about sticky wild

Hi all,
I saw an introduction of a feature called sticky wild here http://www.vegasslotsonline.com/features/sticky-wilds/. I am trying to simulate this feature in a program but it comes up with a huge payback. Could any one help to verify my way in computation make sense or not.

I first created a set of reels. I assume it is a single line game. My code will go through every single stops and evaluate the all wins. The payback is total win over total bet. Now I apply the same code for sticky wild feature in free game. Let's say there is probability (P) to trigger 20 free games and it won't be trigger again during free game. When there is any wild appearing on the screen, sticky the WIL in place until the end of the free game. Same code was used to compute the payback for the free game. But I find that the outcome does not make sense (more than 1500%). For other free game I evaluated before, I run the simulation for at least 80% of the cycle of the reel sets and I multiply the payback with the trigger probability and the number of average spin for the free game, that will give some a reasonable number (less than 100%). I did something similar for the sticky wild but I found that the wild stick on screen very fast so it ends up with full-wild screen if I simulate the game with full cycle (actually, I don't have to go that far, it almost fill up the screen after 100 spins).

I am not sure if it is correct to compute the pay for the sticky-wild free game as P(trigger) x free game pay (simulate full cycle) x average number of spin. But if I directly simulate the free game as

set win=0
set bet=0
for (int c=0; c<base_game_cycle; c++)
bet++
if (trigger free game)
for (int f=0; f<20; f++)
win += any win on the screen
if (any wild)
stick it on screen
end if
end for
end if
end for
payback = win/bet

above code will give me something less than 30% payback. So why the first method does not work?

Since you only get 20 spins on a free game, going through the full cycle - or even 100 spins - does not seem to make much sense.

Questions:
How many reels are there?
How many symbols are on each reel? (I am assuming each symbol on a reel has an equal chance of appearing on the pay line)
How many symbols on a reel are visible at any one time? (I am assuming three, and I am also assuming that if a Wild appears in any of the three positions, then it expands to occupy all three, including the pay line)
How many Wild symbols are on each reel?
Are there any cases where two Wild symbols are next to each other, or are separated by only one symbol (so you can end up with two Wilds on a reel being on the screen at once when the reel stops)?

This sounds like a state-case (Markov chain) situation, where each spin in a free game can be in one of eight states (assuming three reels - if there are five reels, there are 32 states):
No wilds
Reel 1 wild
Reel 2 wild
Reel 3 wild
Reels 1 & 2 wild
Reels 1 & 3 wild
Reels 2 & 3 wild
All three reels wild - in this case, all of your remaining spins will pay the maximum

Quote: ThatDonGuy

Since you only get 20 spins on a free game, going through the full cycle - or even 100 spins - does not seem to make much sense.

Questions:
How many reels are there?
How many symbols are on each reel? (I am assuming each symbol on a reel has an equal chance of appearing on the pay line)
How many symbols on a reel are visible at any one time? (I am assuming three, and I am also assuming that if a Wild appears in any of the three positions, then it expands to occupy all three, including the pay line)
How many Wild symbols are on each reel?
Are there any cases where two Wild symbols are next to each other, or are separated by only one symbol (so you can end up with two Wilds on a reel being on the screen at once when the reel stops)?

This sounds like a state-case (Markov chain) situation, where each spin in a free game can be in one of eight states (assuming three reels - if there are five reels, there are 32 states):
No wilds
Reel 1 wild
Reel 2 wild
Reel 3 wild
Reels 1 & 2 wild
Reels 1 & 3 wild
Reels 2 & 3 wild
All three reels wild - in this case, all of your remaining spins will pay the maximum

It is a 5 reels 3 rows game. Each reel has 60 symbols. No more than 1 WILD appear next to each other on the same column on a screen. I understand that it is a state problem. My question is any possibility that I can find the exact payback for the free game part by programming. Or if exact result is hard to find, what's the better way for simulation to get more precise result.

Quote: ThatDonGuy

Since you only get 20 spins on a free game, going through the full cycle - or even 100 spins - does not seem to make much sense.

Questions:
How many reels are there?
How many symbols are on each reel? (I am assuming each symbol on a reel has an equal chance of appearing on the pay line)
How many symbols on a reel are visible at any one time? (I am assuming three, and I am also assuming that if a Wild appears in any of the three positions, then it expands to occupy all three, including the pay line)
How many Wild symbols are on each reel?
Are there any cases where two Wild symbols are next to each other, or are separated by only one symbol (so you can end up with two Wilds on a reel being on the screen at once when the reel stops)?

This sounds like a state-case (Markov chain) situation, where each spin in a free game can be in one of eight states (assuming three reels - if there are five reels, there are 32 states):
No wilds
Reel 1 wild
Reel 2 wild
Reel 3 wild
Reels 1 & 2 wild
Reels 1 & 3 wild
Reels 2 & 3 wild
All three reels wild - in this case, all of your remaining spins will pay the maximum

I did some research on the Markov chain when you mention the state-case problem. I have a quick question. What is that "state" really refer to? Does it refer to a case when certain number of WILD(s) appearing on a line, so it is a special state of a line? What happens if I change the line game to a way game? For a way game, WILD appearing on any row (on the same column) will play the same role, so does the state refer to a "screen state", e.g. the following screens all refer to the same WILD state?

A W B B C
C C A A A
D D A A C

and

A D B B C
A W A A A
D D C B D

Quote: konglify

It is a 5 reels 3 rows game. Each reel has 60 symbols. No more than 1 WILD appear next to each other on the same column on a screen. I understand that it is a state problem. My question is any possibility that I can find the exact payback for the free game part by programming. Or if exact result is hard to find, what's the better way for simulation to get more precise result.

5 reels, with 60 symbols per reel, is 777,600,000 possible positions per spin. Since having a wild show up on a spin affects all subsequent spins, a "brute force" approach probably would take far too much time.

Since there are five reels, there are 32 possible states - one for each combination of "is there a wild in reel N or isn't there?". For example, "no wilds" is a state, as is, "Reels 2 and 4 wild," as is, "Just reel 5 wild," as is, "All five reels wild."

You may have to work backwards in order to figure this out.
Let F(N, W) be the amount expected to be won with N spins remaining and "wilds state" W (e.g. W = 1 if reel 5 is wild + 2 if reel 4 is wild + 4 if reel 3 is wild + 8 if reel 2 is wild + 16 if reel 1 is wild).
F(0, W) = 0 for all values of W as you cannot win anything on zero spins.
F(N, 0) = (what you expect to win on one spin starting with no wilds) + ( (probability of getting no wilds on the spin) x F(N - 1, 0) + (probability of getting a wild on just reel 5) x F(N - 1, 1) + (probability of getting a wild on just reel 4) x F(N - 1, 2) + (probability of getting a wild on reels 4 and 5) x F(N - 1, 3) + ... + (probability of getting a wild on reels 2, 3, 4, and 5) x F(N - 1, 30) + (probability of getting a wild on all five reels) x F(N - 1, 31).
F(N, 17) = (what you expect to win on one spin starting with wilds on reels 1 and 5) + ( (probability of getting no extra wilds on the spin) x F(N - 1, 17) + (probability of getting a wild on reel 4) x F(N - 1, 19) + (probability of getting a wild on reel 3) x F(N - 1, 21) + (probability of getting a wild on reels 3 and 4) x F(N - 1, 23) + ... + (probability of getting a wild on 2, 3, and 4) x F(N - 1, 31).
Do this for every wild state from 0 to 31, starting with N = 1.
Note that F(N, 31) = whatever you get for having wilds in all five reels + F(N - 1, 31).
Work backwards until you calculate F(20, 0), which is your starting point.