Free Spins RTP with increasing multiplier

Hi, i am trying to calculate free spins with increasing multipliers
We start with N free spins and mult = 1, calculated base win is w, each wild adds +1 spin and increase multiplier, (ex 3 wilds = +3 spins and +3 mult)
there is maximum of 1 wild in each trilpet (maximum 1 wild can be shown on a reel)
Navg = N/(1-Ew) - average amount of free spns
multavg = Navg*Ew + 1 - average multiplier
Ew - average amount of wilds (Ew = p1*1+p2*2+...+p5*5, p2 - probability of exactly two wilds on a map)
Navg and multavg in simulation are very close to ones in spreadsheet
Why average win for this bonus isn't equal to Navg*multavg*w? (1.5 times difference)
Making multiplier const = 1 removes all difference (it becomes to small to have statistical significance)

I think the problem is that a large number of wilds also give higher base wins. So, when you do get a lot of wilds, you’re getting high multipliers and high base wins. I assume you increase the multiplier during the game in which it appears, which makes a spreadsheet calculation quite difficult, maybe impossible.

Hi, it is possible to calculate in the spreadsheet via markov chain.
A[i,j] - probability of spin j to have multiplier i
A[1,1] = 1
A[1,2] = p0
A[2,2] = p1
A[1,3] = p0*p0
etc
if we have n initial spins then
A[i, n+i] = 0
Accuracy of approximation depends on the size of the matrix A
161x161 was enough to get less than 1% difference for 887 average total win from free spins
30x30 was enough for more adequate tapes.
1e5 runs of free spins had 886.13684 av win for one run in simulation, while calculated av win was 887,4267704
Crystal, if you are interested I can share the spreadsheet with you.

Hi,

could you explain me why the average MP is calculated in this way?

And what if every time a wild landed on the screen 2 or 3 or more new fs would be triggered?