I just can't find the answer on the net.

Every piece of software (PokerStove, Combonator, ICMizer etc.) dishes out equities very quickly.
What goes on in the background?

Let's take an example where hero shoves with 88 and villain calls exactly with the range that consists of A5o and 99.


Am I correct in assuming that hand vs. range calculation goes something like this in pseudo code:

1. Calculate how often villain is dealt each hand in range (and allow for card removal which pokerstove doesn't do)

So it would be 6 combinations of 99 and 4 combinations of A5s for a total of ten ways 99 and A5s can be dealt.

2. Calculate how hero's hand performs against each hand that villain calls with by dealing all possible flops

So it would be
.183 vs. 99
.659 vs. A5s

3. Multiple probability of each hand vs. hand showdown with frequency of its occurence

So in this case
(0.183*0.6)+(0.659*0.4)=0.3734 or 37.34%


For range vs. range calculation I would assume it is necessary to add one more cycle of iteration where instead of single hand in hero's range every single hand in hero's range undergoes "confrontation" with every single hand in villain's range?

I also suppose that software would have sped up step 2 if it would be computationally demanding (have no idea if it is), by precalculating each hand vs. hand outcome on all the possible flops and simply retrieve it from a table?

Does it work like this or am I missing a shortcut?

https://en.wikipedia.org/wiki/Monte_Carlo_method

Sounds like you got the method correct, tho I didn't read and reread thoroughly - yes, many have pre-calculated hand vs hand lookups to speed things up.

not however - all possible boards rather than flops.

Thanks _dave_

It was a lapsus calami, that is what I meant - BOARDS.

the most important thing in this calculation is a fast 7-card evaluator. once you figure that out, the rest is pretty easy basic programming skills.

there is a lot of 7-card evaluators out there and plenty of source code too