Random Thoughts

[Blueprint]

Win-Loss tally...?

Would that help you win?

[falkor2k15]

Would that help you win?

Well, Priyanka was playing Six Dozen Options mechanically based on the first available repeat, i.e.:
Option 1... bet option 1
Option 12... bet option 1+2
Option 123... bet option 1+2+3
Option 1231... win!

That's very similar to VdW, i.e. betting for the first available AP regardless of any stats, and was the basis for her "Journey" series of videos.

As with VdW focus on the green spreadsheet/six dozen options seems to be based on the Win-Loss registry:

Priyanka seems to mostly change her bet following a series of losses.

I can certainly make a tally and see if there's any patterns, but I doubt it.

[praline]

Well, Priyanka was playing Six Dozen Options mechanically based on the first available repeat, i.e.:
Option 1... bet option 1
Option 12... bet option 1+2
Option 123... bet option 1+2+3
Option 1231... win!

Amazing!
How did you understood that?

[falkor2k15]

Amazing!
How did you understood that?

It was in part thanks to you - but is no different to the VDW method, and doesn't result in edge, so nothing particularly amazing... an amazing bedtime story, perhaps?

[falkor2k15]

Here's the win-loss registry for Six Dozen Options as per mechanical rules:
L L L L W
L L L L W
L L L L W
L W
L W
L W L L W W
W W
L L L W
L L W
L L L W L W
L L L L L L L
L W
L W
W
L L L L W L L W L L W L
L W L L W
W
L W
W
W
L L L W
W
L L L L W
L L W
L L W
L W
W
L L L L L
L W L L W
L W
L W L L L
L L W
L W
W
W
W
L L W L W
L L W
L W L W L L W
L L W
L W
L L L L L L L
L L W
W
L W
L L W
W
L L L
L L W L L L W
L W
W
L L L L W
L W
L W
W
L L L L L W
L W L L L L W W
L L L W
L L L W
L W
L W
L L L L W W
L W L L W W
L W
L L W
L L L L W W
L W
L L L L L L
L W
L W W
L W L L L L W L L L L L L
W L L L L L L W
W
L W
L W
W
L W
L L L L W
L W
W
L L L L L W
L W
L L L W
L L W
L W
L W
L L L L L W
L L L L W
L W W
L W L W W
L W
L L W
L L L L
W
L L L L W
W
L L L L L
W
L L W
W
L L W
W
W
L L L W
W
L L W
W
W
L L W
L W
W
L L L L L W
L L L L W L L W L L W
L W
L L L W
L W
W
L L L L W
L L L W
W
L W
L L L L W
L L W
W
L L L L L W
L W L L W W
L L L L L L
W
L W
L L L W
L L L W W
L W L L L W
L W
L L W
L W
L L W
L L W
L L L W
L L W
L W
L W
L L W
W
L W
L L W
W
L L L L L L L
L L W W
L W
L W
W
L L L W
W
W
L W
L W
W
L L L L L W
W
L W
L L L L L L L
L L W
W
L L L W L W
W
L L L L W
L L W
L L L W
W
L W
L L W
W
L L W
L L L L L
L L L W
L L L L L L L
L L L
W
L W
L W
L L W
L W
L L L L L L
W
W
W
L L W
L L L L W W
L W W
W
L W
L W
L L L L W L L W W
L L W L W
L L L W
L L L L W
L W
L W
L L L W
W

Any pattern?

[falkor2k15]

There could be a slight bias...? 

[baldguy99]

Hello, I am new to join this forum. I am a Mathematics/Computer Science student that has been studying Combinatorial Theory, and especially Ramsey Theory. One day, I got the interesting idea to play casino games with some important theorems in Ramsey Theory, especially Van der Waerden's Theorem and Shur's Theorem. I started coding up a roulette simulator last night to test my algorithms.
This thread is cool. The first posts took a step in the right direction, but I think that there is lots and lots of room for further development, as well as the potential to lay other casino games in this type of strategy.

I think about the game of roulette as being a set S of 38 elements. We can partition this set into different partitions in different ways. Namely:

%%   =Partitions=
%%   __________________________________________
%%  | elements | partitions | number of ways |
%%  |----------|------------|----------------|
%%  |   12      |      3   |      2       |
%%  |   18      |   2      |   3          |
%%  |   1      |   36      |   1          |
%%  |   4      |   9      |   1          |
%%  |   2      |   18      |   1          |
%%  |   3      |   12      |   1          |
%%  |   6      |   6      |   1          |
%%  |----------------------------------------|
%%

Not to mention the fact that {0,00} will always be in their own disjoint partition of the set. We can actually identify multiple arithmetic progression at the same time, based on a single element being a member of multiple partitions at the same time. Thus, we can tremendously increase the odds of winning. Theoretically, I conjecture that it is possible to get almost 100% win rate.

Set partitions are an interesting area of math. The second kind of sterling number is the number of ways to partition a set of n elements in partitions of size k: S(n,k).  The Catalan Number is the number of non-intersecting partitions. You can calculate it by subtracting all set partitions that intersect from the second Sterling Number. The Catalan number is also the number of full binary trees on n+1 leaves, and is also the number of paths that can be taken to get from point A to point B  without crossing the diagonal straight line between the points.

There are many other applications of combinatorial number theory in Baccarat, for example, which can be thought of as a system of polynomials modulo 10.

[Blueprint]

Yes, first 5 pages of this thread... then it went to s#!t.

And yes, the beginnings are there.

[RouletteGhost]

Hello, I am new to join this forum. I am a Mathematics/Computer Science student that has been studying Combinatorial Theory, and especially Ramsey Theory. One day, I got the interesting idea to play casino games with some important theorems in Ramsey Theory, especially Van der Waerden's Theorem and Shur's Theorem. I started coding up a roulette simulator last night to test my algorithms.
This thread is cool. The first posts took a step in the right direction, but I think that there is lots and lots of room for further development, as well as the potential to lay other casino games in this type of strategy.

I think about the game of roulette as being a set S of 38 elements. We can partition this set into different partitions in different ways. Namely:

%%   =Partitions=
%%   __________________________________________
%%  | elements | partitions | number of ways |
%%  |----------|------------|----------------|
%%  |   12      |      3   |      2       |
%%  |   18      |   2      |   3          |
%%  |   1      |   36      |   1          |
%%  |   4      |   9      |   1          |
%%  |   2      |   18      |   1          |
%%  |   3      |   12      |   1          |
%%  |   6      |   6      |   1          |
%%  |----------------------------------------|
%%

Not to mention the fact that {0,00} will always be in their own disjoint partition of the set. We can actually identify multiple arithmetic progression at the same time, based on a single element being a member of multiple partitions at the same time. Thus, we can tremendously increase the odds of winning. Theoretically, I conjecture that it is possible to get almost 100% win rate.

Set partitions are an interesting area of math. The second kind of sterling number is the number of ways to partition a set of n elements in partitions of size k: S(n,k).  The Catalan Number is the number of non-intersecting partitions. You can calculate it by subtracting all set partitions that intersect from the second Sterling Number. The Catalan number is also the number of full binary trees on n+1 leaves, and is also the number of paths that can be taken to get from point A to point B  without crossing the diagonal straight line between the points.

There are many other applications of combinatorial number theory in Baccarat, for example, which can be thought of as a system of polynomials modulo 10.

Why would 0/00 be different than any of the other numbers?

You said they’d be their own partition.

Curious why

And welcome, interesting contribution there.

[Badger]

Why would 0/00 be different than any of the other numbers?

They don't fall under any dozen or EC ie any subset on the table except their own.

[baldguy99]

They don't fall under any dozen or EC ie any subset on the table except their own.

Because {0,00} cannot be in the partitions for red/black, even/odd, 1st 12, 2nd 12, etc. {0,00} is always disjoint from every other partition

[Badger]

That's what I meant. Except you said it more elegantly. 

[baldguy99]

Also, just to let it be known: I am really only interested in the mathematics. I want to use this to go playing once or twice, but I am most interested in the math. I am hoping that the OP and other interested people will post here so we can talk about it more. The thing is, Red/Black is not the only way to partition the set! there are many ways to do it at the same time. The trick is to keep track of multiple A.P.'s at the same time.

[Badger]

Sorry Baldguy.
I am mathematically challenged, so I guess that excludes me.
Perhaps this attachment might help you.

[Blueprint]

Also, just to let it be known: I am really only interested in the mathematics. I want to use this to go playing once or twice, but I am most interested in the math. I am hoping that the OP and other interested people will post here so we can talk about it more. The thing is, Red/Black is not the only way to partition the set! there are many ways to do it at the same time. The trick is to keep track of multiple A.P.'s at the same time.

Cool, also to let it be known if you're looking for a "mathematical proof" that could be a while.  Just setting expectations here.