Learn to Excel @ Edge!

[falkor2k15]

Following Priyanka's Random Thoughts topic and Reddwarf's advice, I first managed to obtain edge, mathematically, by studying a spreadsheet displaying parallel cycles - generated from 1 million real casino spins put through my computer simulation.


With this excel you do not need to test or simulate roulette over 1 million spins - it's done for you already - you simply need to toggle the filters and find a way to overcome the "constant bet"!
Edit: I had to reduce the data by 50% to successfully attach it here due to space constraints.

Tabs 1-2 = Halves + Dozens
Tabs 3-4 = Dozens + Lines

"No matter how you look at it, or analyse it, any non-random stream such as the dozens we have been looking at, or even VdW et al, will not now nor ever, under any circumstances, provide an edge. This should not be a surprise as this is a single bet and so the odds will assert since there is nothing for a bias to be formed with as it is a single stream. So further streams are necessary in order for a dependency to be involved such that a bias can manifest."--Anonymous

So there you have it... 2+ streams are required!

Let's first look at Dozen Cycles as a separate stream:
Each cycle has 3-6 outcomes:
CL1 = 11 or 22 or 33
CL2 = 121 or 233 or 311, etc.
CL3 = 1231 or 3122, etc.

Order 1 = 11, 212, 3123, etc.
Order 2 = 122, 3212, etc.
Order 3 = 1233 or 3122, etc.

CL1o1 = 11, 22 or 33
CL2o1 = 121, 323, etc.
CL2o2 = 122,233,311, etc.
CL3o1 = 1231, 2312, etc
CL3o2 = 1232, 2131, etc.
CL3o3 = 1233, 2133, etc.

The "Constant Bet" is when you add up the profit/loss from playing an infinite amount of cycles, the result (without adding zeroes to the mix) is break even. Line cycles are the same, but with even more outcomes that break even.

"The thinking tool is the grouped constant bets: can we use structures to ensure that when we combine an infinite number of cycles we still win?"--reddwarf

"In general there are 2 types of relationships:
1. The group one belongs to.
2. The distance"--reddwarf

Can you find an exploit using just the "group" without the "distance"? Only the "group" relationships are recorded in the spreadsheet - not distances. Here's a clue:

Priyanka's defining element: "You will find that the probability that a repeat has the same half as the starting number is larger than 50%." --reddwarf

Defined by same for dozen cycles is 63%
1... 63% the repeat will be dozen 1 because it only requires one more appearance to be awarded the repeat. The other 2 dozens require 2 appearances to overtake dozen 1 and instead be awarded the repeat.

However, playing defined by same (AKA Order 1) in the long run results in break even like the rest of the 3-6 outcomes, so why might order 1 be favored compared to the rest? Since everything breaks even, perhaps the odds and most likely events are irrelevant, leaving only the relationships.





66% may seem like edge at first, but to bet CL2-3 requires a 2 dozen bet and CL1 only a 1 dozen bet, hence break even in the long run.

How can you use the attached Excel spreadsheet and parallel streams to overcome the "constant bet" and in the process, gain edge?

Happy New Year!