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**System Players Only (no advantage play)**

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**Re: Random Thoughts**

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on Jul 31, 11:54 AM 2018 to 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.

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.