I want to calculate the win expectation in a Slot Machine with 3 Reels, including wild (W) symbols R1=[A,B,C,D] R2=[A,B,C,D,W,W,W] R3=[A,B,W,W,W,C,D] After a spin of the 3 reels we get a 3x3 window.
The payments are 1 for doubles of A,B,C,D and 2 for triplets. Wild (W) may substitute left to right:
[A,W,C] is [A,A,C] pays 2.
[A,B,W] payment is 0.
If W in a columns of the 2nd or 3rd all 3 symbols are converted to W.
R1 R2 R3 A C C B D D C W A
we can substituite and get (wich will pay 6)
R1 R2 R3
A W C
B W D
C W A
So, the expectation to get 3 A is: if X1 is the event to get a symbol in the first reel in a line, and R1 the event to get at least 1 W in reel 1, then I get:
P(3A) = P(X1 = A) * P( R2 = A or X2 = A) * P( R3 = A or X3 = A) = 1/4 * ( 5/7 + 1/7)^2 = 0.18 So the expectation to get a triplet is 0.73
I would like to check if this is correct, and how to calculate expected win of doubles. P(2A)
I have tested with an script and I get : 137% of payback: 1P(2A) + 2P(3A)
Can you help me to build the correct combinatories and the expected payback ?