Increasing/decreasing probability in Roulette

[falkor2k15]

As you may already know: Roulette is not about 36 numbers; it's about proportionate risk/reward that results in break even (without any 0s) regardless of your bet selection on the various playing groups/partitions.

By default you can get about 97.3% MLE with 35 numbers and 2.7% LLE with 1 number.

To increase the LLE is quite simple by switching to 72 number Roulette - or once I even did a 144 number Roulette! In other words: if you get the same number in a row twice (19 19) then you have already halved the 2.7% with the potential of increasing your profits above 70 units via letting the bet ride so to speak.

But how to increase MLE at any time? This is a lot more difficult it seems, unless I am missing something simple? With 72 number Roulette we cannot bet more than half of those 72 partitions during any trial.

I can't say I've explored this in great detail before, but here's all I've managed to come up with so far - using Dozen cycles as an example:

1... 62% chance repeat will be on 1, i.e.:

11
121
1231
131, etc.

121... 71% chance 2nd repeat will be on 1, i.e.:

1 2 1 3 1
1 2 1 1
1 2 1 1
1 2 1 1
1 2 1 2 3 1
1 2 1 1
1 2 1 3 2 3 1

1... 44% chance repeat will be on Cycle Length 2, i.e.:

121
122

CL2... 76% chance repeating cycle length will be CL2, i.e.:

CL2 CL2
CL2 CL1 CL2
CL2 CL1 CL3 CL2

And with Six Dozen Options it's about 74% CL2-CL6 instead of normal dozen cycles (66% for CL2-3).

Exactly how that gain in MLE works needs to be understood; not sure if anyone else has thought about this before?

[Herby]

not sure if anyone else has thought about this before?

You should programm Mathematica:

Code Select Expand

Cycle[lst_] := Module[{n, n1, lstds, lenri, tk},
  n = 1; n1 = 1; lstds = {}; lenri = Length[lst];
  While[n < lenri - 1 && n1 + 1 < lenri,
   If[n1++; tk = Take[lst, {n, n1}]; Length[tk] > Length[Union[tk]],
    AppendTo[lstds, tk]; n = n1]];
  lstds]

These few lines give you the cycles of a tuple of numbers.
Another 1 liner gives the cyclelengths.
Again use the funtion above you get the CL of CL.

Somewhere in the wolfram cloud you can test your ideas.

Respect if you still work with Excel.

[Herby]

The lack of readability is mostly caused by the use of my variablenames.