Yet another freespin expected value question

I read a lot of article and posts about freespin slot expected value calculation but i'm unable to find my goal value: how is expected value percentage get from freespins ?
For the purpose i provide concrete data i'm working, as i hope someone can help me (or correct ) my assumption.
Premise freespin rules:
During freespins (FS) player can retrigger fs.
2 or more wild symbols scattered fs, in details:
2 wild -> win 5 fs
3 wild -> win 10 fs
4 wild -> win 15 fs
5 wild -> win 20 fs

Slot cycle : 1488620000
Base slot payout: 0,89644 --> 89,644%

|--------------------------------------------------------------------------------------------------------------------
|wild --------------------------- 2 ----------------- 3 -------------------- 4 ------------------------ 5---------
|-----------------------------------------------------------------------------------------------------------------
|hit wild ------------------ 701576 ------------- 26064 ----------------- 832 ---------------------- 16 -----
|probab (hitw/cycle)-- 0,0004712929 --1,7508833684E-005-- 5,5890690706E-007-- 0,000000010748210
|--------------------------------------------------------------------------------------------------------------------


Here start my doubts, and i aks help to describe next steps to achive how fs increase my "base slot payout".
I try follow rule describe onbut without significant value (i think) as i here to ask clarify.

Thanks all will reply to me

What you need to calculate is, what is the expected number of free spins you are going to get at any point.

First , calculate the number you are expected to get just from a single spin. According to your numbers, this is:
(701576 / 1488620000) x 5 + (26064 / 1488620000) x 10 + (832 / 1488620000) x 15 + (16 / 1488620000) x 20.
This is about 1 / 393.67734.

However, you have to remember that each free spin is expected to generate another 1 / 393.67734 free spins, each of which can generate yet another 1 / 393.67734 free spins, and so on.
Let X = 1 / 393.67734; the total expected number of free spins is X + X² + X³ + X⁴ + ...
Since -1 < X < 1, this is X * (1 / (1 - X)) = X / (1 - X), or about 1 / 392.67734.

The true expected value of a free spin in this case is the EV of a spin (not taking the value of additional free spins into account) divided by 392.67734.

Thank to ThatDonGuy for reply, now is more clear.
But I still can not find the way to calculate, in addition to the rtp Base slot: 0,89644 , what impact the return of free spins will get.
Which will be the overall rtp (base slot rtp + freespin rtp) that i will expected according to model's data ?
Could you clarify me with others numerical example ?

Thanks in advance for patience

The expected number of spins = 1 + the expected number of free spins. In this case, this is 1 + (1 / 392.67734) = 1.00254662 spins.

Since each spin has an ER of 0.89644, the total ER = 0.89644 x 1.00254662 = 0.89872, or 89.872%.

Very appreciate your feedback.
Just now i understand my issue. My math model return numeric result as you describe (your response is a confirmation), but coded algorithm return over 138%.
Issue was that: math consider wild win for FS in line , wheras coded alg wild conside wild as scatter, "2 or more wild in any position" ... now i try fix and then verify match between math and alg.

Thanks a lot for your interesting !!!

Quote: ThatDonGuy

Let X = 1 / 393.67734; the total expected number of free spins is X + X² + X³ + X⁴ + ...
Since -1 < X < 1, this is X * (1 / (1 - X)) = X / (1 - X), or about 1 / 392.67734.

The true expected value of a free spin in this case is the EV of a spin (not taking the value of additional free spins into account) divided by 392.67734.

My math is rusty, Can you explain this part in a bit more detail?

Thanks

Quote: ThatDonGuy

Let X = 1 / 393.67734; the total expected number of free spins is X + X² + X³ + X⁴ + ...
Since -1 < X < 1, this is X * (1 / (1 - X)) = X / (1 - X), or about 1 / 392.67734.

The true expected value of a free spin in this case is the EV of a spin (not taking the value of additional free spins into account) divided by 392.67734.

My math is rusty, Can you explain this part in a bit more detail?

Thanks