range. The problem is: how does one weight the different hands in each range?

For example: Let us say we have the range {AA, 76o} and opponent's range is only AKs. Without removal effect, our range is 6 combinations AA and 12 combinations 76o. So weighting each hand equity against AKs, one gets 0.875*6/18 + 0.365*12/18 = 0.535.

However, a program like Pokerstove yields an equity of 0.465 for this range.

One idea one might get is to remove 3 of the AA combinations due to the opponent having AKs, but this doesn not yield the corrent value either.

Answer 1

It is correct to say there are only 3 ways to get the AA, when you do that calculation you get 0.467

The rest of the difference in equity comes from the fact that AKs doesn't have the same equity over all cases of 76o. It depends on whether or not those cards share a suit with the AK.

You will get the correct value for equity if you split it into all these cases:

3 ways to make AA 4 ways to make 76o where the 7 has the same suit as the AK 4 ways to make 76o where the 6 has the same suit as the AK 4 ways to make 76o where neither suit matches the AK

I am on my phone and don't have the individual equities available, but I'll edit them in later.