Birthday paradox

[falkor2k15]

I'm attempting to play the Birthday Paradox using the dual dependency created between various dozens and associated inner and outer cycle constants - all have to repeat as part of a series of events with different probabilities that are dynamically changing.



INNER CYCLE CONSTANTS

CL = Cycle Length
d = Defining Element (Dozen)
o = Order

OUTER CYCLE CONSTANTS

OCL = Outer Cycle Length
OO = Outer Order
ODC = Outer Defining Cycle
ODCL = Outer Defining Cycle Length
ODD = Outer Defining Element (Dozen)
ODO = Outer Defining Order

For example... Outer Cycle Length is dependent on the Inner Cycle Length:

108393	38%	Average
124802	44%
52405	18%
285600
29806	34%	CL1…
41482	47%
17684	20%
88972
69983	44%	CL2…
64329	41%
23065	15%
157377
8604	22%	CL3…
18991	48%
11656	30%
39251

CL1... more chance for OCL2 followed by OCL3
CL2... more chance for OCL1
CL3... more chance for OCL3 followed by OCL2

[Herby]

For example... Outer Cycle Length is dependent on the Inner Cycle Length:

108393	38%	Average
124802	44%
52405	18%
285600
29806	34%	CL1…
41482	47%
17684	20%
88972
69983	44%	CL2…
64329	41%
23065	15%
157377
8604	22%	CL3…
18991	48%
11656	30%
39251

CL1... more chance for OCL2 followed by OCL3
CL2... more chance for OCL1
CL3... more chance for OCL3 followed by OCL2

Hi falkor,
maybe you give an example what this numbers mean.
I programmed the cycles with Mathematica and could do a statistics check.
Greets

[Herby]

Just posted and got it. 

[falkor2k15]

CL2 > CL2 is most common sequence for 2 dozen cycles (inner) and it happens to be a repeat CL too to close the outer cycle @ OCL1. So when we get:
CL2... then there's more chance for outer CL1 because we expect CL2 > CL2 most of the time. And the stats confirm.

[praline]

9 â€" Event 1. -1
14 â€" Event 2. -2
11 â€" Event 1. -1
3 â€" Event 1. +1

can i ask why we bet is like this
9 â€" Event 1. -1
14 â€" Event 2. -2
11 â€" Event 1. -1   
       event repeated, count back three spins, and we have events 2 and 1 BUT next bet is made only for event 1
3 â€" Event 1. +1

[Utetopia]

Most of you know birthday paradox. And most of you might have dismissed its application in roulette.

Does anyone know what is the most popular birthday in europe and US? October 1st week. Why? Because hmm, christmas and new years eve. So something strange happening on new years eve which is making the odds tilt and make it better than 1/365 for days in october 1st week. So going back to the birthday paradox, does it tilt the odds of two people having the birthdays on October 1st week? I dont know the answer, but an interesting question to ask and think about. Where's Bayes. I could use his help.

Changing this to roulette, if there is a particular event out of a set of events that occurs in a higher frequency, is it highly likely that we are able to find a repeat of that event faster than expectation? Hmm.. good to think and thats what am thinking right now. Trying to find an event in a set of events that is highly likely to happen.




Its been over a year since this was posted, and I've only just come across it.
Is this something you're still interested in?
I too think that the birthday paradox/problem can be applied, and have run some tests, and would be interested in knowing your thoughts regarding my thinking and ideas.