Tiers et Tout

This roulette strategy called Tiers et Tout (a Third and All) is ascribed to Thomas Garcia.
Therefore, it is called Garcia Strategy or Garcia System sometimes.

The bets are always against the winning easy chance.
At first a third of the capital is placed.
On loss, the rest of the capital.
On win, again a third of the capital.

After two consecutive losses the offense is lost and the strategy restarts.
This strategy wins on every spin, as long as no series gets longer than two.

step tree

The "step tree" of this roulette strategy:

                                  1

                               +/    \-

                             2         1

                        +/      \-

                   3               4

             +/        \-        +/  \

          5               6     3      1

       +/   \-         +/   \-

      7       8       9       1

    +/\-    +/\-    +/\-

    10 11   12 1    7  8



     10      11      12

    +/\-    +/\-    +/\-

    13 14   10 1    15 16



     13      14      15      16

    +/\-    +/\-    +/\-    +/\-

    17 18   19 1    19 20   21 1



     17      18      19      20      21

    +/\-    +/\-    +/\-    +/\-    +/\-

    22 23   24 1    24 25   26 1    26 20



     22      23      24      25      26

    +/\-    +/\-    +/\-    +/\-    +/\-

    27 28   29 1    29 30   31 1    32 33

    

     27      28      29      30      31      32      33

    +/\-    +/\-    +/\-    +/\-    +/\-    +/\-    +/\-

    34 35   36 37   38 39   40 1    41 42   43 44   45 1

...

The steps in notation:
Number. Red/Black stake / capital

1. R 0/9
2. B 3/9
3. R 4/12
4. B 6/6
5. B 5/16
6. R 8/8
7. R 7/21
8. B 11/11
9. B 5/16
10. B 9/28
11. R 14/14
12. R 7/22
13. R 12/37
14. B 19/19
15. B 9/29
16. R 15/15
17. B 16/49
18. R 25/25
19. R 12/38
20. B 20/20
21. B 10/30
22. R 21/65
23. B 33/33
24. B 16/50
25. R 26/26
26. R 13/40
27. B 28/86
28. R 14/44
29. R 22/66
30. B 34/34
31. B 17/52
32. B 17/53
33. R 27/27
34. R 38/114
35. B 58/58
36. B 19/58
37. R 30/30
38. B 29/88
39. R 34/34
40. R 22/68
41. R 23/69
42. B 35/35
43. R 23/70
44. B 36/36
45. B 18/54
...

a little tolerance

If a little tolerance is kept on stakes / capital,
some steps and therefore whole strings can be saved.

Example:
31. B 17/52
32. B 17/53 - if this single piece difference is ignored, the whole string could be saved.

As this strategy is a demonstration, I did not make those simplifications!

The dot-mode flowchart illustrates the step tree quite nice: Tiers et Tout

Possibly it would be possible to model this classic of the roulette strategies further
and more extensively in the simulator by means of factored inserts.

Who would like to accept the topic gladly! ;-)

This step tree is amazing and very nice illustrated with the strategy flowchart.

Are there other roulette strategies built with the usage of trees?

What is the limit in depth?

Gerald:

What is the limit in depth?

How much do you think, you will need?
You won't beat roulette alone with a huge strategy!

Gerald:

Are there other roulette strategies built with the usage of trees?

I remember these:
last SC win-4 loss+6
Inaudi Wechselmarsch
color slide back
simple chances bet increase and decrease

Gerald:

What is the limit in depth?

Simple answer: there is no limit.
I am curious about how deep you will go!

I'm always amazed at what ideas people come up with.
Of course, there are endless approaches to building a roulette strategy,
but this variety is very amazing.
With the flowcharts you can get the strategies very quickly!

trizero:

Simple answer: there is no limit.
I am curious about how deep you will go!

Good to know, then I can rip from the full.

trizero:

Simple answer: there is no limit.

Every known computer is a limited, deterministic machine!
There must be a limit. I'll try to break the negative balance! ;-)