Sample positions, both ways
The rule page shows four positions where the Timmes Race Rule beats Isight. Those four were picked because Isight's mistakes there are large. To be fair, this page shows positions picked at random: eight where Timmes is right and Isight wrong, and eight where Isight is right and Timmes wrong.
How the positions were picked
- Only positions from the half of Tom Keith's database that the rule was never tuned on.
- "Timmes" means the whole-pip version (the app's default). The exact version is shown too.
- Only the first double and the take are compared, with the cube in the middle.
- For each race length, two positions were drawn at random from each group (Python
random.Random(2026)). The four positions from the rule page were left out.
All disagreements, not just these sixteen
Every double and take decision in the held-out half where exactly one of the two methods is right:
| Roller's pips | Timmes right, Isight wrong | Points Isight loses | Isight right, Timmes wrong | Points Timmes loses |
|---|---|---|---|---|
| 12 or less | 301 | 88.4 | 148 | 33.2 |
| 13–30 | 560 | 75.6 | 403 | 57.2 |
| 31–60 | 189 | 13.3 | 126 | 10.3 |
| Over 60 | 206 | 7.2 | 134 | 4.0 |
| All | 1,256 | 184.6 | 811 | 104.7 |
"Points lost" is the total equity given away on those decisions, per point of cube value, from Keith's rollouts. The held-out half has 51,502 double and take decisions; on all the others the two methods are both right or both wrong.
How to read each position: White is on roll at the bottom, the cube is in the middle, and the equities are Keith's rollouts for White. Doubling is right when Double/take beats No double; taking is right when Double/take is below +1.000. The GNU Backgammon ID only records the checkers: paste it into GNU Backgammon with White on roll and the cube centred to check the position yourself.
Where Timmes is right and Isight is wrong
1. 12 or less pips: White 8, Black 13
White (on roll, bottom) 8 pips, 5 checkers · Black 13 pips, 4 checkers · White wins 68% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) pgAAYAcAAAAAAA
See how each method counts it:
- 8 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 4-point, opponent holds his
- +1 empty 5-point, opponent holds his
- +1 1 more checker left than the opponent (5 vs 4)
- 13 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
12 + 12/6 = 14 · 14 − 13 = 1 → Double / pass
- 8 pips
- +3 base
- +4 2 on the ace point × 2
- +4.5 3 on the 2-point × 1½
- +½ 3 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (5)
- 13 pips
- +3 base
- +3 2 on the 2-point × 1½
- +½ 1 on the 4-point × ½
Timmes whole pips: short bear-off count (White has 8 pips, both sides home). No boost; double if the difference is ≤ 7 − 21.5/10 = 4.85, take if ≥ 1
21.5 − 19.5 = 2 → Double / take
- 8 pips
- +3 base
- +4 2 on the ace point × 2
- +4.5 3 on the 2-point × 1½
- +½ 3 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (5)
- 13 pips
- +3 base
- +3 2 on the 2-point × 1½
- +½ 1 on the 4-point × ½
Timmes exact: short bear-off count (White has 8 pips, both sides home). No boost; double if the difference is ≤ 7 − 21.5/10 = 4.85, take if ≥ 1
21.5 − 19.5 = 2 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 12 + 1/6 = 14 | 13 | 1 | Double / pass ✗ |
| Timmes (whole pips) | 21.5 (short count) | 19.5 | 2 | Double / take ✓ |
| Timmes (exact) | 21.5 (short count) | 19.5 | 2 | Double / take ✓ |
The Isight mistake costs 0.449 of a point per cube.
2. 12 or less pips: White 7, Black 9
White (on roll, bottom) 7 pips, 6 checkers · Black 9 pips, 5 checkers · White wins 80% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) WwAAwBcAAAAAAA
See how each method counts it:
- 7 pips
- +6 5 checkers on the 1-point: 2 each beyond 2
- +1 1 more checker left than the opponent (6 vs 5)
- 9 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
14 + 14/6 = 16.3 · 16.3 − 9 = 7.3 → No double
- 7 pips
- +3 base
- +10 5 on the ace point × 2
- +1½ 1 on the 2-point × 1½
- +1½ 5 on the 1-point: ½ each beyond 2
- 9 pips
- +3 base
- +4 2 on the ace point × 2
- +3 2 on the 2-point × 1½
- +1 1 on the 3-point × 1
- +1½ odd number of checkers (5)
Timmes whole pips: short bear-off count (White has 7 pips, both sides home). No boost; double if the difference is ≤ 7 − 23/10 = 4.7, take if ≥ 1
23 − 21.5 = 1.5 → Double / take
- 7 pips
- +3 base
- +10 5 on the ace point × 2
- +1½ 1 on the 2-point × 1½
- +1½ 5 on the 1-point: ½ each beyond 2
- 9 pips
- +3 base
- +4 2 on the ace point × 2
- +3 2 on the 2-point × 1½
- +1 1 on the 3-point × 1
- +1½ odd number of checkers (5)
Timmes exact: short bear-off count (White has 7 pips, both sides home). No boost; double if the difference is ≤ 7 − 23/10 = 4.7, take if ≥ 1
23 − 21.5 = 1.5 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 14 + 1/6 = 16.3 | 9 | 7.3 | No double ✗ |
| Timmes (whole pips) | 23 (short count) | 21.5 | 1.5 | Double / take ✗ |
| Timmes (exact) | 23 (short count) | 21.5 | 1.5 | Double / take ✗ |
The Isight mistake costs 0.408 of a point per cube.
3. 13–30 pips: White 20, Black 15
White (on roll, bottom) 20 pips, 5 checkers · Black 15 pips, 8 checkers · White wins 82% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) dwMAANQIAAAAAA
See how each method counts it:
- 20 pips
- +1 1 more crossover than the opponent (1 vs 0)
- 15 pips
- +2 3 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 4-point, opponent holds his
- +3 3 more checkers left than the opponent (8 vs 5)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
21 + 21/6 = 24.5 · 24.5 − 22 = 2.5 → Double / take
- 20 pips
- +1 1 more crossover than the opponent (1 vs 0)
- 15 pips
- +2 3 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 4-point, opponent holds his
- +6 3 more checkers left than the opponent (8 vs 5) × 2 (race of 30 pips or less)
Timmes whole pips (roller has 20 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
21 + 21/7 = 24 · 24 − 25 = -1 → Double / pass
- 20 pips
- +1 1 more crossover than the opponent (1 vs 0)
- 15 pips
- +2 3 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 4-point, opponent holds his
- +4.5 3 more checkers left than the opponent (8 vs 5) × 1.5 (race of 30 pips or less)
Timmes exact (roller has 20 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
21 + 21/7 = 24 · 24 − 23.5 = 0.5 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 21 + 1/6 = 24.5 | 22 | 2.5 | Double / take ✗ |
| Timmes (whole pips) | 21 + 1/7 = 24 | 25 | -1 | Double / pass ✓ |
| Timmes (exact) | 21 + 1/7 = 24 | 23.5 | 0.5 | Double / pass ✓ |
The Isight mistake costs 0.272 of a point per cube.
4. 13–30 pips: White 27, Black 19
White (on roll, bottom) 27 pips, 7 checkers · Black 19 pips, 11 checkers · White wins 84% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 7xcAANANgAAAAA
See how each method counts it:
- 27 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +2 2 more crossovers than the opponent (2 vs 0)
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +4 6 checkers on the 2-point: 1 each beyond 2
- +4 4 more checkers left than the opponent (11 vs 7)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
30 + 30/6 = 35 · 35 − 31 = 4 → Double / take
- 27 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +2 2 more crossovers than the opponent (2 vs 0)
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +4 6 checkers on the 2-point: 1 each beyond 2
- +8 4 more checkers left than the opponent (11 vs 7) × 2 (race of 30 pips or less)
Timmes whole pips (roller has 27 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
30 + 30/7 = 34.3 · 34.3 − 35 = -0.7 → Double / pass
- 27 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +2 2 more crossovers than the opponent (2 vs 0)
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +4 6 checkers on the 2-point: 1 each beyond 2
- +6 4 more checkers left than the opponent (11 vs 7) × 1.5 (race of 30 pips or less)
Timmes exact (roller has 27 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
30 + 30/7 = 34.3 · 34.3 − 33 = 1.3 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 30 + 1/6 = 35 | 31 | 4 | Double / take ✗ |
| Timmes (whole pips) | 30 + 1/7 = 34.3 | 35 | -0.7 | Double / pass ✓ |
| Timmes (exact) | 30 + 1/7 = 34.3 | 33 | 1.3 | Double / take ✗ |
The Isight mistake costs 0.301 of a point per cube.
5. 31–60 pips: White 60, Black 67
White (on roll, bottom) 60 pips, 15 checkers · Black 67 pips, 15 checkers · White wins 79% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 7e4SAgDbdhcAAA
See how each method counts it:
- 60 pips
- 67 pips
- +1 1 more crossover than the opponent (2 vs 1)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
60 + 60/6 = 70 · 70 − 68 = 2 → Double / take
- 60 pips
- 67 pips
- +1 1 more crossover than the opponent (2 vs 1)
Timmes whole pips (roller has 60 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
60 + 60/8 = 67.5 · 67.5 − 68 = -0.5 → Double / pass
- 60 pips
- 67 pips
- +½ 3 checkers on the 3-point: ½ each beyond 2
- +1 1 more crossover than the opponent (2 vs 1)
Timmes exact (roller has 60 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
60 + 60/8 = 67.5 · 67.5 − 68.5 = -1 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 60 + 1/6 = 70 | 68 | 2 | Double / take ✗ |
| Timmes (whole pips) | 60 + 1/8 = 67.5 | 68 | -0.5 | Double / pass ✓ |
| Timmes (exact) | 60 + 1/8 = 67.5 | 68.5 | -1 | Double / pass ✓ |
The Isight mistake costs 0.037 of a point per cube.
6. 31–60 pips: White 37, Black 42
White (on roll, bottom) 37 pips, 12 checkers · Black 42 pips, 10 checkers · White wins 65% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 6V4AANj1BgAAAA
See how each method counts it:
- 37 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 6-point, opponent holds his
- +2 2 more checkers left than the opponent (12 vs 10)
- 42 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
41 + 41/6 = 47.8 · 47.8 − 42 = 5.8 → Double / take
- 37 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 6-point, opponent holds his
- +2 2 more checkers left than the opponent (12 vs 10)
- 42 pips
Timmes whole pips (roller has 37 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
41 + 41/8 = 46.1 · 46.1 − 42 = 4.1 → No double
- 37 pips
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 6-point, opponent holds his
- +2 2 more checkers left than the opponent (12 vs 10)
- 42 pips
Timmes exact (roller has 37 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
41 + 41/8 = 46.1 · 46.1 − 42 = 4.1 → No double
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 41 + 1/6 = 47.8 | 42 | 5.8 | Double / take ✗ |
| Timmes (whole pips) | 41 + 1/8 = 46.1 | 42 | 4.1 | No double ✓ |
| Timmes (exact) | 41 + 1/8 = 46.1 | 42 | 4.1 | No double ✓ |
The Isight mistake costs 0.054 of a point per cube.
7. Over 60 pips: White 75, Black 81
White (on roll, bottom) 75 pips, 15 checkers · Black 81 pips, 15 checkers · White wins 71% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 8u4HAgC23QsBAA
See how each method counts it:
- 75 pips
- +1 1 more crossover than the opponent (2 vs 1)
- 81 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
76 + 76/6 = 88.7 · 88.7 − 81 = 7.7 → No double
- 75 pips
- +1 1 more crossover than the opponent (2 vs 1)
- 81 pips
- +1 6 checkers on the 6-point: 1 each beyond 5
Timmes whole pips (roller has 75 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
76 + 76/6 = 88.7 · 88.7 − 82 = 6.7 → Double / take
- 75 pips
- +1 1 more crossover than the opponent (2 vs 1)
- 81 pips
- +1 6 checkers on the 6-point: ½ each beyond 4
Timmes exact (roller has 75 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
76 + 76/6 = 88.7 · 88.7 − 82 = 6.7 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 76 + 1/6 = 88.7 | 81 | 7.7 | No double ✗ |
| Timmes (whole pips) | 76 + 1/6 = 88.7 | 82 | 6.7 | Double / take ✓ |
| Timmes (exact) | 76 + 1/6 = 88.7 | 82 | 6.7 | Double / take ✓ |
The Isight mistake costs 0.019 of a point per cube.
8. Over 60 pips: White 79, Black 82
White (on roll, bottom) 79 pips, 15 checkers · Black 82 pips, 15 checkers · White wins 74% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 2/gRBQBq9ysAAA
See how each method counts it:
- 79 pips
- 82 pips
- +1 empty 4-point, opponent holds his
- +1 empty 5-point, opponent holds his
- +2 2 more crossovers than the opponent (4 vs 2)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
79 + 79/6 = 92.2 · 92.2 − 86 = 6.2 → No double
- 79 pips
- +1 6 checkers on the 6-point: 1 each beyond 5
- 82 pips
- +1 6 checkers on the 6-point: 1 each beyond 5
- +1 empty 4-point, opponent holds his
- +1 empty 5-point, opponent holds his
- +2 2 more crossovers than the opponent (4 vs 2)
Timmes whole pips (roller has 79 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
80 + 80/6 = 93.3 · 93.3 − 87 = 6.3 → Double / take
- 79 pips
- +1 6 checkers on the 6-point: ½ each beyond 4
- 82 pips
- +1 6 checkers on the 6-point: ½ each beyond 4
- +1 empty 4-point, opponent holds his
- +1 empty 5-point, opponent holds his
- +2 2 more crossovers than the opponent (4 vs 2)
Timmes exact (roller has 79 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
80 + 80/6 = 93.3 · 93.3 − 87 = 6.3 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 79 + 1/6 = 92.2 | 86 | 6.2 | No double ✗ |
| Timmes (whole pips) | 80 + 1/6 = 93.3 | 87 | 6.3 | Double / take ✓ |
| Timmes (exact) | 80 + 1/6 = 93.3 | 87 | 6.3 | Double / take ✓ |
The Isight mistake costs 0.055 of a point per cube.
Where Isight is right and Timmes is wrong
9. 12 or less pips: White 11, Black 12
White (on roll, bottom) 11 pips, 7 checkers · Black 12 pips, 7 checkers · White wins 76% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) +wAAAPcAAAAAAA
See how each method counts it:
- 11 pips
- +2 3 checkers on the 1-point: 2 each beyond 2
- +2 4 checkers on the 2-point: 1 each beyond 2
- 12 pips
- +3 5 checkers on the 2-point: 1 each beyond 2
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
15 + 15/6 = 17.5 · 17.5 − 15 = 2.5 → Double / take
- 11 pips
- +3 base
- +6 3 on the ace point × 2
- +6 4 on the 2-point × 1½
- +½ 3 on the 1-point: ½ each beyond 2
- +1 4 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (7)
- 12 pips
- +3 base
- +4 2 on the ace point × 2
- +7.5 5 on the 2-point × 1½
- +1½ 5 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (7)
Timmes whole pips: short bear-off count (White has 11 pips, both sides home). No boost; double if the difference is ≤ 7 − 29/10 = 4.1, take if ≥ 1
29 − 29.5 = -0.5 → Double / pass
- 11 pips
- +3 base
- +6 3 on the ace point × 2
- +6 4 on the 2-point × 1½
- +½ 3 on the 1-point: ½ each beyond 2
- +1 4 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (7)
- 12 pips
- +3 base
- +4 2 on the ace point × 2
- +7.5 5 on the 2-point × 1½
- +1½ 5 on the 2-point: ½ each beyond 2
- +1½ odd number of checkers (7)
Timmes exact: short bear-off count (White has 11 pips, both sides home). No boost; double if the difference is ≤ 7 − 29/10 = 4.1, take if ≥ 1
29 − 29.5 = -0.5 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 15 + 1/6 = 17.5 | 15 | 2.5 | Double / take ✓ |
| Timmes (whole pips) | 29 (short count) | 29.5 | -0.5 | Double / pass ✗ |
| Timmes (exact) | 29 (short count) | 29.5 | -0.5 | Double / pass ✗ |
The Timmes mistake costs 0.020 of a point per cube.
10. 12 or less pips: White 5, Black 3
White (on roll, bottom) 5 pips, 1 checkers · Black 3 pips, 1 checkers · White wins 86% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) BAAAQAAAAAAAAA
See how each method counts it:
- 5 pips
- 3 pips
- +1 empty 5-point, opponent holds his
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
5 + 5/6 = 5.8 · 5.8 − 4 = 1.8 → Double / pass
- 5 pips
- +3 base
- +1½ odd number of checkers (1)
- 3 pips
- +3 base
- +1 1 on the 3-point × 1
- +1½ odd number of checkers (1)
Timmes whole pips: short bear-off count (White has 5 pips, both sides home). No boost; double if the difference is ≤ 7 − 9.5/10 = 6.05, take if ≥ 1
9.5 − 8.5 = 1 → Double / take
- 5 pips
- +3 base
- +1½ odd number of checkers (1)
- 3 pips
- +3 base
- +1 1 on the 3-point × 1
- +1½ odd number of checkers (1)
Timmes exact: short bear-off count (White has 5 pips, both sides home). No boost; double if the difference is ≤ 7 − 9.5/10 = 6.05, take if ≥ 1
9.5 − 8.5 = 1 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 5 + 1/6 = 5.8 | 4 | 1.8 | Double / pass ✓ |
| Timmes (whole pips) | 9.5 (short count) | 8.5 | 1 | Double / take ✗ |
| Timmes (exact) | 9.5 (short count) | 8.5 | 1 | Double / take ✗ |
The Timmes mistake costs 0.444 of a point per cube.
11. 13–30 pips: White 19, Black 34
White (on roll, bottom) 19 pips, 10 checkers · Black 34 pips, 7 checkers · White wins 84% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 4Q4AAO8OAAAAAA
See how each method counts it:
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +3 3 more checkers left than the opponent (10 vs 7)
- 34 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
29 + 29/6 = 33.8 · 33.8 − 34 = -0.2 → Double / pass
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +6 3 more checkers left than the opponent (10 vs 7) × 2 (race of 30 pips or less)
- 34 pips
Timmes whole pips (roller has 19 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
32 + 32/7 = 36.6 · 36.6 − 34 = 2.6 → Double / take
- 19 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +1 3 checkers on the 2-point: 1 each beyond 2
- +½ 3 checkers on the 3-point: ½ each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +4.5 3 more checkers left than the opponent (10 vs 7) × 1.5 (race of 30 pips or less)
- 34 pips
Timmes exact (roller has 19 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
31 + 31/7 = 35.4 · 35.4 − 34 = 1.4 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 29 + 1/6 = 33.8 | 34 | -0.2 | Double / pass ✓ |
| Timmes (whole pips) | 32 + 1/7 = 36.6 | 34 | 2.6 | Double / take ✗ |
| Timmes (exact) | 31 + 1/7 = 35.4 | 34 | 1.4 | Double / take ✗ |
The Timmes mistake costs 0.295 of a point per cube.
12. 13–30 pips: White 17, Black 30
White (on roll, bottom) 17 pips, 10 checkers · Black 30 pips, 9 checkers · White wins 87% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) 6zQAALwvAAAAAA
See how each method counts it:
- 17 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +3 5 checkers on the 2-point: 1 each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +1 1 more checker left than the opponent (10 vs 9)
- 30 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
27 + 27/6 = 31.5 · 31.5 − 30 = 1.5 → Double / pass
- 17 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +3 5 checkers on the 2-point: 1 each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +2 1 more checker left than the opponent (10 vs 9) × 2 (race of 30 pips or less)
- 30 pips
Timmes whole pips (roller has 17 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
28 + 28/7 = 32 · 32 − 30 = 2 → Double / take
- 17 pips
- +4 4 checkers on the 1-point: 2 each beyond 2
- +3 5 checkers on the 2-point: 1 each beyond 2
- +1 empty 5-point, opponent holds his
- +1 empty 6-point, opponent holds his
- +1½ 1 more checker left than the opponent (10 vs 9) × 1.5 (race of 30 pips or less)
- 30 pips
- +½ 3 checkers on the 3-point: ½ each beyond 2
Timmes exact (roller has 17 pips: boost 1/7, double if ≤ 5, take if ≥ 1)
27.5 + 27.5/7 = 31.4 · 31.4 − 30.5 = 0.9 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 27 + 1/6 = 31.5 | 30 | 1.5 | Double / pass ✓ |
| Timmes (whole pips) | 28 + 1/7 = 32 | 30 | 2 | Double / take ✗ |
| Timmes (exact) | 27.5 + 1/7 = 31.4 | 30.5 | 0.9 | Double / pass ✓ |
The Timmes mistake costs 0.462 of a point per cube.
13. 31–60 pips: White 60, Black 67
White (on roll, bottom) 60 pips, 14 checkers · Black 67 pips, 15 checkers · White wins 76% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) s90PAABr7QcAAA
See how each method counts it:
- 60 pips
- 67 pips
- +1 1 more checker left than the opponent (15 vs 14)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
60 + 60/6 = 70 · 70 − 68 = 2 → Double / take
- 60 pips
- +1 6 checkers on the 6-point: 1 each beyond 5
- 67 pips
- +1 6 checkers on the 6-point: 1 each beyond 5
- +1 1 more checker left than the opponent (15 vs 14)
Timmes whole pips (roller has 60 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
61 + 61/8 = 68.6 · 68.6 − 69 = -0.4 → Double / pass
- 60 pips
- +1 6 checkers on the 6-point: ½ each beyond 4
- 67 pips
- +1 6 checkers on the 6-point: ½ each beyond 4
- +1 1 more checker left than the opponent (15 vs 14)
Timmes exact (roller has 60 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
61 + 61/8 = 68.6 · 68.6 − 69 = -0.4 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 60 + 1/6 = 70 | 68 | 2 | Double / take ✓ |
| Timmes (whole pips) | 61 + 1/8 = 68.6 | 69 | -0.4 | Double / pass ✗ |
| Timmes (exact) | 61 + 1/8 = 68.6 | 69 | -0.4 | Double / pass ✗ |
The Timmes mistake costs 0.073 of a point per cube.
14. 31–60 pips: White 33, Black 36
White (on roll, bottom) 33 pips, 8 checkers · Black 36 pips, 9 checkers · White wins 79% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) uTYAAGhrAAAAAA
See how each method counts it:
- 33 pips
- 36 pips
- +1 1 more checker left than the opponent (9 vs 8)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
33 + 33/6 = 38.5 · 38.5 − 37 = 1.5 → Double / pass
- 33 pips
- 36 pips
- +1 1 more checker left than the opponent (9 vs 8)
Timmes whole pips (roller has 33 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
33 + 33/8 = 37.1 · 37.1 − 37 = 0.1 → Double / take
- 33 pips
- 36 pips
- +½ 3 checkers on the 3-point: ½ each beyond 2
- +1 1 more checker left than the opponent (9 vs 8)
Timmes exact (roller has 33 pips: boost 1/8, double if ≤ 4, take if ≥ 0)
33 + 33/8 = 37.1 · 37.1 − 37.5 = -0.4 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 33 + 1/6 = 38.5 | 37 | 1.5 | Double / pass ✓ |
| Timmes (whole pips) | 33 + 1/8 = 37.1 | 37 | 0.1 | Double / take ✗ |
| Timmes (exact) | 33 + 1/8 = 37.1 | 37.5 | -0.4 | Double / pass ✓ |
The Timmes mistake costs 0.080 of a point per cube.
15. Over 60 pips: White 78, Black 86
White (on roll, bottom) 78 pips, 15 checkers · Black 86 pips, 15 checkers · White wins 77% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) xv5VAADl7gsBAA
See how each method counts it:
- 78 pips
- 86 pips
- +1 empty 4-point, opponent holds his
- +1 1 more crossover than the opponent (3 vs 2)
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
78 + 78/6 = 91 · 91 − 88 = 3 → Double / take
- 78 pips
- 86 pips
- +3 8 checkers on the 6-point: 1 each beyond 5
- +1 empty 4-point, opponent holds his
- +1 1 more crossover than the opponent (3 vs 2)
Timmes whole pips (roller has 78 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
78 + 78/6 = 91 · 91 − 91 = 0 → Double / pass
- 78 pips
- +½ 5 checkers on the 6-point: ½ each beyond 4
- 86 pips
- +2 8 checkers on the 6-point: ½ each beyond 4
- +1 empty 4-point, opponent holds his
- +1 1 more crossover than the opponent (3 vs 2)
Timmes exact (roller has 78 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
78.5 + 78.5/6 = 91.6 · 91.6 − 90 = 1.6 → Double / pass
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 78 + 1/6 = 91 | 88 | 3 | Double / take ✓ |
| Timmes (whole pips) | 78 + 1/6 = 91 | 91 | 0 | Double / pass ✗ |
| Timmes (exact) | 78.5 + 1/6 = 91.6 | 90 | 1.6 | Double / pass ✗ |
The Timmes mistake costs 0.052 of a point per cube.
16. Over 60 pips: White 61, Black 65
White (on roll, bottom) 61 pips, 13 checkers · Black 65 pips, 13 checkers · White wins 70% (cubeless) · GNU Backgammon ID (checkers only; White on roll, cube centred) dO8DAIC69wAAAA
See how each method counts it:
- 61 pips
- 65 pips
Isight: boost 1/6, double if ≤ 6, take if ≥ 2
61 + 61/6 = 71.2 · 71.2 − 65 = 6.2 → No double
- 61 pips
- 65 pips
Timmes whole pips (roller has 61 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
61 + 61/6 = 71.2 · 71.2 − 65 = 6.2 → Double / take
- 61 pips
- 65 pips
- +½ 5 checkers on the 6-point: ½ each beyond 4
Timmes exact (roller has 61 pips: boost 1/6, double if ≤ 7, take if ≥ 2)
61 + 61/6 = 71.2 · 71.2 − 65.5 = 5.7 → Double / take
| Method | White (+ boost) | Black | Difference | Says |
|---|---|---|---|---|
| Isight | 61 + 1/6 = 71.2 | 65 | 6.2 | No double ✓ |
| Timmes (whole pips) | 61 + 1/6 = 71.2 | 65 | 6.2 | Double / take ✗ |
| Timmes (exact) | 61 + 1/6 = 71.2 | 65.5 | 5.7 | Double / take ✗ |
The Timmes mistake costs 0.008 of a point per cube.
What this shows
Many disagreements are close calls, where either answer costs only a few hundredths of a point. The Timmes rule wins more of them, and gives away fewer points overall, most of all in short races (30 pips or less), where its extra checker penalty and wider windows matter most. Isight still gets plenty right that Timmes misses, in every race length.
Back to the Timmes Race Rule · Comments and corrections: [email protected]