Applying Fractals to Roulette

[falkor2k15]

Numbers are seemingly random and unpredictable - yet fractals are totally predictable!

This raises 2 questions:
1) What exactly is predictable about fractals?
link:s://:.youtube.com/watch?v=kbKtFN71Lfs
In this fractal example we can observe that the dots form a predictable pattern in terms of what areas are likely to hit and what areas are likely to remain unhit, i.e. the small black upside-down triangle regions - and this pattern must form based on a trail that "snakes" around the big white triangle region.
If it were totally unpredictable then the enclosed area would form a solid triangle of equal distribution without any of the small black upside-triangles (representing mostly unhit areas) - and not all areas of the triangle are accessible at any one time - hence has more to do with the snake's intelligence for want of a better interpretation.

2) How to apply fractals to roulette?
link:s://:.youtube.com/watch?v=kbKtFN71Lfs
Observation A: It seems the most obvious mechanism behind the fractal example is dependency: each trial forms a dot and draws a line based on where the previous dots and lines were drawn - forming a trail of dots and lines that are connected by their relationship = dependency. If the fractal was based on independent trials then the starting point would always be the same, and the dots and lines would never form a predictable pattern - unless they were not equally-likely. However, the fractal example is in fact using equally-likely outcomes.

How to apply this mechanism to Roulette? Answer: cycles! A cycle begins and ends on a repeat, which is carried over to the next cycle as the defining element:
1231
11
122
22
22
212

The cycle always has more chance of ending in order 1 because the outcome depends on the starting partition:
2... more chance finish on 2.

Observation B: The fractal example is based on 3 outcomes that are used to create multiple outcomes - representing the many possible spaces where a dot/line could end up being drawn within the enclosed area of the triangle.

With cycles we can use 3 outcomes to generate multiple outcomes too, i.e. 9 Dozen Options:
Order 1, Dozen 1
Order 1, Dozen 2
Order 1, Dozen 3
Order 2, Dozen 1
Order 2, Dozen 2
Order 2, Dozen 3
Order 3, Dozen 1
Order 3, Dozen 2
Order 3, Dozen 3

Observation C: some areas of the triangle are hit more than other areas of the triangle.

With Cycles, Order 1 is going to hit more than Order 2 or 3 - but just betting Order 1 doesn't result in any edge because risk/reward is the same ratio as betting Order 2 or Order 3 = equivalent.

Observation D: the most important! The snake cannot repeat the same outcome as the last outcome, i.e. it cannot return to the previous dot immediately - but it can return there later after several trials have taken place!

How to apply this to Roulette? In 9 Dozen Options (see above), Order 2 Dozen 1 cannot immediately follow Order 1 Dozen 1 - but it can return there later in a set of cycles.

What other observations are there and what further refinements must we make to our dozen cycles to make this applicable? Or if it's not applicable then why not?

[sugtips]

Thanks God and Good Morning All.

Thanks falkor for this good post.

note for critics (I know who falkor is and read all his post previously, but I like his this very post.)

Love and Light,
SugTips

[stringbeanpc]

In the video a new point is created halfway between the old point and (A, B or C).

What the triangle look like if the new point was created 1/3 or 1/4 (instead of halfway)? Be interesting to see.

What software is he using to create this serpinksi triangle ?

[falkor2k15]

I've been puzzling over this for a few days now and cannot seem to get my head around it. Here's where I'm at...

I found that with the following four outcomes, CL1 defined by Red cannot be followed by CL1 defined by Black (and vice versa):
CL1dR
CL2dR
CL1dB
CL2dB

And unlike order 1, the above 4 outcomes are 25% ratios each.

So what is the difference between playing for a repeat (or deadlock) on the above vs. traditional Quads?

[falkor2k15]

I found that with the following four outcomes, CL1 defined by Red cannot be followed by CL1 defined by Black (and vice versa):
CL1dR = 1
CL2dR = 3
CL1dB = 2
CL2dB = 4

And unlike order 1, the above 4 outcomes are 25% ratios each.

This one is strange...

2
3
1
4
3
1
3
4
3
3
4
2
2
2
2
2
4
2
3
1
1
3
1
3
1
3
1
3
1
4
2
3
4
2
2
4
3
1
1
1
4
2
2
2
2
4
2
4
3
1
1
1
1
4
2
2
2
2
4
2
4
3
4
2
2
4
2
3
1
3
4
3
1
1
1
1
1
1
1
1
1
3
1
1
4
3
1
3
3
4
2
4
2
4
2
2
3
1
1
3
1
1
1
4
2
3
4
2
2
2
4
4
4
2
4
2
2
4
2
2
2
4
4
4
2
3
3
1
1
1
1
3
4
2
2
4
3
4
4
4
2
3
1
1
4
2
2
2
4
2
2
2
3
1
4
3
1
4
2
4
4
4
3
3
1
3
4
3
1
4
3
1
4
2
2
3
4
2
3
3
4
2
4

All 25% chance each! Though a CL1 is just 1 spin and CL2 requires 2 spins.

Playing for a repeat gets more stranger still:

23143
313
343
33
3422
22
22
22
242
2311
131
131
131
131
14234
422
24311
11
1422
22
22
242
24311
11
11
1422
22
22
242
2434
422
242
2313
343
311
11
11
11
11
11
11
11
131
11
1431
133
3424
424
422
2311
131
11
11
14234
422
22
244
44
424
422
242
22
22
244
44
4233
311
11
11
13422
2434
44
44
42311
1422
22
242
22
22
23143
31424
44
44
433
313
343
3143
31422
2342
233
3424
4233
311
131
11
1431
1343
311
133
344
433
311
11
1344
433
33
3422
22
22
22
22
22
22
2343
33
33
33
31423
33
33
3143
313
311
11
1422
23144
44
424
422
23142
22
22
22
22
2311
1431
131
11
131
11
11
11
14233
31422
242
22
22
2342
242
242
22
22
233
3424
44
422
22
242
242
2433
343
344
424
424
4311
11
11
11
11
11
133
311
133
343
344
44
44
4234
422
22
2342
22
233
311
1422
22
22
22
22
22
244
433
3144
44
422
22
2311
11
11
11
11
131
131
13424
4314
422
244
433
311
1431
11
11
144
44
434
44
422
244
42311
144
422
242
244
4233
311
1424
4233
344
4234
4311
11
1422
22
242
242
22
22
23143
311
1434
42311
133
311
1424
434
424
4234
424
4313
33
3144
4234
424
44
424
44
4311
11
11
11

Average      
   134160   40%
   120492   36%
   63236   19%
   21150   6%
   339038   
1…      
CL1   49838   50%
CL2   24766   25%
CL3   18382   19%
CL4   6246   6%
   99232   
2…      
CL1   49036   50%
CL2   24476   25%
CL3   18275   19%
CL4   6146   6%
   97933   
3…      
CL1   17558   25%
CL2   35696   50%
CL3   13266   19%
CL4   4307   6%
   70827   
4…      
CL1   17728   25%
CL2   35554   50%
CL3   13313   19%
CL4   4450   6%
   71045   

You may recall that standard Quads were different:


Back to main example: Order 1 can be either 67% or 51% depending on starting partition and how things develop in the (outer) cycle.

Yet everything began with equally-likely 25%...!

Here's an interesting thought...

Let's say we have all cycles starting with 1:
131
131
131
131
14234
11
1422
11
11
1422
11
11
11
11
11
11
11
131
11
1431
133
131
11
11
14234
11
11
13422
1422
131
11
1431
1343
133
11
1344
11
1422
1431
131
11
131
11
11
11
14233
11
11
11
11
11
133
133
1422
11
11
11
11
131
131
13424
1431
11
11
144
144
1424
11
1422
133
1424
11
11
11
144
1424
1431
11
131

vs. all cycles starting with 2:

23143
22
22
22
242
2311
24311
22
22
242
24311
22
22
242
2434
242
2313
2311
22
244
242
22
22
244
2434
22
242
22
22
23143
2342
233
22
22
22
22
22
22
2343
23144
23142
22
22
22
22
2311
242
22
22
2342
242
242
22
22
233
22
242
242
2433
22
2342
22
233
22
22
22
22
22
244
22
2311
244
244
242
244
22
242
242
22
22
23143
242
22
233
2343
22
242
22
22
22
22
244

I think you will find a deadlock is probably impossible! A repeat must happens extremely quickly on 1 side or the other (2).

[donik7777]

I found that with the following four outcomes, CL1 defined by Red cannot be followed by CL1 defined by Black (and vice versa):
CL1dR
CL2dR
CL1dB
CL2dB

Gil maybe we can use that if we see imbalance here?

[falkor2k15]

Here's a fractal I generated from quads based on the same rules as the triangle - but using up, down, left, right in a square formation.

0   500
0   -750
-500   -750
750   -750
-875   -750
-875   -125
-875   -438
938   -438
31   -438
485   -438
485   719
-743   719
-743   -860
-743   930
872   930
-936   930
-936   -965
-32   -965
-32   -18
-32   -491
-32   746
-32   127
-32   437
-32   -719
-32   -141
516   -141
516   571
516   -786
242   -786
-621   -786
-190   -786
595   -786
595   893
-798   893
899   893
899   54
51   54
475   54
475   473
263   473
369   473
369   264
-685   264
-158   264
-158   368
-158   -684
-158   842
-421   842
711   842
711   -921
711   961
711   20
711   -510
-856   -510
-856   -245
928   -245
-964   -245
-18   -245
-491   -245
746   -245
746   623
746   -812
746   906
746   47
746   -524
746   762
127   762
127   119
127   -560
437   -560
437   780
282   780
-641   780
-180   780
-410   780
-295   780
-353   780
-353   -890
-353   -55
-353   -473
-353   737
-353   -869
-353   935
-324   935
-324   33
-324   -517
-338   -517
-338   759
669   759
-835   759
-835   -880
-835   -60
-835   -470
-835   735
-83   735
-83   -868
-83   934
-459   934
-271   934
636   934
636   -967
182   -967
182   -17
182   509
409   509
-705   509
853   509
74   509
463   509
-732   509
-134   509
567   509
217   509
392   509
-696   509
-696   246
-152   246
-424   246
712   246
712   -623
712   -189
144   -189
-572   -189
-214   -189
-214   595
-393   595
-393   -798
697   -798
697   899
697   -950
697   975
-849   975
-849   13
-849   494
925   494
925   253
925   -627
925   -187
-963   -187
-19   -187
510   -187
245   -187
245   -407
-623   -407
812   -407
94   -407
453   -407
453   704
453   -852
453   926
-727   926
864   926
864   -963
864   982
864   -991
864   996
864   -998
68   -998
68   -1
-534   -1
-534   501
-233   501
-233   250
-233   -625
617   -625
617   813
617   -907
617   954
192   954
192   -977
192   989
192   6







Up next: will do the same with:
CL1dR
CL2dR
CL1dB
CL2dB

[falkor2k15]

Looks a bit different now:

[Bigbroben]

[RouletteGhost]

Stop this stupid nonsense before you kill more brain cells

[Bigbroben]

Never!

[falkor2k15]

Apologies, but there was a mistake in my calculations before. The correct data generates the following instead:

Quads


4 EC Options


500   0
500   -500
-250   -500
-250   250
-250   -375
-625   -375
-625   -688
-625   156
-625   -422
-625   -711
-625   145
188   145
594   145
797   145
899   145
950   145
950   573
975   573
975   -214
-13   -214
-507   -214
-507   -607
-754   -607
-754   -804
-877   -804
-877   -902
-939   -902
-939   -951
-970   -951
-970   25
15   25
15   -488
15   256
508   256
754   256
754   628
etc.

[falkor2k15]

Above was 2K spins; below is 10K spins for 4 EC options:


Zoomed in


NOTE: The 4 EC options (some outcomes cannot follow others) are more concentrated in specific areas compared to equally-likely quads.