243 Variable Reels

Hello, I am wondering if anyone could help me with a question about a 243 way slot specifically where each reel is not set, i.e each reel widow is generated every spin by sampling without replacement from an array. I am trying to calculate the rtp for a slot machine with this design, but my simulated rtp is not matching the theoretical rtp I calculated. I believe where I am going wrong is in my calculation for the 3 and 4 of a kind total hit calculation. For the three of a kind total hit calculation equation I used is:
Total hits=n(s,1)*n(s,2)*n(s,3)*x(s,4)*( (x(s,4)-1)_P_2/ (t(4)-1)_P_2) *v^3 where
• Let v = number of visible rows on the machine.
• Let n(s,r) = number of times symbol s or a wild appears on reel r.
• Let t(r) = Total length of reel r
• Let x(s,r)=t(r)-n(s,r)
• Let n_P_k= k permutations of n

Could anyone comment if I am doing this correctly or what I have done wrong. Thank you.

Quote: agb0808

Hello, I am wondering if anyone could help me with a question about a 243 way slot specifically where each reel is not set, i.e each reel widow is generated every spin by sampling without replacement from an array. I am trying to calculate the rtp for a slot machine with this design, but my simulated rtp is not matching the theoretical rtp I calculated. I believe where I am going wrong is in my calculation for the 3 and 4 of a kind total hit calculation. For the three of a kind total hit calculation equation I used is:
Total hits=n(s,1)*n(s,2)*n(s,3)*x(s,4)*( (x(s,4)-1)_P_2/ (t(4)-1)_P_2) *v^3 where
• Let v = number of visible rows on the machine.
• Let n(s,r) = number of times symbol s or a wild appears on reel r.
• Let t(r) = Total length of reel r
• Let x(s,r)=t(r)-n(s,r)
• Let n_P_k= k permutations of n

Could anyone comment if I am doing this correctly or what I have done wrong. Thank you.
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I think Ask the Wizard #305 can help you. See the second question on the page.

This question is a little different then the Ask the Wizard#305 as the reels in that question are preset where in my question the reels showing are generated based off a distribution.

Quote: agb0808

Hello, I am wondering if anyone could help me with a question about a 243 way slot specifically where each reel is not set, i.e each reel widow is generated every spin by sampling without replacement from an array. I am trying to calculate the rtp for a slot machine with this design, but my simulated rtp is not matching the theoretical rtp I calculated. I believe where I am going wrong is in my calculation for the 3 and 4 of a kind total hit calculation. For the three of a kind total hit calculation equation I used is:
Total hits=n(s,1)*n(s,2)*n(s,3)*x(s,4)*( (x(s,4)-1)_P_2/ (t(4)-1)_P_2) *v^3 where
• Let v = number of visible rows on the machine.
• Let n(s,r) = number of times symbol s or a wild appears on reel r.
• Let t(r) = Total length of reel r
• Let x(s,r)=t(r)-n(s,r)
• Let n_P_k= k permutations of n

Could anyone comment if I am doing this correctly or what I have done wrong. Thank you.
link to original post

For starters, there are v^5 ways of getting a three of a kind (243 ways for three lines). Every line is independent, so you just need to multiply the fraction of symbols per column for the first three reels/columns and divide by v^5. No combinatorics are needed.

Maybe I don't understand what you mean by 'three of a kind total hit calculation' - is it expected number of trips on each spin?

The probability of trips on any one line is simply n(s,1)/t(1) * n(s,2)/t(2) * n(s,3)/t(3) not exclusive of quads and quints.

The probability of quads on any one line is n(s,1)/t(1) * n(s,2)/t(2) * n(s,3)/t(3) * n(s,4)/t(4), etc.

The expected number of trips on each spin exclusive of quads and quints is obtained by subtracting off those probabilities from the probability of nonexclusive trips and multipied by v^3