Probabilities

[Slotmachine]

I would expect the length of the reel to be a power of 2, either 64 or 128.

From what I've seen, reel length of 28 seems to have appeared in several other "cracked" 5 reel slots. Simmo! had counted 30 symbols on thunderstruck.

I'm sure there's some math behind your reasoning. What is it?

Cheers,
SM

 

[Simmo!]

staff? I always called it "Thor's cock"

 

[Simmo!]

This is harder than I expected!
Got a bit stuck on reel 1 - nearly there though!
Reel 2: Think I cracked it! Got chain of 28 symbols that link end to end!
Reel 3: Made my head explode! There seems to be 4 Tigers which makes it very confusing. Have got 34 symbols so far, but I think I've gone wrong as I have 2 chains & the ends don't match!
That's 3 hours already I'm taking a break!

AH yes...I forgot to mention how long it takes...sorry I actually emailed Microgaming to get the layouts but (unsurprisingly) never even got a reply.

 

[Zoozie]

I have started the programming on the MG 5-reel slot simulator, making a design so each slot is a 'template' which means once the program is finished, you just need the make the slot-template to analyze another slot. But I still need a lot of work on it - just started.

This first version of the simulator will not be able to handle weigthed reels. Anyway the probabilities would be next to impossible to pry out of the slots unless you write down several 1000's of spins... So the first run of the program might show the idea is 'doomed' without using weights of the reels, as it could show a payout of 200% etc. because the model is too unrealistic.


The program will be able to handle:
1) Scatters bonus
2) Wild/wild multiplier
3) Symbols can be flagged if they can be replaced by wild. (ie. some symbols can not be substituted by wild in cashville)
4) Number of lines played (actually this does not seem important when the reels are not weigthed. think about that...)

Here are the problems I currently face:
1) Getting non free-spin bonus games like in cashville (scatters) or Wasabi-San(fishies) needs a paytable. A good (and only?) solution will to have hardcoded
the average wins. (ie. for 3,4 or 5 fish for Wasabi-San). Actually I dont know if the number of scatters in cashville gives higher bonus rounds... never gotten 4 scatters there. So I need the average(bet multiplier) wins here for the slot template. If the average value is correct, the simulation will be 100% correct and not an approximation.

2) Value of the free spins. Ie. This is more difficult and I am open for ideas. Problem is ability to get retriggers for some games. I suggest free spins value is: freespins*bet*win-multiplier. So for thunderstuck this is 45*bet value. This estimate comes from using 100% payback and no-respins. The first assumption is an too high and the second too low. If someone can give the average value of free-spins (including re-spins) this will again be an excact and not an approximation.

I think what I descripted here should cover everything. Games like 'Loaded' where you select spins/multiplier is actually identical to Thunderstuck. You just need the average wins. (it is obvious the avg. wins is identical wether you choose 12,16 og 24 spins)

Anyone knows for sure that the reels are 'looped' in MG 5 reel slots?

Zoozie

 

[Slotmachine]

This first version of the simulator will not be able to handle weigthed reels. Anyway the probabilities would be next to impossible to pry out of the slots unless you write down several 1000's of spins...

This is true. I don't think the 5-reel multiline video slots are weighted, but can't be sure of course.

Quote from the Wizard:
"Multi-line slots, both with physical as well as video display reels usually do not have weighted reels. Otherwise the process is the same as above. In video display slots representations of actual reels are used, which can be quite large, 60 symbols or more."

4) Number of lines played (actually this does not seem important when the reels are not weigthed. think about that...)

True. The expected return % is the same no matter how many lines you bet on. (EXCEPT of course for those machines that have progressive or otherwise bigger jackpots on certain lines, usually requiring max lines bet)

1) Getting non free-spin bonus games like in cashville (scatters) or Wasabi-San(fishies) needs a paytable. A good (and only?) solution will to have hardcoded the average wins.

True again. Impossible to know the math behind the bonus game. So it's just going to have to be an estimate of averages based on empiric data.

2) Value of the free spins. Ie. This is more difficult and I am open for ideas. Problem is ability to get retriggers for some games. I suggest free spins value is: freespins*bet*win-multiplier. So for thunderstuck this is 45*bet value. This estimate comes from using 100% payback and no-respins. The first assumption is an too high and the second too low. If someone can give the average value of free-spins (including re-spins) this will again be an excact and not an approximation.

Assuming the free spins are using the same reels as normal spins, there should be no need for approximation, the free spins factor should be mathematically, accurately incorporated into the formula? I think... I couldn't do it as I don't know the math myself, but it should be possible?

I think what I descripted here should cover everything. Games like 'Loaded' where you select spins/multiplier is actually identical to Thunderstuck. You just need the average wins. (it is obvious the avg. wins is identical wether you choose 12,16 og 24 spins)

True, the expected return is the same, doesn't matter which free spin combo you pick in Loaded.

Anyone knows for sure that the reels are 'looped' in MG 5 reel slots?

If the Wizard is right in saying the video slots are based on virtual representations of reels, then the reels will be "looped" as you say. It's our best guess anyway.

Thanks Zoozie, good stuff

Cheers,
SM

 

[Zoozie]

4) Number of lines played (actually this does not seem important when the reels are not weigthed. think about that...)

True. The expected return % is the same no matter how many lines you bet on. (EXCEPT of course for those machines that have progressive or otherwise bigger jackpots on certain lines, usually requiring max lines bet)

Actually there could be a difference IF the reels are weighted. Ie. if
it is a common situation(high weight) where a wild symbol is in left upper corner, then some lines should be better than others. Line 1 will not benefit from this, but line 3(or is it 2) and 5 (or is it 4) will benefit from this. Maybe I wrong, but I have been wondering for this for some time, and this is my conclusion.

 

[mgibson99]

With all due respect, I'm not exactly sure what the purpose of this thread is. By your own admission, you are not a math whiz, but yet you are trying to figure out what is obviously a very complex mathematical problem. Haven't some of the math/probability gurus already analyzed the slots and isn't this information already available?

 

[Zoozie]

Current there does not seem to be this kind of information on MG slot anywhere.

If the tests shows gives a payout close to what we know, then it very
strong evidence the slots are not weigthed. And we can simulate them. I think that is the goal of this.

If they seems to be weigthed (ie. the test gives way wrong result). Then we learned that at least, and we can probably not go no further. There is described how to slot analyze(find reel probabilities) weighted reels on wizardofodds, but it is tedious. And it someone does do this, it can be put into a program also.

 

[Slotmachine]

With all due respect, I'm not exactly sure what the purpose of this thread is. By your own admission, you are not a math whiz, but yet you are trying to figure out what is obviously a very complex mathematical problem. Haven't some of the math/probability gurus already analyzed the slots and isn't this information already available?

Just for fun, baby, just for fun

Cheers,
SM

 

[Slotmachine]

Actually there could be a difference IF the reels are weighted. Ie. if
it is a common situation(high weight) where a wild symbol is in left upper corner, then some lines should be better than others. Line 1 will not benefit from this, but line 3(or is it 2) and 5 (or is it 4) will benefit from this. Maybe I wrong, but I have been wondering for this for some time, and this is my conclusion.

A pleasantly futile task, analyzing slot machines

That's right, there would be a difference, but in my opinion this is unlikely. I don't see how the software maker or the casino would benefit from such weighting. A non-weighted slot is simpler to program = cheaper to produce = more efficient business, therefore according to my (modest) logic weighting is unlikely. I think a weighted 5-reel 9-line slot would actually be a lot more complicated to program, while achieving the desired return%? Anyway, which line would you weight, and why? With 24,300,000 possible natural outcomes, weighting would just complicate matters for the programmer...

The purpose of a (single line) weighted slot, the way I see it, is to produce a maximum number of "almost-big-hits" to excite the player, with a limited number of possible symbols, as the 3-reel single-line slot might have just say 30^3=27,000 possible combinations so the jackpot would happen too often without weighting. Also a single-line 3-reel weighted slot is probably dead simple to program. In a five-reel, multi-line slot, the "near-bigwin" effect can be achieved without weighting because there are a lot more natural possibilities for a near-miss combination.

It would also be unfair to weigh a certain line without informing the player. This would add an element of predictability to a random game and give one player an advantage over the other player, and this is not a characteristic of fair casino games (VP and BJ etc skill factor notwithstanding). The weighted single line slot is fair, because it's the same line, for everyone. The payout-weighted progressives are fair because they tell you which line has the biggest possible payout.

I guess what I'm saying is it would not make much sense to weight a slot like that. What's the big idea? Also, the Wizard says multiline slots are usually not weighted, so I think it's a fair guess they're not weighted.

Cheers,
SM

 

[KasinoKing]

I would expect the length of the reel to be a power of 2, either 64 or 128.

I'm pretty happy that my reel 2 layout is complete at 28 symbols. Of course it could be 56 or 84 symbols with the same pattern repeated!
Mind you - that would not effect the probability of each symbol hitting - the whole object of the exercise.

Zoozie: I would not get too tied up in knots trying to work out the overall payout % of the slot. I don't think anyone here is too concerned about that.

All I want to know (and I'm sure others do to) is what is the probability of hitting certain combinations. e.g. What are the odds of hitting 3, 4 or 5 scatters, the jackpot!, etc...

All we need to work this out is the quantity of each symbol on each reel, then it's fairly simple maths... (for some - not me! )

 

[Zoozie]

All I want to know (and I'm sure others do to) is what is the probability of hitting certain combinations. e.g. What are the odds of hitting 3, 4 or 5 scatters, the jackpot!, etc...

Actually that can be calculated that quite easy.

For the jackpot it is '1 to 24.3M' given there are 30 symbols on each reels and it must be a specific bet-line. I know MG have written somewhere that chance for jackpot is 1 to a 'few' millions. Why these numbers are different I dont know.

For 5 scatters: They can be placed in 3*3*3*3*3=243 different positions.
So P(5 scatters)= #positions/#total=243/24.3M= 100000

For 3 and 4 scatters you need a little more work, but it is the same method. I can post it later unless someone else wants the excercise

 

[GrandMaster]

I'm pretty happy that my reel 2 layout is complete at 28 symbols. Of course it could be 56 or 84 symbols with the same pattern repeated!
Mind you - that would not effect the probability of each symbol hitting - the whole object of the exercise.

Fair enough, if you publish what you the layout of the reel is, it is easy to check whether it is correct or not.

 

[Slotmachine]

Answers to some of the questions were posted in the beginning of this thread:

....24,300,000 combinations.....That would make it 1:2,700,000 odds for 5 Thors (if just one Thor per reel)

....For the 5 Sheep, provided just one per reel, would I be right in calculating that the possible combinations of 5 Rams = 3^5=243. That would make the odds exactly 1:100,000 for hitting those 5 Rams.

..the number of possible combinations for 3 rams would be 8*3^3*30^2=194,400 -making the odds of hitting the free spins 1:125

..although I wasn't quite sure if I'd got the last one correct.

N.B. Jackpot in Thunderstruck can be won on any line.

oh, and KK, that's actually what I'm after - the expected return% of the whole slot! All we need is the reel data. How many of each symbols on each reel. Then it's just a big calculation - just the reel data is needed, then some number crunching and we've got it.

Cheers,
SM

 

[vinylweatherman]

Not Futile

The total % for each slot would be useful in knowing if one is better than another to play. Also, the variance can be calculated - another useful value from which "risk of ruin" calculations can be done. Some slots seem to have contributions mainly from improbable high wins whereas others have many lower value wins. Thunderstruck is a high variance game, as the players who get their bankroll eaten quickly can testify to. Cabin Fever is lower variance, and the "Double Magic" slots with only 800/1600 jackpots can make your money last for ages.
I expect the information will be useful in deciding which slots are best value in playing off WR on slots bonuses.
I am sure MG do not want to make this easy, and it is interesting what might be revealed! (Possibly something we are not supposed to know - perhaps the slots run as a "prize bingo" with the probabilities nothing to do with the symbol distribution).

 

[cjb]

50 spins on thunderstruck

I did 50 spins on thunderstruck and have them on a spreadsheet. I hate to post them here because it would take up so much room..I did see some repeating of symbols in each real but don't really have the know-how to put it together. Any one want me to send it to them to look at? I would be curious now that I saw it to see what others think

 

[Holly]

The only times I played thunderstruck it absolutely wiped me out like no one's business. I stick to cosmic cat to decrease my variance. I think the lower the jackpot the lower swings right?

 

[Zoozie]

Ram calculations.(Thunderstuck, 1 ram on each reel, 30 symbols on each reel, 15 free spins on feature)


P (Excacly 3 rams) = 3/30*3/30*3/30*27/30*27/30*10=0.0081
P (Excacly 4 rams) = 3/30*3/30*3/30*3/30*27/30*5=0.00045
P (Excacly 5 rams) = 3/30*3/30*3/30*3/30*3/30*1=0.00001
The last number (10,5,1) is the multiplier for how many ways the rams(or non rams, which is easier) can be distributed amoung the reels.

P (free spins) = P(Excacly 3 rams) + P(Excacly 4 rams)+P (Excacly 5 rams)= 0.00856 ~ (1 to 117)


Chance of not getting any respins during a feature is: (1-0.00856)^15 ~ 0.8790155
Which makes chance of at least 1 respin:1-0.8790155~0.12098

These data seems to be consistent with my observations. So I find it very likely there only is 1 ram on each reel and that the number of symbols on each reel is 30 or very close.

 

[KasinoKing]

All I want to know (and I'm sure others do to) is what is the probability of hitting certain combinations. e.g. What are the odds of hitting 3, 4 or 5 scatters, the jackpot!, etc...

Actually that can be calculated that quite easy.

For the jackpot it is '1 to 24.3M' given there are 30 symbols on each reels and it must be a specific bet-line. I know MG have written somewhere that chance for jackpot is 1 to a 'few' millions. Why these numbers are different I dont know.

(And for Grandmaster) So far my early indications are that there are different numbers of symbols on each of the five reels on Tomb Raider - which is quite possible. (Other slots, like ThunderCrap, could well have equal numbers per reel). As long as we know how many per reel & how many of each symbol per reel we can still work out the probabilities.
Hope to do another couple of hours this evening & will report back later...

 

[Slotmachine]

So far my early indications are that there are different numbers of symbols on each of the five reels on Tomb Raider - which is quite possible.

Somehow that seems unlikely, but it'll be interesting to see how it turns out!

Cheers,
SM

 

[Slotmachine]

I expect the information will be useful in deciding which slots are best value in playing off WR on slots bonuses.
I am sure MG do not want to make this easy, and it is interesting what might be revealed!

I agree

I did 50 spins on thunderstruck and have them on a spreadsheet. I hate to post them here because it would take up so much room..I did see some repeating of symbols in each real but don't really have the know-how to put it together. Any one want me to send it to them to look at? I would be curious now that I saw it to see what others think

You could just post it as text:

AKTHR (Ace, King, Thor, Hammer, Ram)
9JASC (9, Jack, Ace, Staff, Castle)
RALQJ (Ram, Ace, Lightning, Queen, Jack)

etc...50 times

it would be good, because then it would be open source data. maximizing the efficiency of this project

Cheers,
SM

 

[KasinoKing]

Drum roll please!!!
I'm 99.9% sure I've cracked reel 1 on Tomb Raider!
I developed a better way of doing it by sorting the data on an Excel spreadsheet. Still reckon it will take about 5-6 hours to do a complete slot though...

Reel 1: 2x10, 2xA, 1xBonus Laura (scatter), 4xIdol, 3xJ, 2xK, 2xLaura, 1xMap, 3xQ, 2xTiger, 2xWild. Total 24 symbols.
This is the layout:-

I Idol
K King
M Map
T Tiger
I Idol
Q Queen
J Jack
L Laura
10 Ten
J Jack
I Idol
10 Ten
Q Queen
W Wild
B Bonus Laura
K King
A Ace
I Idol
T Tiger
L Laura
J Jack
W Wild
Q Queen
A Ace
I Idol } same I K as at the top
K King}

If anyone would like to check it - be my guest - I've had enough of this for today!

 

[Slotmachine]

Good going KK! :notworthy

With only 24 symbols, it should make a lot of things easier. The only problem with Lara is that there's that treasure bonus round, which effectively keeps us from being able to calculate the expected return. However, we'll still get agood estimate from empiric bonus data.


Cheers,
SM

 

[KasinoKing]

Reel 2 is definitely 28 symbols, but reel 3 is melting my brain again!
Trouble is, there are 4 places on it with the same pair of symbols.
Trying to fit the strings together is like the blinking Crypton Factor!

Enough for today. Zzzzzzzzzzz...

 

[KasinoKing]

Jeeeezus H Christ!!!!
This reel analysis is way, way harder than I thought it would be!
Each successive reel is harder that the previous one!

But still - FOUR down - just one to go...
I'm 99.99% certain I have the numbers of symbols per reel on Tomb Raider so far:-

Reel 1: 26
Reel 2: 28
Reel 3: 34
Reel 4: 40
Reel 5: Early indications = 34. To be continued....

I need to sleeeeeeeeeeeeeep!