Cracking the slot reels - Here you go!

[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.