Tiers et Tout – Roulette Strategy Explained (Garcia System)

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

The bets are always against the winning easy chance.
(In game theory, this would be called evil.)
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, those simplifications were not made!

Flowchart of Tiers et Tout

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

This classic of roulette strategies could potentially be modeled further
and more extensively in the simulator using factored stakes.

Anyone is welcome to take up the topic! ;-)

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

Are there other roulette strategies based on trees?
What is the depth limit?

Gerald:

What is the limit in depth?

How much depth is actually needed?
Roulette cannot be beaten by a huge strategy alone!

Gerald:

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

These come to mind:
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.
Curious to see how deep this will go!

It is always impressive what ideas people come up with.
Of course, there are endless approaches to building a roulette strategy,
but this variety is remarkable.
The flowcharts make it very easy to grasp the strategies quickly!

trizero:

Simple answer: there is no limit.
Curious to see how deep this will go!

Good to know - plenty of room to work with!

trizero:

Simple answer: there is no limit.

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