blackbaron
blackbaron
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Joined: Jun 5, 2015
October 20th, 2015 at 6:53:38 AM permalink
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
ThatDonGuy
ThatDonGuy
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Thanked by
Dorukan
October 20th, 2015 at 7:49:47 AM permalink
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.
blackbaron
blackbaron
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October 20th, 2015 at 8:59:17 AM permalink
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
ThatDonGuy
ThatDonGuy
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Dorukan
October 20th, 2015 at 11:58:53 AM permalink
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%.
blackbaron
blackbaron
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October 21st, 2015 at 6:21:08 AM permalink
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 !!!
LordTony
LordTony
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June 12th, 2016 at 9:35:20 AM permalink
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
LordTony
LordTony
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Joined: May 10, 2016
June 12th, 2016 at 9:35:21 AM permalink
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
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