Probabilities

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...
 
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! :D )
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! :eek:

Someone else's turn... :rolleyes:
 
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....:confused:
 
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?
 
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.
 
managra said:
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! :thumbsup:

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!) :cool:
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!)
 
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EUREKA!!!

KasinoKing said:
(I'll see if I can link them to match managra's results!)
Yep - spot on! :thumbsup:

FINISHED AT LAST!!! :D

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. :mad:
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! :thumbsup:

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! :rolleyes:
.
 
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.
 
Well done KK!:thumbsup:

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
 
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. :)
 
Slotmachine said:
Well done KK!:thumbsup:

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)
.
 
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.
 
Zoozie said:
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.
 
KasinoKing said:
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...
 
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.
 
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
 
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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
 
'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.
 
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Zoozie said:
'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
 
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.
 
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Zoozie said:
'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

33.5 or thereabouts in my test last year if memory serves.
 
Slotmachine said:
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). However, there must be a mathematical formula to figure in the exact effect the free spins feature has on the payout...?
SM
Sorry I can't help with Thunderstruck - I rarely play it cos it always MURDERS my bankroll :(

As for the free-spins payback - surely you can just work out the average return from 15 normal spins & then just multiply by 3?
Then, also knowing the odds of hitting free spins, you can calculate the odds of a re-trigger and the resulting extra return.

Zoozie, I haven't the faintest idea what you talking about with your maths, but it looks mighty impressive stuff to me! Well done! :notworthy
 
"As for the free-spins payback - surely you can just work out the average return from 15 normal spins & then just multiply by 3?"

The word 'normal' in your setence is the problem. We dont know what
the return% is before we know how much the free spins are worth.
I probably just need to think about it.

There also is the lazy way just by brute force. Playing a gazillion random spins
with the correct freespin feature implemented. Maybe the program can run tomorrow while I am at work. Nothing more fun than playing thunderstruck with
play-money mode AND ascii graphics on autospin
 
After 145M spins the payback seems to be between 95.1% and 95.4% and staying in this interval. So there is no reasons to burn brain cells trying to figure out how much the free spins are worth, just let the program run for some hours and you will have 4-5 digits correct (95.36% etc).


I have attached the program if anyone interested in seeing the simulation. (and see how long it takes before you hit the 5 Thors during free spins).

0) You need to have Java installed. But you probably have this allready even though you dont know it.
1) Unzip
2) click 'start_simulation.cmd'

Every few minutes it will print the current state of the simulation. (payback%)

Zoozie
 
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It does not work for me. :(
java.lang.NoClassDefFoundError: SlotTestCaseRunner
Exception in thread "main"

I would be really interested in seeing this work.
 
I had a thought on calculating the free spins multiple. Ignore the fact the slot may or may not be "weighted":

If you start with $9 million balance, do 1 million "ordinary" spins at say $9 (IE: taking the 3x free spins multiple out of the equation) take the balance left at the end & divide this amount by 1 million (no. of spins), and you have the average return per spin. Then multiply this by 45 (15 spins x 3x multiplier).

That gives you the total average amount won in the bonus round, so divide by 9 (wager amount) and you have the average multiple which you can stick back into the program (ie 35x).

Probably best to do it over 10 million spins or even 100 million if poss.

I think thats right anyway. There may be a simpler way - its late :D
 
Very impressive, Zoozie. I am working on the template of the reels for Harvey. So far almost reel 1 finished; ran into a snag with one (valid) group of 3 that i cannot seem to fit in anywhere. I was interested in this since the so-called "scatters" really are just cheap stuff but the bonus round can be very rewarding. Of course, the two occasions when i played for real money, i never saw a bonus round :( If i ever manager to finish this, do you want me to post something?
 
Managra:
This version can not handle "Harvey's". It is too special and does not fit into same template as ThunderStruck.
1) scatters must be alligned on left reels
2) champagne on reel 2 and 4

I could make the program know this template but it would take some hours.
And from my experience the feature multipliers are heavily weigthed (you rarely get *25). So I will not be able to simulate it 100% like thunderstruck where there was no weights involved.
 
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I had not expected my program to run that fast. After 1 hour the maximum
value for the 'int' was reached.

This happens after 2147483647 spins! (2^31 -1)

So it is not really important unless you want to find the payback% with 4 digits. The program still shows how fast your money converge towards the payback%, and that there is no way to get back on tracks again :)

But it was CERTAIN that the payback% is between 94.9% and 95.0%.

It will only take 1 minute to 'upgrade' the int to long in Java but will need
to attach the program again in a new post. Think I will improve it with better logging and more lines and maybe more slots if someone makes the template. Now the program is made I should be able to make these changes fast.
If you have any ideas for improvement/logging, just tell me.
 
Zoozie, in my opinion you're turning out to be a star on this forum and I hope you stick around.

Nice to see some positive and informed action on a rather esoteric subject, and I know that you will enhance the contributions frequently made here by experts like Grandmaster. WTG!
 
jetset said:
Zoozie, in my opinion you're turning out to be a star on this forum and I hope you stick around.

Couldn't have said it better. I'm glad this thread is getting sustained interest and people are busy analyzing the slots :)

When we play BJ or VP, we know what the return% is. It's only fair that we slot players can make some informed decisions, too.

I find it comforting that T'struck is close to the 95% mark (even though I know this is terrible from a BJ player's point of view), I was afraid it might be a lot lower, like 91-92%.

Many thanks Zoozie :notworthy for proving that practically any gambling related question can be answered right here in the CM forum!:thumbsup:

Cheers,
SM
 
*blush* - thanks for the kind words.

I have been running the test over and over all day and they all converge to the same result. (as they should do mathematically, you cant beat the casino)

Payback% = 95.0% +- 0.1%. (94.9-95.1).

However this result is only valid IF we got the reels correct and there are no bugs in my program. The last part I can check myself again.

Anyone downloaded it and started the simulation?
In the start it will log lots of spins and you can check that the
pay involved is correct. (it only play 1-line). Just stop it and start over. (and see how long it takes before you hit the jackpot)

Zoozie
 
This is new version now using all 9 lines. Same result as before (as expected).

1) unzip all files to a new folder.
2) click 'start_simulation.cmd'

I only have one question. Are the reels 'looped'? (as going in a circle.)
Ie. if a reel is like this : 1,2,3,4,5,6,7 (7 different symbols, each only once)

is 7,1,2 and 6,7,1 then a 'legal' spin?

In my program I have assumed this, but it would not take long to fix if I was
wrong.

Zoozie
 
Zoozie said:
Yeah. My computer can do 6M spins/second.
So if you play 0.09$ pr spin, your hourly expected loss would be 1.6M $ at 95% payback!

Maybe I should sell this autoplay program to the casinos :)

LOL.. Microgaming might send you a big $$$ check just for not doing this sort of thing anymore:D

Your program is definitely eye-opening. Playing 200 million spins in a matter of minutes....hitting the jackpot once...well, it sort of makes me wonder...It's a deep look into the metaphysical nature of slot machine gambling....and into the quantum and probabilistic nature of life, the universe and everything...

Instead of gambling for years to come, I could just let your program run for 10 minutes, see how I did, then move on to other things..

Cheers,
SM
 
Actually I was wrong (sorry)

It is you expected loss each MINUTE that is 1.6M$.
Hourly rate is 97M$.

Not that it makes it any better......

I agree it is kind if depressing to see the simulation.. Just no way to get back
up after allready 100000 spins.

I got an idea for next modification. I will also log whenever your payback%
makes a new record, so we can see how late this can happen.

Edit: new program attached with this improvement
 
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Simmo! said:
Zoozie - did you include the formula for calculating the free spin probability as mentioned last night?

No. There really is no need. But I can have the program calculate the
avg. win for a feature. I will do that tomorrow. I will of course make
possible respins wins still count as the original respin wins.

This program is an random spin autoplay simulation that also emulates the
free spins and *3 multiplier. Just let it run for some hours if you want to
see if the excact payback is 95.04% or 94.99 %. The longer it runs, the more
digits you will see not changing.
 

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