System 2

[Andre Chass]

Basically, it is played using the last two balls thrown; the anterior and posterior of the last one, and the anterior and posterior of the second last.
Follow this example for better understanding:
Number 20 is thrown, then 3. You should bet in the next ball numbers 19, 21, 2, 4.
Then 10 is thrown. You should bet numbers 2, 4, 9, 11.
Then 30 is thrown. You should bet numbers 9, 11, 29, 31.
And so on...
Clarifications
If 0 or 36 is thrown, you should only bet numbers 1 and 35 respectively, since there isn't an anterior number for 0 and a posterior for 35.
If the last two numbers thrown are, for example, 5 and 7, only three numbers should be bet: 4, 6, 8.
For Double Zero Roulettes, the double zero will be treated as the zero.
Betting

Despite is proven that there isn't secure method to beat the roulette, this method increments the chance for success.
The betting strategy is the most sensible issue of this system, since using progressions is always risky.
It is recommended to play it only once per displacement (a displacement is a consecutive series of 36 balls). Therefore, if we have won in the ball number fifteen, you should wait for the displacement to complete before starting over.

A safe way to play it is to wait between 12 and 14 balls without achieving victory and then begin.
It can also be played directly, without waiting. In this the case, you should define a maximum chips limit for the progression, for example 50 chips. At this point you should stop and start over; otherwise the progression might become very big.

[Firefox]

Despite is proven that there isn't secure method to beat the roulette, this method increments the chance for success.

How?

I think your system of neighbours of the number which has hit is a better shot, and has some slight logic.

The numbers numerically one greater and lesser have no connection with the number hit eg 29 and 31 have no connection with 30, they are just labels for pockets; they could be A, B, and C or J R and Z.