Another FreeSpin expectation return Thread

I've been looking everywhere for a solution to the 5x3 slot game that I'm designing.
In the base game we have WILD which can appear anywhere and expand to cover the entire column. WILD triggers free spin with sticky WILD
Depend on the amount of WILD players receive they will get different initial number of free spins.

For example:
1 WILD --> 1 FS
2 WILDs --> 5 FS
3 WILDs --> 10 FS
4 WILDs --> 15 FS

Players can get WILD during FS too which gives an extra FS for each WILD.
Each WILD appear on a FS will stick on the next FS.
Each WILD sticks up to 3 FS If new WILD appear on preceding spin

Maximum numbers of consecutive FS is 25.


Right now, The way Im doing this is:
1. Calculate expected return for the base game.
2. Calculate the expected value then expected return for FS of the base game.
3. Calculate the expected value for FS of the free spin.
4. Calculate expected return for each of the 20 FS.

Combine all together I should get expected return for the base game + free spin.

Im looking for some verification on my solution. If it is not correct, Im greatly appreciated any feedback and advices.

Thanks

Write a simple simulator in a programming language such as C++, run a billion games, and check the result is close.

If you're actually building a game in software then use that software to perform the simulation.

You need to do something like this, because even if you're using the correct approach its still possible to introduce errors in your calculations (and even if you're calculations are correct, you still need to check the software as you may have made errors there).