I've created a dos-box program (attatched to this post), that simulates "2^(-1) + 2^(-2) + 2^(-3) + ..." method. I've extended it a bit, now it works like this:
A aimed c-value is entered. The stop points are chosen by the program to make the c-value when reaching one of them stay lower than the aimed c-value, no matter how many trials are performed. The numer of total trials can be limited by the user to make the program stop after a reasonable number of trials. Every stop point is allowed to 'consume' a certain percentage (or less) of the remaining "aimed c-value reservoir". This percentage can be chosen by the user as 3rd input (0.01 - 0.99). Example:
The aimed c-value is 0.05. The percentage is 0.4.
The c-value for the 1st stop point must be smaller than 0.05*0.4 = 0.02, this is the case for
6/6, c-value = 0.0156. The "reservoir" is now 0.05-0.0156 = 0.0344.
What's added by the next stop point to the c-value must be smaller than 0.0344*0.4 = 0.0138. This is the case for
8/9, c-value = 0.0273. "reservoir": 0.0227. Next stop point must add 0.0091 or less:
10/12., c-value = 0.0354
...
Here's an example showing how the percentage value affects the stop points:
For comparison the number of trials is limited to 50, but there's no limit in practice (besides limits caused by overflow in software etc.):
Aimed c-value = 0.01.
1. Percentage = 0.1:
1. Stop point: (10/10) C-Value: 0.000976563
2. Stop point: (13/14) C-Value: 0.00158691
3. Stop point: (15/17) C-Value: 0.00223541
4. Stop point: (17/20) C-Value: 0.00282192
5. Stop point: (19/23) C-Value: 0.00332022
6. Stop point: (21/26) C-Value: 0.00373085
7. Stop point: (23/29) C-Value: 0.0040638
8. Stop point: (24/31) C-Value: 0.00459897
9. Stop point: (26/34) C-Value: 0.00496011
10. Stop point: (28/37) C-Value: 0.00523142
11. Stop point: (29/39) C-Value: 0.00564917
12. Stop point: (31/42) C-Value: 0.00592204
13. Stop point: (32/44) C-Value: 0.00632385
14. Stop point: (34/47) C-Value: 0.00657883
15. Stop point: (36/50) C-Value: 0.00676343
2. Percentage = 0.31. Stop point: (9/9) C-Value: 0.00195313
2. Stop point: (11/12) C-Value: 0.00415039
3. Stop point: (14/16) C-Value: 0.00511169
4. Stop point: (16/19) C-Value: 0.00601006
5. Stop point: (18/22) C-Value: 0.00676394
6. Stop point: (20/25) C-Value: 0.00737441
7. Stop point: (22/28) C-Value: 0.00786117
8. Stop point: (24/31) C-Value: 0.00824657
9. Stop point: (26/34) C-Value: 0.00855083
10. Stop point: (28/37) C-Value: 0.00879084
11. Stop point: (30/40) C-Value: 0.00898025
12. Stop point: (31/42) C-Value: 0.00927956
13. Stop point: (33/45) C-Value: 0.00947899
14. Stop point: (35/48) C-Value: 0.00962775
3. Percentage = 0.51. Stop point: (8/8) C-Value: 0.00390625
2. Stop point: (11/12) C-Value: 0.00585938
3. Stop point: (13/15) C-Value: 0.00769043
4. Stop point: (16/19) C-Value: 0.00844574
5. Stop point: (18/22) C-Value: 0.00913858
6. Stop point: (21/26) C-Value: 0.00942713
7. Stop point: (23/29) C-Value: 0.00969638
8. Stop point: (26/33) C-Value: 0.00981075
9. Stop point: (29/37) C-Value: 0.00986504
10. Stop point: (31/40) C-Value: 0.00991874
11. Stop point: (34/44) C-Value: 0.0099426
12. Stop point: (36/47) C-Value: 0.00996601
4. Percentage = 0.81. Stop point: (7/7) C-Value: 0.0078125
2. Stop point: (11/12) C-Value: 0.00952148
3. Stop point: (16/18) C-Value: 0.00973511
4. Stop point: (19/22) C-Value: 0.00986528
5. Stop point: (22/26) C-Value: 0.00993642
6. Stop point: (25/30) C-Value: 0.00997436
7. Stop point: (28/34) C-Value: 0.00999449
8. Stop point: (33/40) C-Value: 0.00999717
9. Stop point: (36/44) C-Value: 0.00999893
10. Stop point: (40/49) C-Value: 0.00999945
5. Percentage = 0.91. Stop point: (7/7) C-Value: 0.0078125
2. Stop point: (11/12) C-Value: 0.00952148
3. Stop point: (15/17) C-Value: 0.00994873
4. Stop point: (21/24) C-Value: 0.00997794
5. Stop point: (25/29) C-Value: 0.00998824
6. Stop point: (28/33) C-Value: 0.00999505
7. Stop point: (31/37) C-Value: 0.00999912
8. Stop point: (36/43) C-Value: 0.0099997
9. Stop point: (40/48) C-Value: 0.0099999