Volatility Range for total game

Hallo!

I calculate simple slot with free and bonus game. But i have difficult with calculation of free and bonus game when it part of main game.

Formula of Volatility range is good for main (base) game only.
R = EV +/- VI/sqrt(n),
where R - range,
EV - estimated value or RTP,
VI - volatility index, ==SD*CI, where
SD - standard deviation,
CI - confidence interval (by Z-score, 90%~1,65)

We can't use classic formula because of n-spins in MG don't related to n-spins in FG directly. In other words 10 rounds of MG isn't same like 10 rounds of FG. We should to take in account probability of FS to calculate how FG influence on results of total game.

I found for me next formula:

R(fg) = factor(fs) * ( EV(fs) +/- VI/sqrt(ms * p(fs)) ), where

fs - free spins, == p(x3)*10 + p(x4)*20 + p(x4)*30, where 10-30 is numbers of free spins by rules
FS-factor, == "multiplier"x3 * "probability"x3 * "spins by rules x3" + (for x4) + (for x5);
Result of "-" belong to low border of range, "+" to hi one.

But i am nut sure in it. I don't have simulator of game, excel calculator only. Other approaches give impossible results.

Can someone help with advice?

To get the most accurate variance, it should be done with simulation. It isn’t really possible to calculate the variance because of the covariance between paylines.

There are regulators who will ask for the single line variance, but that is garbage, in my opinion. Two games, one with stacked wilds and one with dispersed wilds, will show the same single line variance, but the stacked wilds actually produces a higher volatility game.

You said the simulation provided impossible results. Can you expand on that?

Edit: I see you don’t have a simulator, so maybe that’s a good thing to work on.

Thank you for answer.
Really, now i don't have simulator. I will work on.
When i said "another approaches give impossible results" i did mean excel calculation too, but in in other way.

Now machine (3x5) have low pay table (600 is max game odd), no multiplier, free and bonus game.
Range looks like this. It seems close to reality. Sorry, i can't load pictures.

Spins "-" "+"
1 0,00% 724,80%
10 0,00% 296,34%
25 16,01% 223,50%
50 26,05% 186,80%
100 40,40% 160,84%
300 62,00% 134,36%
500 70,16% 126,20%
1000 78,37% 118,00%
3000 86,74% 109,62%
5000 89,32% 107,04%
10000 91,91% 104,45%
50000 95,38% 100,98%
100000 96,20% 100,16%

Thank you!