Cracking the slot reels - Here you go!

[KasinoKing]

What a fantastic thread, how did I miss it?
This maybe the most important thread ever posted here...

Absolutely agree (with all of your post - no need to quote the whole thing)!

The stuff these guys are producing is incredibly interesting.
If I only had half a clue what all those figures meant - it might even be useful!

Only kidding guys! Excellent work - keep it up! :notworthy

KK

 

[gerilege]

The reelpositions are the accual position on the reels, and for all three symbols not the middle symbol. A zero (0) would mean that the reel is in its first possition showing the three first symbols from the top. First number is reel 1 from top to bottom, next is second reel and lastly the third number is the final reel.

I also have the data for the symbols on each reel, however this data is meaningsless and why I dropped it in the text file. I can regenerate the text files with more data if someone would have interest in this. I can also set a flash casino to do 10.000 spins, however the data from my spins clearly shows that the reels are weighted.

I hope I got it right.

Reel2 is:
Pink,Fries,Red,Wheel,Pie,Coffee,Wild,Yellow,Hamburger,Bottle,Dices,Scatter

Weights are:
0.0235,0.1819,0.033,0.0255,0.0465,0.0245,0.059,0.054,0.2219,0.2244,0.056,0.0495

I'm almost sure that this is for the middle symbol. Which means that 0.0495 means that the scatter is the middle symbol on reel1 with 0.0495 probability. Because if each number would mean the top symbol, it would mean that the scatter is visible on second reel with 0.2244+0.0056+0.0495 probability, which is too high I guess. 0.056 + 0.0495 + 0.0234 seems more reasonable for the real payout.

 

[steinhaug]

You are correct, I see it now. Since I have been working on the % of reel positions I havn't really needed to check this (I am not calculating % payout). All the numbers (reel positions and symbol layout) are served from the MG server, so it has to be correct. This in turn means:

Reel 2 has the following symbols from top to bottom:
reel symbol 0: Pink lady with car
reel symbol 1: French fries
reel symbol 2: Red man with truck
reel symbol 3: Burning wheel with start flag
reel symbol 4: Pie slice
reel symbol 5: Cup of coffe
reel symbol 6: Wild
reel symbol 7: Yellow man with car
reel symbol 8: Hamburger
reel symbol 9: bottle and cup
reel symbol 10: Dices
reel symbol 11: Scatter

Since the highest reel position on reel 2 is 10, this means that the reel would display the symbols from position: 9,10,11. This confirms that the position is for payline 1 (the middle symbol) and not for payline 3 which I assumed.

 

[Zoozie]

I guess I have it now. After experiencing problems with the scatter payout I realized that if the reels are weighted, winlines DO matter. You can't simplify the analysis to one winline any more.

Sorry, I should have told you this after our PM mails. But it raises an interesting question. Payout now depend on number of lines play if same weights are used. (for scatter win this does not matter though, only for line wins)

Can you make a payout% for 1,2,...,9 lines played?

But I ran your program and it say 101% payout for 1 line played. Since I do not believe this really, could it mean that other weights are used when playing 1 line? Or generally 9 different weights for depending on you play 1 or 9 lines.

MG really made it hard for themself by creating their rigged video slots.

So Kimms, I have a small wish. Maybe you could make another sample of "5 reel drive" with only 1 line played? We can then see if the weights are different.

Gerilege: You programming in java now, or are you still using a C++ to Java translater?

 

[gerilege]

Sorry, I should have told you this after our PM mails. But it raises an interesting question. Payout now depend on number of lines play if same weights are used. (for scatter win this does not matter though, only for line wins)

Can you make a payout% for 1,2,...,9 lines played?

But I ran your program and it say 101% payout for 1 line played. Since I do not believe this really, could it mean that other weights are used when playing 1 line? Or generally 9 different weights for depending on you play 1 or 9 lines.

MG really made it hard for themself by creating their rigged video slots.

So Kimms, I have a small wish. Maybe you could make another sample of "5 reel drive" with only 1 line played? We can then see if the weights are different.

Gerilege: You programming in java now, or are you still using a C++ to Java translater?

I'm programming now in JAVA. I believe that the one line result calculationis incorrect in analyze. I will check it in a few minutes with analyze1.

 

[steinhaug]

MG really made it hard for themself by creating their rigged video slots.

Assuming fair play that is... If you were to end the player at 95% overall payout the weighting becomes far simpler... there goes mr. conspiracy again,

So Kimms, I have a small wish. Maybe you could make another sample of "5 reel drive" with only 1 line played? We can then see if the weights are different.

I'll do 1, 2, 3, 4, 5, 6, 7, 8 and 9 lines for 2500 spins.

 

[gerilege]

I'm programming now in JAVA. I believe that the one line result calculationis incorrect in analyze. I will check it in a few minutes with analyze1.

Analyze calculates the payout for line2, not line1. But you can only choose line1 first in the real game, and line2 only after. So it's possible that line2 alone would produce more than 100%. I'm checking this right now.

 

[steinhaug]

Analyze calculates the payout for line2, not line1. But you can only choose line1 first in the real game, and line2 only after. So it's possible that line2 alone would produce more than 100%. I'm checking this right now.

I could expand my data file, since the data served from MG also tells what line the win is on, and what the win was. This means I can give you excat figures on what line pays what I did this with the data for Thunderstruck, which you can see in the datafile (however i dropped the win sum, only added the win lines).

 

[steinhaug]

Here are the reelstats for 2500 spins on 1 line and 2 lines bet.

 

[gerilege]

Sample size matters

Here are the reelstats for 2500 spins on 1 line and 2 lines bet.

I don't think that different weightings exist. I think that the first sample was simply a good session, probably good line wins on winline1. The second sample was a bad session, but the first one was much better than average, the second was only slightly below average (I assume this because of the combined results, see below).

I made some corrections, and reran the extrapolated simulation with
-Original first sample only, 2000 spins (weightset 1)
-Second sample only, first recent sample of 2500 spins (weightset 2)
-First and second sample, 2000+2500 spins combined. (weightset 3)

Please find attached the results. Highlights:

Number of winlines: 1
Weightset used: 1
Payout ratio: 1.0137243209419724

Number of winlines: 4
Weightset used: 1
Payout ratio: 0.9151179228378415

Number of winlines: 5
Weightset used: 1
Payout ratio: 0.9513881379078132

Number of winlines: 9
Weightset used: 1
Payout ratio: 1.002396223151912
__________________________
Number of winlines: 1
Weightset used: 2
Payout ratio: 0.9118255004155771

Number of winlines: 4
Weightset used: 2
Payout ratio: 0.8568190079218757

Number of winlines: 5
Weightset used: 2
Payout ratio: 0.8894922862113461

Number of winlines: 9
Weightset used: 2
Payout ratio: 0.9482225993767085
____________________________

Number of winlines: 1
Weightset used: 3
Payout ratio: 0.9626296600537657

Number of winlines: 4
Weightset used: 3
Payout ratio: 0.885674539193263

Number of winlines: 5
Weightset used: 3
Payout ratio: 0.9204153397040318

Number of winlines: 9
Weightset used: 3
Payout ratio: 0.9750664675151187

I am yet to add the third sample (recent, second 2500 spins), we will see the combined results. I have also created a weightset 4 (First and second sample combined, but different sample size were considered,2000 spins for 1 and 2500 spins for 2), but whis is only slightly different from weightset 3, however I added it to the file.

I think that the payouts will be close in case of different number of lines played, but the maximum will probably be at 9 lines, the minimum will be at 4 lines. The current order is (based on the combined results):

9 lines, 8 lines, 1 lines, 7 lines, 2 lines, 6 lines, 3 lines, 5 lines, 4 lines. But this might very well change with the sample size.

 

[steinhaug]

I don't think that different weightings exist. I think that the first sample was simply a good session, probably good line wins on winline1. The second sample was a bad session, but the first one was much better than average, the second was only slightly below average (I assume this because of the combined results, see below).

This might be true, I will set my system to do more spins - and write down the credits on start and end so we know % payout to distinguish between a good and bad session. I will keep going for all 9 lines, and then maby do some of the liners again to try get other streks. Like 1 line was a good streak, maby get data from a bad streak and so.

I will look more into your calculations later, good work!

 

[Zoozie]

This shows clearly that we need the weights VERY accurate if it is to be of any use. A much bigger sample size (*10 at least) is required.

I would still be interesting to find this, so we could see the difference in payout% by playing less than the full 9 lines. And I also still believe it uses
the same weights no matter how many lines you play.

It would be interesting if etc. 7.lines played showed a payout% at 101%

Zoozie

 

[gerilege]

Some updates

I added the second recent sample (2lines,2500 spins). This is weightset 5. As you can see it is very similar to weightset 2 (1lines,2500 spins), but slightly worse.
And I combined all the samples together (2000 spins@ 9lines,2500 spins@ 1lines,2500 spins@ 2lines). This is weightset 6. Result highlights:

Weightset used: 5
Number of winlines: 1
Payout ratio: 0.8810925563628642
________________________
Number of winlines: 4
Payout ratio: 0.8401273829500333
________________________
Number of winlines: 5
Payout ratio: 0.8727128501718763
________________________
Number of winlines: 9
Payout ratio: 0.9429614368000651
________________________
________________________
Weightset used: 6
Number of winlines: 1
Payout ratio: 0.9302859426131334
________________________
Number of winlines: 4
Payout ratio: 0.8672654419330631
________________________
Number of winlines: 5
Payout ratio: 0.9010453783128208
________________________
Number of winlines: 9
Payout ratio: 0.961373671673185

Adding more elements to the sample shows that 9lines passes 1line by. Playing 4 lines consistently seems to be the worst choice. I will check weightset 1 once more searching for typos.

 

[Zoozie]

Nice work again Gerilege!
Even if the weights you used are not exact it is now totally clear that payout depends heavily on number of lines player for these few weighted 5-reel slots.
An important discovery I would say. (If you program is correct, but I am sure it is)

When I played them years ago I normally always played them at 5-lines and this really gave me the worst of it. It is a disgrace MG can let this happen or
assume everyone always plays 9-lines. So MG does have slots that have 90% payout.
(Important: For the normal newer non-weighted 5-reel slots, number of lines played all give same payout%)

I have updated the slot-analyzer with a new slot. It is the first non MG slot I have analyzed. I got the reels layout and payout-report made by ITG labs for "Cleopatra". Of course this is non-weighted and I get the same payout% as the papers state, so there is no doubt the analyzer is working correct. However I get 0.015% higher payout and this is because the slots only allow 180 freespins maximum and I have not implemented a stop-limit yet. In any case the difference is negligible.

I have added both the 95.02% and the 96.21% version of the slot. Both have been seen at WagerWork casinos which started with the 96.2% version but now have downgraded to the 95.02% version.

All parameters of Cleopatra are very extremely close to Thunderstruck actually - like the 3+ scatter frequency, average feature win and payout%.

I have added a "Hit frequency" statistic that says how often you win when playing 1 line counting both line-win and scatter-win.

If you are too lazy to run the simulation, then here is the results from the 95.02% Cleopatra:

----------------------- Analysis complete -------------------------
Seconds running:91.9
Number of iterations:33210000
Total cost:33210000
Total added wins:23099142
Number of feature starts:240975
Base payback(no free spins):0.6955477868112014
Probability for getting a feature each spin:0.00725609756097561~1/138
Average number of spins each feature with retriggers (calculated):16.832021895313034
Average number of win each feature(in bet size):35.12242673052799
Total number of hits:3831681
Hit frequency:0.1153773261065944
Total payout (exact!)= 0.9503995417461302~ 95.04%

 

[steinhaug]

Here is 2500 spins of 4line wager. I also included line 1 and 2 again so we have all in same post. I also added a html file, same as screenshot, if someone need the percentage numbers for cut'n'paste. Also you find the data files.

 

[steinhaug]

By the way, here are the datafiles also with data for what lines the win came from, together with total win on that spin.

The linewin data is like this,
0,0,0,0,0,0,0,0,0

Each zero symbolises the lines starting from line 1. 5Reel Drive uses a 10th winning combination, -1, which is for scatter win. Since none of the files attached are with 9 lines I used the 9th line for scatter win. So where you see a 1 in the 9th place, this is not win on line 9 but a scatter win.

 

[aka23]

The reels and pips data for the AWP slot Pandemonium are below. "Pips" correspond to the numbers listed by some of the symbols.

Reel1="9,1,3,2,1,5,4,3,2,7,1,6,2,5,4,3,8,1,2,6,5,7,1,8,2,4,3,5,1,2"
Reel2="9,2,1,8,3,6,5,4,2,1,5,6,2,7,1,3,4,3,1,2,4,7,2,1,5,3,4,2,7,1"
Reel3="9,3,6,4,8,1,2,5,2,4,1,6,3,1,4,2,1,2,5,9,1,6,2,7,3,8,4,1,3,2"

Pips1="0,2,0,0,0,1,0,0,0,0,0,0,2,0,0,3,0,0,0,0,0,0,0,4,0,0,0,2,0,0"
Pips2="0,0,1,0,0,0,1,0,0,0,0,5,0,0,0,0,0,3,0,0,0,0,2,0,0,0,2,0,0,0"
Pips3="0,0,2,0,0,0,0,4,0,0,0,0,1,0,0,2,0,0,0,0,0,3,0,0,0,0,0,0,1,0"

I don't have time to checkwhich symbols correspond to which numbers now.

Several other AWP slots are similar. For example Dubya Money is below. Note that 4 occurs in place of 3, 6 occurs in place of 5, 3 occurs in place of 2, ...

Reel1="9,1,4,3,1,6,5,4,3,8,1,7,3,6,2,4,2,1,3,7,6,8,1,2,3,5,4,6,1,3"
Reel2="9,3,1,2,4,7,6,2,3,1,6,7,3,8,1,4,5,7,1,3,5,2,3,1,6,4,5,3,8,1"
Reel3="9,4,7,5,2,1,3,6,3,5,1,7,4,1,5,3,1,3,6,2,1,7,3,8,4,2,5,1,4,3"

Pips1="0,2,0,0,0,1,0,0,0,0,0,0,2,0,0,3,0,0,80,0,0,0,0,4,0,0,0,2,0,0"
Pips2="0,0,1,0,0,0,1,0,0,0,0,5,0,80,0,0,0,3,0,0,0,0,2,0,0,0,2,0,0,0"
Pips3="0,0,2,0,0,0,0,4,0,0,0,0,1,0,0,2,0,0,0,0,0,3,0,0,0,0,80,0,1,0"

 

[aka23]

The reels and pips data for the AWP slot Pandemonium are below. "Pips" correspond to the numbers listed by some of the symbols.

Reel1="9,1,3,2,1,5,4,3,2,7,1,6,2,5,4,3,8,1,2,6,5,7,1,8,2,4,3,5,1,2"
Reel2="9,2,1,8,3,6,5,4,2,1,5,6,2,7,1,3,4,3,1,2,4,7,2,1,5,3,4,2,7,1"
Reel3="9,3,6,4,8,1,2,5,2,4,1,6,3,1,4,2,1,2,5,9,1,6,2,7,3,8,4,1,3,2"

Pips1="0,2,0,0,0,1,0,0,0,0,0,0,2,0,0,3,0,0,0,0,0,0,0,4,0,0,0,2,0,0"
Pips2="0,0,1,0,0,0,1,0,0,0,0,5,0,0,0,0,0,3,0,0,0,0,2,0,0,0,2,0,0,0"
Pips3="0,0,2,0,0,0,0,4,0,0,0,0,1,0,0,2,0,0,0,0,0,3,0,0,0,0,0,0,1,0"

I don't have time to check which symbols correspond to which numbers now.

The symbols are:
1 - Cherry
2 - Orange
3 - Bat
4 - Gold Bar
5 - Red Guitar
6 - Number 7
7 - Purple Guitar
8 - Watermelon
9 - Panda

Note that this order is the order the symbols are listed on the initial screen, if you go from high to low.

The slot only has 1 line and 3 reels, so basic analysis (not including bonus rounds, nudges, etc) can be done with basic probability:
The chance of three pandas is (1/30)*(1/30)*(2/30)
The chance of three watermelons is (2/30)*(1/30)*(2/30)
The chance of three purple guitars is (2/30)*(3/30)*(1/30)
...

 

[gerilege]

Added the new sample

Here is 2500 spins of 4line wager. I also included line 1 and 2 again so we have all in same post. I also added a html file, same as screenshot, if someone need the percentage numbers for cut'n'paste. Also you find the data files.

I have added the new sample to the analysis. First of all, one wish to kimss:
Next time could you please create the overview to have the weights the following way:
0.02,0.06,0.0453,....,0.123
So no percents, but decimal fractions, and the numbers are separated with comma, semicolon or space, etc. It would help me a lot, boost the speed and spare me an ugly part. Thanks in advance.

Regarding the results, the first lesson learned was that the original 9-line sample was somehow strange. 0.5% is missing from the sum of weights, but that shouldn't influence the results so much. So it's probably really just a good session. But please do one more round for 9 lines. Thanks.

Because I'm wondering what was wrong with sample1, I measured the Eucledian norm distance (A norm that tells us about how individual weight elements differ in two weightsets) of the weight sample vectors. Please find attached(norm.txt), the numbers doesn't mean anything special, just shows the convergence, and how similar the samples are.

Now about the results:

The new 4line sample (Sample4) is again quite a good one, as you will see. kimss? what was your bet size, because I see your start and end balance, so you loss, but I don't know the bet size to compare...
I added 3 new configurations:
weightset 8: Sample4
weightset 9 Sample1 + Sample2 + Sample3 +Sample4
weightset 10 Sample2 + Sample3 +Sample4
I added the weight definitions to the beginning of the result file (result.txt). Some highlights:

Weightset used: 8
Number of winlines: 1
Payout ratio: 0.9536818313113836
________________________
Number of winlines: 4
Payout ratio: 0.8789279372267511
________________________
Number of winlines: 5
Payout ratio: 0.9069407073703996
________________________
Number of winlines: 9
Payout ratio: 0.9741875212939399
________________________
________________________
Weightset used: 9
Number of winlines: 1
Payout ratio: 0.9365907042718327
________________________
Number of winlines: 4
Payout ratio: 0.8707779128526536
________________________
Number of winlines: 5
Payout ratio: 0.9029750880543317
________________________
Number of winlines: 9
Payout ratio: 0.9652168424588984
________________________
________________________
Weightset used: 10
Number of winlines: 1
Payout ratio: 0.9163695174210392
________________________
Number of winlines: 4
Payout ratio: 0.8592553207885669
________________________
Number of winlines: 5
Payout ratio: 0.8902809701625094
________________________
Number of winlines: 9
Payout ratio: 0.9555634903453744

I attach also the source code, Zoozie, could you please have a look whether you see something odd? I will try to add some comments later. It is a standard eclipse java project.

 

[steinhaug]

Great woprk gerilege, I will create some better exports for you the way you want the numbers. I will also include higher prescision in the percentage points, like 2.23456 for instance.

All wagers are done with $1 coinsize, so 4 lines would be $4. I will do 2500 more for you with 9 lines, Ill post later today.

 

[Rusty]

Great job guys.
Any chance of a summary of results so far so that those of us not involved in the simulations and data analasis can get a better understanding of just where you are right now.

Are you saying that not all 5 reel slots are weighted and have you concluded this as some slots have a full reel set while others(weighted slots) do not?

As regards the weighted slots are you basing the weights on an assumed 95%payout or have you accessed data that reveals the weights?

Did you say that slots with scatter symbols or features are not weighted?

What conclusions, of importance to players, can be drawn from the results so far?

Thanks in advance.

 

[aka23]

Great job guys.
Any chance of a summary of results so far so that those of us not involved in the simulations and data analasis can get a better understanding of just where you are right now.

Are you saying that not all 5 reel slots are weighted and have you concluded this as some slots have a full reel set while others(weighted slots) do not?

As regards the weighted slots are you basing the weights on an assumed 95%payout or have you accessed data that reveals the weights?

Did you say that slots with scatter symbols or features are not weighted?

What conclusions, of importance to players, can be drawn from the results so far?

Thanks in advance.

It seems that Microgaming most slots work in 1 of 2 ways:

Games released in recent years, like Thunderstruck and many of the bonus 5 reels, have a complete set of reels in which each point on the reels is equally likely to occur.

Older Microgaming slots, like 5 Reel Drive and many of the 3 reels, have reels in which each symbol only appears once. Instead of having a true reel, they a 2nd file that specifies how often the symbols occur. This weight file is not sent in a txt file like the reel data. I suspect integral values are used for weights, such as "1" or "2", then these values are divided by their sum (equivalent to number of symbols on complete reel). If playing with a single line, integral values produces the same results as a complete reel without weights. However, other lines than the 1st one produce different average payouts since the symbols that occur most often on that line differ (if symbol X occurs often on the 2nd row, then the symbol below X on the reel occurs often on the 3rd).

 

[steinhaug]

Attached is the results of 5000 spins on 9 lines, 9 "chips" value. Also, here is the numbers for each reel position. Just devide the numbers by 50 to get the % (5000 spins).

Total spins: 5000
Reel1:133,284,130,136,491,1438,428,136,232,551,911,130
Reel2:117,971,114,143,268,129,254,255,1051,1182,247,269
Reel3:117,264,396,136,637,142,270,141,1075,410,1277,135
Reel4:1604,362,585,118,124,140,118,790,250,261,266,382
Reel5:535,557,125,137,133,398,681,1258,419,117,514,126

 

[gerilege]

Great job guys.
Any chance of a summary of results so far so that those of us not involved in the simulations and data analasis can get a better understanding of just where you are right now.

Are you saying that not all 5 reel slots are weighted and have you concluded this as some slots have a full reel set while others(weighted slots) do not?

As regards the weighted slots are you basing the weights on an assumed 95%payout or have you accessed data that reveals the weights?

Did you say that slots with scatter symbols or features are not weighted?

What conclusions, of importance to players, can be drawn from the results so far?

Thanks in advance.

What we (I) think:

The older 5-reels, 9-lines slots (like 5 reel drive) are very likely weighted.
The older 5-reels, 5-lines slots (like oriental fortune) are very likely weighted.
The newer slots (like Lotsaloot or Thunderstruck or Loaded) are very likely not weighted.

This is based on the payout tables, and the reel configuration captured by kimss. Some of these reel configurations are verified, because Zoozie and the others got the same result when they manually cracked the reels, and the results match.

The analysis proved that with the given reels and the payout table, some of the above slots must be weighted, otherwise the payout would be too high. I also gave a straight mathematical proof for 5 reel drive that the reels should be weighted without using computer analysis.

The reel weights are not based on the payout, rather from samples from kimss. And we extrapolate the results, which means that we assume that the sample reflects the reel weighting, and let's see what happens. However it seems that these slots with the collected weighting sample seem to pay out 95% when playing 9 lines.

Scatter symbols doesn't really matter in this issue, just the question whether it's an older slot or not. Actually exactly scatter symbols and their payout made me think that 5reel drive was weighted when I saw the reel configuration from kimss. And when Zoozie confirmed some reelsets from kimss, and my analysis matched Zoozie's, we concluded that the reels are weighted.

Conclusions? The analysis seems to show that playing less than 9 lines on weighted slots is inferior to playing 9 lines. But the payout for playing different number of lines might depend on the weighting and the payout table for each slot. I will also examine the same for 5liners.

 

[Zoozie]

What we (I) think:

The older 5-reels, 9-lines slots (like 5 reel drive) are very likely weighted.
The older 5-reels, 5-lines slots (like oriental fortune) are very likely weighted.
The newer slots (like Lotsaloot or Thunderstruck or Loaded) are very likely not weighted.

I more than think it.
I am 100% certain it is true without any shadow of doubt whatsoever!
The only surprise here was that the old 5-reel slots are weighted.

 

[steinhaug]

It is in plain view that the reels are weighted, it's infact staring you right in the face. Looking at the stats from 5 Reel Drive, 12.500 spins worth of data, we get consistend data. Take reel 3 as example, looking at reel position 0 and 6.

9 Lines:
0: 32.08 %
6: 2.36 %

4 lines:
0: 30.72%
6: 2.84%

2 lines:
0: 31.40%
6: 2.92%

1 line:
0: 33.04%
6: 2.76%

It is very obvious that the zero position will occure, infact it's ~1/3 chance it will hit.

 

[gerilege]

It is in plain view that the reels are weighted, it's infact staring you right in the face. Looking at the stats from 5 Reel Drive, 12.500 spins worth of data, we get consistend data. Take reel 3 as example, looking at reel position 0 and 6.

9 Lines:
0: 32.08 %
6: 2.36 %

4 lines:
0: 30.72%
6: 2.84%

2 lines:
0: 31.40%
6: 2.92%

1 line:
0: 33.04%
6: 2.76%

It is very obvious that the zero position will occure, infact it's ~1/3 chance it will hit.

You're both right, that's just a matter of wording. Btw. I will try to find the exact integer weighting. I have already started to do that, and I have some assumptions, but the smallest common denominator for the fraction is not obviuos at the moment. We seem to have some 1/3x and 3x and maybe 4x, but it's open yet.

 

[gerilege]

New data included

Attached is the results of 5000 spins on 9 lines, 9 "chips" value. Also, here is the numbers for each reel position. Just devide the numbers by 50 to get the % (5000 spins).

This sample was also very useful.

Highlights and consequences (I remove now 4 and 5 lines from the highlights, because we had already seen the tendency, and nothing has been changed):

I have created the following new weightsets:
weightset 11: The new 5000 spins @ 9lines. This is to see the payout, and to verify my program, because it gave high payout for the first 2000 spins @ 9 lines. Another aim is to verify that different weightings don't exist for different number of lines.
Weightset used: 11
Number of winlines: 1
Payout ratio: 0.9234210949091466
________________________
Number of winlines: 9
Payout ratio: 0.9604137186813795
________________________
So the new sample is again better than average. It confirms that the weighting is the same for playing 9 lines or any number of lines. (Compare it with weightset 2,5,8 in the detailed results)

weightset 12: All samples combined so far. The aim is to see the overall payout, and to see how the influence of the very first sample is decreased now.
Weightset used: 12
Number of winlines: 1
Payout ratio: 0.9323132757010111
________________________
Number of winlines: 9
Payout ratio: 0.9636783962961434
________________________
The very first, much better than average sample still influences the results, but it is now decreasing. (Compare it with weightset4 in the detailed results)

weightset 13. All samples except the first. The aim is to see the overall difference if we ignore the first sample set. (i.e the difference between 12 and 13).
Weightset used: 13
Number of winlines: 1
Payout ratio: 0.9194004833959175
________________________
Number of winlines: 9
Payout ratio: 0.9575662999079975
________________________
________________________
If we remove the very first sample, the payouts we get with the newer samples are very similar. (Compare weightset 7, 10 and 13 for more details)

weightset 14: The very first 2000 spins@9 lines and the new 5000 spins@ 9 lines. This is to verify that the first 2000 spins were lucky, and also that weightings don't exist for different number of lines.
Weightset used: 14
Number of winlines: 1
Payout ratio: 0.9494164081624558
________________________
Number of winlines: 9
Payout ratio: 0.9725142058640782
________________________
________________________
This result is very important. it confirms that the first sample was lucky, no different weighting exist for different number of lines, and my program is likely correct. (Compare it with 1 and 2 for details).

Overall results are attached.
I have also added the overall weighting so far if somebody has the intention to "find" the integer weighting.

Next time I will try to compile all the results into an excel file.

 

[gerilege]

Something I forgot to mention

It's worth mentioning the below result. It is based on 12500 spins (all but the very first sample combined). I think this result is the closest one to the final result so far, although it's still just an estimation.

Weightset used: 13
Number of winlines: 1
Payout ratio: 0.9194004833959175
________________________
Number of winlines: 2
Payout ratio: 0.9271562638623874
________________________
Number of winlines: 3
Payout ratio: 0.9019138179400753
________________________
Number of winlines: 4
Payout ratio: 0.8632260258722383
________________________
Number of winlines: 5
Payout ratio: 0.895356369724244
________________________
Number of winlines: 6
Payout ratio: 0.9160139373943699
________________________
Number of winlines: 7
Payout ratio: 0.9334019828915717
________________________
Number of winlines: 8
Payout ratio: 0.9483154507193674
________________________
Number of winlines: 9
Payout ratio: 0.9575662999079975

Why it's important? Because it shows the different payout for different number of lines! So far it seems that the order is 9,8,7,2,1,6,3,5,4, but this is still somehow uncertain. But playing 5 and especially 4 lines consistently seems terrible on this slot. And now that it seems to be verified that the weighting is the same for playing different number of paylines, the above tendency is more credible.

I'm still fighting with a suitable integer-based weighting. It's definitely not simple.

 

[Zoozie]

I'm still fighting with a suitable integer-based weighting. It's definitely not simple.

It is not certain it is integer based through! But IF the data shows integer weights and you can find them, we will have an exact simulation, which is
theoretically interesting. But for payout% etc. the results we have already will be very close to the final results.

 

[gerilege]

It is not certain it is integer based through! But IF the data shows integer weights and you can find them, we will have an exact simulation, which is
theoretically interesting. But for payout% etc. the results we have already will be very close to the final results.

There's no obvious integer values exist, so I postpone it. I would do Oriental Fortune, but I have a small problem. It seems that there's a wild on each real (number 5), but I couldn't find a payout for 5 wilds. Anyone any idea?

 

[steinhaug]

If you need more spin data for any game available in the flash section please notify me, and I will fix it. Also note how many spins you like. I will do batches of 5000 for each session.

 

[gerilege]

Oriental fortune

If you need more spin data for any game available in the flash section please notify me, and I will fix it. Also note how many spins you like. I will do batches of 5000 for each session.

Yes, please provide more data for Oriental fortune! 5.000 spins would be nice!

I have finished the first version of the analysis for this slot. I assumed that five ladies(wilds) pay out the same like 5 oriental fortune symbols. There should be no such payout like four wilds, because that's a five-of-a-kind from the other direction. So I also assumed that there's no such thing like 3 wilds, it's always some 4-of-a-kind, and so on. Left-to-right, right-to-left issues are considered, 5-of-a-kinds are counted only once. But this slot is really simple.

I only have a 1000 element sample, but it seems that this slot seriously penalize playing 1 line. Preliminary results based on 1000 extrapolated spins:
Oriental Fortune:
Number of winlines: 1
Payout ratio: 0.7389455863757433
________________________
Number of winlines: 2
Payout ratio: 0.8651402183357862
________________________
Number of winlines: 3
Payout ratio: 0.9072050956557987
________________________
Number of winlines: 4
Payout ratio: 0.9204102480534427
________________________
Number of winlines: 5
Payout ratio: 0.9283333394920275
________________________
________________________

This sample has very high uncertainity, so this is only for your information.

For your information, this would be the payout ratio for this slot without weighting:
Number of winlines: 5
Payout ratio: 8.5896 (858,96%)

 

[Zoozie]

Mega Moolan analyzed

----------------------- Analysis complete -------------------------
Seconds running:357.3
Number of iterations:77586432
Total cost:77586432
Total added wins:50904326
Number of feature starts:530550
Base payback(no free spins):0.6560982982179152
Probability for getting a feature each spin:0.006838180160159962~1/146
Average number of spins each feature with retriggers (calculated):16.71444588342117
Average number of win each feature(in bet size):32.8989584993042
Total number of hits:7740318
Hit frequency(1-line):0.09976380921860152 ~ 0.99%
Total payout (exact!)= 0.8810673035177832~ 88.11%


I am not taking the rapid fire jackpot into account since we do not know how often it triggers or how often you win the different jackpots.

But I had expected the payout to be higher than 88.11% - maybe around 92-93%. So I have no idea what the actual payout% is now with the current jackpots.

The reel are very large and the total number of combination is a factor 2-3 times larger than the other slots.

This is the maximum win-combination for "Mega Moolah"


A J J T T
J W G W Z
W K W Q W

Total win :16293
Scatter win:0
Line 1:0
Line 2:0
Line 3:12
Line 4:80
Line 5:120
Line 6:3
Line 7:0
Line 8:0
Line 9:0
Line 10:0
Line 11:0
Line 12:0
Line 13:1000
Line 14:0
Line 15:15000
Line 16:30
Line 17:30
Line 18:0
Line 19:0
Line 20:0
Line 21:6
Line 22:0
Line 23:6
Line 24:0
Line 25:6


I will upload this slot to the slot-analyzer applet later. I will check again that I really got the reels right, but I am very certain I did though. I have also
implemented "expanding wilds" for the analyzer, but we have no slots yet with the expanding wilds. Unfortunately "Twin samurai" or "Hitman" are not yet
in flash mode, and we would also have a problem with "Hitman" because of the unknown weights for the execution feature and picking feature.

Zoozie

 

[gerilege]

I would need input sample

I would need some additional spins from either Oriental Fortune or any other 5liner slot, or any old 9liner slots (like Big Top) for further analysis.

In the meantime I will try to do another progressive slot.

 

[gerilege]

Fruit Fiesta

I would need some additional spins from either Oriental Fortune or any other 5liner slot, or any old 9liner slots (like Big Top) for further analysis.

In the meantime I will try to do another progressive slot.

I have finished Fruit Fiesta. I considered that 4 wilds are better than any five-of-a-kind except 5 sevens. 3 wilds are better than any four-of-a-kind except 4 sevens.

The chance for a jackpot is 1:4151500. (The chance for Lotsaloot is 1:4562280)

Fruit Fiesta
___________________
Jackpot: 5000$
Payout ratio: 0.9212019751896905
Jackpot: 10000$
Payout ratio: 0.9276256774659761
Jackpot: 15000$
Payout ratio: 0.9340493797422619
Jackpot: 20000$
Payout ratio: 0.9404721185113815
Jackpot: 25000$
Payout ratio: 0.9468958207876671
Jackpot: 30000$
Payout ratio: 0.9533195230639527
Jackpot: 40000$
Payout ratio: 0.9661659641093581
Jackpot: 50000$
Payout ratio: 0.9790124051547633
Jackpot: 75000$
Payout ratio: 1.0111299530290256
Jackpot: 100000$
Payout ratio: 1.043246537396122
Jackpot: 125000$
Payout ratio: 1.075363121763218
Jackpot: 150000$
Payout ratio: 1.1074806696374804

Probably Zoozie could confirm the above payout info.
I edited the post, because I have found an error in my program. Payouts updated.

 

[Zoozie]

Probably Zoozie could confirm the above payout info.

I will do this one and Major Millions later. If results does not match yours, then I will look at your code.

 

[lojo]

The chance for a jackpot is 1:4151500. (The chance for Lotsaloot is 1:4562280)

That's about 10x better than the Powerball lottery!!!

 

[gerilege]

Major Millions

Major Millions

This progressive slot seems to have a higher base payout. The followings were considered:
-Wild multiplies by 3.
-3 wilds are better than any four-of-okind which are less than 4 airplane.
-Four wilds are worse than any five-of-a-kind except five googles. Results:

Jackpot: 250000$
Payout ratio: 0.9484672118005452
Jackpot: 300000$
Payout ratio: 0.9506939768050879
Jackpot: 350000$
Payout ratio: 0.9529208754208754
Jackpot: 400000$
Payout ratio: 0.955147774036663
Jackpot: 450000$
Payout ratio: 0.9573745390412057
Jackpot: 500000$
Payout ratio: 0.9596014376569932
Jackpot: 550000$
Payout ratio: 0.9618283362727807
Jackpot: 600000$
Payout ratio: 0.9640551012773235
Jackpot: 650000$
Payout ratio: 0.966281999893111
Jackpot: 700000$
Payout ratio: 0.9685088985088985
Jackpot: 750000$
Payout ratio: 0.9707356635134413

The results are a bit highish, so I will check for errors.

The chance for the jackpot is 1:7484400

 

[gerilege]

Results are void

Major Millions

This progressive slot seems to have a higher base payout. The followings were considered:
-Wild multiplies by 3.
-3 wilds are better than any four-of-okind which are less than 4 airplane.
-Four wilds are worse than any five-of-a-kind except five googles. Results:

Jackpot: 250000$
Payout ratio: 0.9484672118005452
Jackpot: 300000$
Payout ratio: 0.9506939768050879
Jackpot: 350000$
Payout ratio: 0.9529208754208754
Jackpot: 400000$
Payout ratio: 0.955147774036663
Jackpot: 450000$
Payout ratio: 0.9573745390412057
Jackpot: 500000$
Payout ratio: 0.9596014376569932
Jackpot: 550000$
Payout ratio: 0.9618283362727807
Jackpot: 600000$
Payout ratio: 0.9640551012773235
Jackpot: 650000$
Payout ratio: 0.966281999893111
Jackpot: 700000$
Payout ratio: 0.9685088985088985
Jackpot: 750000$
Payout ratio: 0.9707356635134413

The results are a bit highish, so I will check for errors.

The chance for the jackpot is 1:7484400

The above payout info is void! I made an error during the analysis. More details later.

 

[steinhaug]

Been away for some time, has consumed alot of time lately so have to take care of business aswell while the wheels are spinning, Anyways, here are the awaited Oriental Fortune stats from 4 different casinoes.

The raw numbers would be (look for balance in screenshots):

Spin Palace, max wager, Total spins: 7204
613,1235,872,2142,213,252,213,208,399,1057
425,1206,1472,1766,206,204,225,214,213,1273
1693,206,2326,1698,196,211,221,217,198,238
209,190,1451,883,203,224,218,1108,2513,205
220,225,196,3452,216,214,202,428,1836,215

Ruby Fortune, 5 wager, Total spins: 7128
581,1274,850,2051,213,204,186,248,430,1091
437,1210,1503,1692,191,226,197,209,209,1254
1765,211,2250,1710,191,220,203,204,179,195
190,224,1456,827,191,205,224,1072,2555,184
200,222,202,3318,214,224,227,363,1948,210

Mummys Gold, 5 wager, Total spins: 7186
611,1255,870,2142,210,206,215,225,437,1015
429,1271,1420,1690,222,227,227,217,203,1280
1638,197,2347,1711,203,224,205,212,239,210
216,227,1523,841,234,188,212,982,2543,220
212,205,186,3389,207,218,213,401,1925,230

32 Red, 5 wager, Total spins: 7250
578,1241,856,2180,222,226,202,191,458,1096
418,1233,1503,1688,233,225,220,204,224,1302
1690,228,2317,1706,203,237,220,195,231,223
212,213,1493,887,216,210,204,1054,2523,238
205,218,199,3403,205,201,217,424,1943,235

 

[gerilege]

Major Millions results corrected

I have found several errors in my previous work, and finally i managed to localize them. Many thanks to Zoozie for his suggestions, they really helped. The payout for Major Millions is the following:

Jackpot: 250000$
Payout ratio: 0.9052573352573352
Jackpot: 500000$
Payout ratio: 0.9163915611137833
Jackpot: 750000$
Payout ratio: 0.9275257869702315
Jackpot: 1000000$
Payout ratio: 0.9386601464379242
Jackpot: 1250000$
Payout ratio: 0.9497943722943722
Jackpot: 1500000$
Payout ratio: 0.9609285981508203
Jackpot: 1750000$
Payout ratio: 0.9720629576185131
Jackpot: 2000000$
Payout ratio: 0.9831971834749612
Jackpot: 2250000$
Payout ratio: 0.9943314093314093
Jackpot: 2500000$
Payout ratio: 1.0054657687991022

I will double-check Fruit Fiesta as well, as I might have the same error in that simulation.

 

[gerilege]

I will double-check Fruit Fiesta as well, as I might have the same error in that simulation.

Payout for Fruit Fiesta (also posted on previous thread page) is also incorrect. I will try to fix it today.

Sorry if it caused any inconvinience for anybody.

 

[Zoozie]

I have found several errors in my previous work, and finally i managed to localize them. Many thanks to Zoozie for his suggestions, they really helped. The payout for Major Millions is the following:

Jackpot: 250000$
Payout ratio: 0.9052573352573352
Jackpot: 500000$
Payout ratio: 0.9163915611137833
Jackpot: 750000$
Payout ratio: 0.9275257869702315
Jackpot: 1000000$
Payout ratio: 0.9386601464379242
Jackpot: 1250000$
Payout ratio: 0.9497943722943722
Jackpot: 1500000$
Payout ratio: 0.9609285981508203
Jackpot: 1750000$
Payout ratio: 0.9720629576185131
Jackpot: 2000000$
Payout ratio: 0.9831971834749612
Jackpot: 2250000$
Payout ratio: 0.9943314093314093
Jackpot: 2500000$
Payout ratio: 1.0054657687991022

I will double-check Fruit Fiesta as well, as I might have the same error in that simulation.

I can confirm these results are correct!
And I can add:
Hit frequency (1-line):0.08119929453262786
The break-even point for the jackpot is 2376100$

Later today I will upload this slot to the slot-analyzer.

 

[sdaddy]

Payout for Fruit Fiesta (also posted on previous thread page) is also incorrect. I will try to fix it today.

Sorry if it caused any inconvinience for anybody.

gerilege,

Just wondering if you ever recalculated the payout for Fruit Fiesta?

 

[gerilege]

gerilege,

Just wondering if you ever recalculated the payout for Fruit Fiesta?

Good point, thanks for the heads-up. Frankly, I don't remember, but I think I was unable to find the error if there was any. I hope I can check it soon, but it heavily depends on my workload, which is quite high nowadays.

You know we reached a few important results those days, and finding a misterious bug was not a big challenge any more, and I was quite tired of another probabilitic approach I followed without success, so I think I gave up finding the error, my bad. But I will post the latest version of my analyzer, and check my work again, and post the results... No broken promises

But considering the following info...

Avg When Hit $ 24,541.62
Max hit. $ 162,304.08
Start at $ 800.00
And what I posted:
Jackpot: 5000$
Payout ratio: 0.9212019751896905
Jackpot: 10000$
Payout ratio: 0.9276256774659761
Jackpot: 15000$
Payout ratio: 0.9340493797422619
Jackpot: 20000$
Payout ratio: 0.9404721185113815
Jackpot: 25000$
Payout ratio: 0.9468958207876671
Jackpot: 30000$
Payout ratio: 0.9533195230639527
...
Jackpot: 150000$
Payout ratio: 1.1074806696374804

... those payout seems quite realistic. Probably Zoozie could please have a look again as well...

By the way still no feedback about the weighted 9liners from MG, that makes me a bit sad...

 

[sdaddy]

But I will post the latest version of my analyzer, and check my work again, and post the results... No broken promises

Great. Whenever you find time, I'd appreciate it. I'm really interested in learning the payouts of all the MG progressives.

 

[sdaddy]

problem with Lotsaloot analysis

I've been reviewing the previous analysis of the progressive Lotsaloot, and something doesn't quite add up.

What I mean is, the payout percentage and spins per jackpot cycle should agree with what's found in the historical data available on Slotcharts, and I find it's not even close. Here's my independent mathematical analysis:

Let
DELTAJ = increase in jackpot from average level to break-even level
W = amount wagered per jackpot cycle
HA = house edge

Have the formula:
HA = DELTAJ/W ---> W = DELTAJ/HA

From Slotcharts the average jackpot level is $22,355, which gives an HA of 0.0691 from Zoozie's slot analyzer.
Also, the slot analyzer calculates a break even jackpot level of $71625.
Making the substitutions into the above equation gives

W = $49270/0.0691 = $713,024

The problem is that this does not agree at all with the amount wagered per cycle that is solely predicted from the slot analyzer. That value is

W = spins per jackpot cycle * wager per spin = 4562280 * $2.50 = $11,405,700.

That's over 10x difference! Could it be that the prediction of the number of spins per jackpot is way too high?

 

[Zoozie]

That's over 10x difference! Could it be that the prediction of the number of spins per jackpot is way too high?

Not sure I understand what you mean. I will read it later again. But we have no way of knowing how much of the wager is used to increase the jackpot. Say if the current jackpot gives 92% payout, what happen to the last 8% ? The casino probably takes 7.99% and then 0.01% are added to jackpot.

 

[sdaddy]

zoozie,

I'll try to make it clearer how I got the formula above.

Let
W = wagers per jackpot cycle
PA = payouts per jackpot cycle at the average jackpot level
DELTAJ = payouts per jackpot cycle at the break even jackpot level minus payouts per jackpot cycle at the average jackpot level (i.e., the difference in the jackpot between the break even level and the average level)
PF = payout fraction at the average jackpot level = PA/W

So at the break even point:
W = PA + DELTAJ
--->1 = PF + DELTAJ/W
--->1 - PF = HA = DELTAJ/W

My analysis should have nothing to do with the jackpot meter rate.