Probabilities

[cjb]

reel 1-thunderstruck

I'm going to try to put this here in as little space as possible. First, the letters will be going across in a line here but they are really up and down on the reel. Second, I=the thing that looks like a horn because I used H for hammer and I left the S for staff inspite of what someone thought it was. I can only say that I think there is only 1 Thor on each reel...
ITS x5, JQ9x3,ARJx2, IHSx5, QLIx4, LITx3, ILAx1, CJ10x2, K10Jx2, 10JIx2, RJQx2, HCJx2, TS9x2, LARx2, 9JQx2. The rest of these combinations came up once..SK10, JQC, HSK, J10I, IAJ, 10AJ, 10IA, JQL, SHC, AJQ, S9I. If anyone can figure it out, I will do the same for the other reels...

 

[KasinoKing]

cjb: That is probably just about enough data if it is 32 symbols on each reel.
For Tomb Raider I found 70 spins was enough data for reels 1 & 2, but when I got to 3,4 & 5 I had to do literally hundreds of extra spins looking for missing combinations. (Fun money mode, of course! )
What I mean by this is, for example: if I had Tiger in the top position with 4 different symbols underneath, but only 2 sets of data with Tiger in the middle - I knew I had to look for two more different reel positions with Tiger in the middle.
What really gave me a major headache was, for example, on reel 3 there are two identical strings of King-Tiger-Jack. This really throws a spanner in the works!

BTW no time today - but hope to finish reel 5 at the weekend...
Then NEVER AGAIN!

Someone else's turn...

 

[cjb]

more combinations

I know what you mean,KK, I was playing thunderstruck today and just for curiosity, was checking what I already had and found 3 more combinations just on reel 1..JIL, CSH, QCS. I can't even imagine how you put them together. I started to do that but kept kept having more than one that fit. All I know is for all that I did, there's only 1 Thor in all of it. Guess I'm not surprised....

 

[Zoozie]

Maybe there are other ways to do things. Someone taked about taking screenshoots while spinning. There is a very small chance this would work, but I actually think MG just make the spinning a constant non-realistic animation to simulate motion.

However, maybe there is a windows or c++ expert that somehow can decompile the code and figure it out. I did a very fast examination just to find it all binary in the windows installation directory. I never tried MG flash casino, but if you can play the 5-reel slots there, this could be another easy way to attack the problem by looking at the code. Any windows/microsoft/flash(or is it active-x) code geeks around here?

 

[managra]

Hello everyone. First post here, after some time lurking.

KK, i can confirm your data of reel 1 of Tomb Raider. Having done reel 5 of TR, i can also confirm that it is indeed a major headache trying to figure it out. Used excel with the sets of three symbols and then used columns with x's to work out the sequences between those sets.

I got 40 symbols for reel 5 of TR, consisting of:

Bonus Lara: 1
Wild: 1
Idol: 3
Map: 5
Lara: 4
Tiger: 5
Ace: 4
King: 4
Queen: 5
Jack: 4
Ten: 4

And the reel sequence is:

queen
king
map
tiger
ace
jack
tiger
king
map
idol
ace
queen
lara
ten
map
queen
wild
ten
idol
jack
queen
lara
map
jack
king
bonusL
ten
tiger
ace
lara
queen
king
tiger
jack
idol
lara
ace
ten
tiger
map
queen (duplicate from above)

I also got a Lara/Queen/Ten sequence. It didn't fit anywhere and after lots and lots of spins unsuccessfully trying to get a Queen/Ten/? sequence, i wrote it off as a goof on my part and the rest of the reel fell into place then. Let me know if anyone comes up with different results.

 

[KasinoKing]

Hello everyone. First post here, after some time lurking.

I also got a Lara/Queen/Ten sequence. It didn't fit anywhere and after lots and lots of spins unsuccessfully trying to get a Queen/Ten/? sequence, i wrote it off as a goof on my part and the rest of the reel fell into place then. Let me know if anyone comes up with different results.

Welcome to the posters club! Stick around - it's good here!

Reel 5 is definitely the hardest of the lot!
I too am using Excel and the difficulty faced can be clearly seen in the screenshot below.
On each string (which are definitely correct) there are two symbols top & bottom in red with yellow bars at the side. These pairs of symbols are repeated twice each which makes establishing the EXACT sequence of the symbols impossible.
However there will be a way to link them all up which will tell me for definite how many of each symbol there is in on the reel, and the total number.... (coming soon!)
This is all that's important at the end of the day.

(I'll see if I can link them to match managra's results!)

 

[KasinoKing]

EUREKA!!!

(I'll see if I can link them to match managra's results!)

Yep - spot on!

FINISHED AT LAST!!!

Now we can see why:
We get wound up that Idols often appear on reels 1 & 2, but that 3rd reel one is so rare to hit.
Same with Bonus Lauras - one on each reel, but less chance if hitting it on 3,4 & 5 than on 1 & 2.

But on the other hand, we can now get excited when we line up 3 Maps, Lauras or Tigers on the first 3 reels, because they have an even higher chance of hitting on reels 4 & 5!

Well now I know just what is involved in analysing slot reels, so if anyone wants me to do another one, just let me know...

... and as soon as your $250 hits my Neteller account I'll get right on it!
.

 

[managra]

Well, KK, interesting to see the analysis of all five reels. It's even worse than one expected. The only token of "generosity" is that there are a whopping two wild symbols on reel 1. Really clever how they have 40 symbols in reels 4 and 5. It also explains the many glorious near-misses with the screen filled with tigers or maps except for reel 1. Gives the player the feeling he almost got it but in reality he never has much chance to begin with. After having looked at your chart for a while, i'm now sorta amazed that i've had good sessions at all.

 

[Slotmachine]

Well done KK!

So there are 36556800 possible combinations...

So.. the odds of getting 5 bonus Lauras are ~ 1/150,000
Odds of 5 wilds on a winning line ~ 1/2,400,000

In fact, now it should be possible to calculate the expected return% of this slot. Of course, the treasure bonus needs to be factored in as an estimate averaging past wins - KK probably has some pretty good empiric data about that.

I think it would be a worthwhile achievement, as gambling forum achievements go, to calculate and publish the actual expected return % of some of the more popular Microgaming slots. Demystify them if you will..

Zoozie?

Cheers,
SM

 

[Pinababy69]

You guys make my head spin......really, lol. I have a pretty good mathematical, logical type of mind, but this is so far beyond me. But have at it, I'd love to read the results on the more popular slots.

 

[KasinoKing]

Well done KK!

So there are 36556800 possible combinations...

So.. the odds of getting 5 bonus Lauras are ~ 1/150,000

That's what I made it!

When I was in school (about a million years ago!) maths was my best subject, but the old braincells are a bit rusty these days. Does the below look right to you?

Seems about right: Chance of 4 Bonus Laras = 1 in 2,718, chance of 3 = 1 in 124.

(The 1's represent no Lara present, obviously)
.

 

[Zoozie]

I havent worked on the program the last weeks,but it is only a matter of putting some hours into it. Cracking the reels seemed to go slow, and I had lots of other stuff to do.

Still I would prefer to have reels with the right order of the symbols and not just how many times each symbol occours.

 

[KasinoKing]

I havent worked on the program the last weeks,but it is only a matter of putting some hours into it. Cracking the reels seemed to go slow, and I had lots of other stuff to do.

Still I would prefer to have reels with the right order of the symbols and not just how many times each symbol occours.

Only being able to see any 3 symbols at a time makes getting the sequence of reels 3 4 & 5 on Tomb Raider impossible. There was at least two ways of putting the strings together on each of those reels.

But I don't understand why you need that - it does not effect the probabilities.

 

[Zoozie]

Only being able to see any 3 symbols at a time makes getting the sequence of reels 3 4 & 5 on Tomb Raider impossible. There was at least two ways of putting the strings together on each of those reels.

But I don't understand why you need that - it does not effect the probabilities.

It is true that does not effect the payback%, but if I have the right order, I
would also be able to catch the maximal win using all lines... So just for completeness...

 

[cjb]

reel 1 thunderstruck

to the best fo my ability, this is reel1 of thundrstruck..
J
Q
C
S
H
C
J
10
I
A
J
Q
9
J
Q
L
I
T
S
9
I
H
S
K
10
J
I
L
A
R

 

[Zoozie]

Worked 2 more hours on the program today. I estimate there is 10 hours work left for me on it.

 

[Zoozie]

Program nearly finished. I wouldnt mind someone helping checking that I
calculate wins correct. It will just be a log of spins where I calculate
the win for a given spin result. Think I will take thunderstruck as first
case since I know that best.

 

[cjb]

calculating

Zoozie..what do you need...all 5 reels at one time per spin? I've got 1-4 done but 5 is being a problem.

 

[Zoozie]

Zoozie..what do you need...all 5 reels at one time per spin? I've got 1-4 done but 5 is being a problem.

For this testing it is not that important they are correct. I can just make
up reel#5 for the test.

 

[cjb]

thunderstruck reels

OK..here they are..
Reel 1--J-Q-C-S-H-C-J-10-I-A-J-Q-9-J-Q-L-I-T-S-9-I-H-S-K-10-J-I-L-A-R.
Reel 2--J-10-C-J-S-L-C-A-J-L-9-K-Q-J-T-9-R-L-S-H-9-J-I-A-K-J-9-L-I-C.
Reel 3--10-Q-I-A-10-K-C-Q-L-H-Q-10-J-Q-T-S-10-Q-H-L-K-10-Q-A-10-R-C-H-A-9.
Reel 4--10-J-C-K-L-I-9-K-C-R-A-S-H-I-A-10-9-T-L-J-K-9-A-I-H-S-K-Q-K-9.
Reel 5--J-H-10-A-Q-K-I-C-Q-J-C-H-S-I-10-A-L-J-H-I-R-S-L-T-C-S-J-Q-L-H-S-I-K-9-A-10-Q-K-S-L-10-C-A-9.

 

[Zoozie]

Thank you.

I have taken the program for a first test

I used your previous post of reel1 for ALL reels, and used your symbols. Tomorrow I will change it so I use your new reels for reel2-5.

The program takes approx. 5 minutes iterate through all spins. Whenever
I encountered a win higher than a previous, I printed it just for debugging purpose and fun. The program also handles win from scatters, but the 15 spins are not included yet. So the payback% should be even higher. We just need to set a fixed value for how much 15 free spins are worth (included respins). In this test I only played line#1, but this does actually not affect the payback I think. (Can test it later when I implement lines #2-9)

What is interesting is that the payback is 101.5%, but remember I used reel1 for all reels. Still this is an indication that we are on track, since the payback% is not way off.



************ start ************
J J J J J
Q Q Q Q Q
C C C C C
totalWin:100
iterations:1
payback:100.0
-------------------
I J J J J
T Q Q Q Q
S C C C C
totalWin:200
iterations:17
payback:29.41176470588235
-------------------
I I I I J
T T T T Q
S S S S C
totalWin:2000
iterations:446897
payback:0.783164800837777
-------------------
I I I I I
T T T T T
S S S S S
totalWin:10000
iterations:13406897
payback:0.9178910675602266
-------------------
************ finished ************
iterations:24300000
payback:1.0154430041152263

 

[Slotmachine]

Looks promising, Zoozie! The payout seems likely to go down just the right % once you figure in the final reels. Calculating the effect of the free spins feature is tricky...I guess you could just rely on empiric data about the average return of the feature (KK should have some data). Howeve, there must be a mathematical formula to figure in the exact effect the free spins feature has on the payout...?

It's way beyond my armchair math. I'm sure you can figure it out Zoozie. Maybe the Wizard could help, unless he's designed the slot and has some confidentiality agreement with MG..dunno. Or maybe our resident mathematician, Grandmaster?

Cheers,
SM

 

[Zoozie]

'Thunderstruck' is one of the most easy slots to calculate value of free spins for. I came up with very good estimate earlier. (45 times the bet size). I can change the value and see how much it changes the payout%. So this is not really an issue

In games like 'Harveys' it is a lot harder since you also have to estimate the weights of the win-multipliers and number of spins.

This first version of the program only works on thunderstruck like games. (ie. no symbols that only occours on 2 reels or wierd features like 'Secret Admirerer'). Actually it also would work on 'Cashville' since the symbols can be marked for if they can be substituted by wild.

However the real challenge now is to guess the reels. Eigther the hard way by watching spins and guess how to glue the reel-parts together, but we can never be sure we got it right this way. Another way could be by looking into the code(active-x or windows client), but this is beyond my skill. For the payout% only the number of times each symbols occours is needed, but for a true simulation it would be nice to have the actual reels.

 

[Slotmachine]

'Thunderstruck' is one of the most easy slots to calculate value of free spins for. I came up with very good estimate earlier. (45 times the bet size).

LOL. Damn, Thor's been nasty to me. My average is nowhere close to 45xbet. It's usually 5-15xbet...I'm sure I'm just on the wrong end of the variance. (My personal Thunderstruck payout% for the past 6 months is exactly 85%, not so good). I estimate I've done about 200,000 spins in the past 6 months alone, and probably about a million spins in all. Never hit 5 scatters...about 0.0013% probability of not hitting 5 scatters in one million spins...ah well.

Cheers,
SM

 

[Zoozie]

I have run the simulation again using the reels posted by CJB.
The value of the free spins is an extremely important parameter.
Here are the results for the value 0,40,45 times betsize.

total iterations:35640000
-------------------
free spins = 0 * bet
payback:0.7026915824915825
-------------------
free spins = 40*bet
payback:0.983237037037037
-------------------
free spins = 45 * bet.
payback:1.0183052188552189
-------------------

As you can see, using 45*bet as value for 15 spins at 3 times multiplier gives
a payout% just over 100%. But I have changed my mind after realizing how important
the parameter is and agree it is lower. This comes from the fact that without freespins the payout% is only 70%. I will think some more about it.

Still I need to check my program for bugs, but it passed the first tests.
I will modify it to collect some more data for now.

This is the template for thunderstruck:
(The forum formatter inserted a few spaces that shouldnt be there)

public static ReelSymbol thor = new ReelSymbol("T",true,false,false,new int[]{0,10,200,2000,10000});

public static ReelSymbol ram = new ReelSymbol("R",false,true,false,new int[]{0,2,5,20,500});

public static ReelSymbol staff = new ReelSymbol("S",false,false,true,new int[]{0,2,25,100,750});

public static ReelSymbol hammer = new ReelSymbol("H",false,false,true,new int[]{0,2,25,100,750});

public static ReelSymbol castle = new ReelSymbol("C",false,false,true,new int[]{0,0,15,100,400});

public static ReelSymbol lightning = new ReelSymbol("L",false,false,true,new int[]{0,0,10,75,250});

public static ReelSymbol horn = new ReelSymbol("I",false,false,true,new int[]{0,0,10,50,250});

public static ReelSymbol ace = new ReelSymbol("A",false,false,true,new int[]{0,0,10,50,125});

public static ReelSymbol king = new ReelSymbol("K",false,false,true,new int[]{0,0,5,50,125});

public static ReelSymbol queen = new ReelSymbol("Q",false,false,true,new int[]{0,0,5,25,100});

public static ReelSymbol jack = new ReelSymbol("J",false,false,true,new
int[]{0,0,5,25,100});

public static ReelSymbol ten = new ReelSymbol("10",false,false,true,new int[]{0,0,5,25,100});

public static ReelSymbol nine = new ReelSymbol("9",false,false,true,new int[]{0,2,5,25,100});

public static ReelSymbol[] reel1Symbols= new ReelSymbol[]{jack,queen,castle,staff,hammer,castle,jack,ten,horn,ace,jack,queen,nine,jack,queen,lightning,horn,thor,staff,nine,horn,hammer,staff,king,ten,jack,horn,lightning,ace,ram};

public static ReelSymbol[] reel2Symbols= new ReelSymbol[]{jack,ten,castle,jack,staff,lightning,castle,ace,jack,lightning,nine,king,queen,jack,thor,nine,ram,lightning,staff,hammer,nine,jack,horn,ace,king,jack,nine,lightning,horn,castle};

public static ReelSymbol[] reel3Symbols= new ReelSymbol[]{ten,queen,horn,ace,ten,king,castle,queen,lightning,hammer,queen,ten,jack,queen,thor,staff,ten,queen,hammer,lightning,king,ten,queen,ace,ten,ram,castle,hammer,ace,nine};

public static ReelSymbol[] reel4Symbols= new
ReelSymbol[]{ten,jack,castle,king,lightning,horn,nine,king,castle,ram,ace,staff,hammer,horn,ace,ten,nine,thor,lightning,jack,king,nine,ace,horn,hammer,staff,king,queen,king,nine};

public static ReelSymbol[] reel5Symbols= new ReelSymbol[]{jack,hammer,ten,ace,queen,king,horn,castle,queen,jack,castle,hammer,staff,horn,ten,ace,lightning,jack,hammer,horn,ram,staff,lightning,thor,castle,staff,jack,queen,lightning,hammer,staff,horn,king,nine,ace,ten,queen,king,staff,lightning,ten,castle,ace,nine};

public static int wildMultiplier= 2;



If anyone makes the template for another similar slot, I can run it through my program.
The 3 boolean are: isWild,isScatter,symbolCanBeReplacedByWild. You should be able to
figure it you if you know Thunderstruck allready.