Here's the doubling windows as calculated by my little python script. My initial approach was to calculate the cube action using both methods and
only output the scores where they differ, but a simpler and more
illuminating way to present it is to just output the doubling window for
each pipcount for the player on roll.

This is for initial doubles. For recubes, narrow the doubling window by
adding one to the first number. Include endpoints.

Comments cheerfully accepted.

Pips Trice ISight
99 : (107, 110) (109.5,113.5)
98 : (106, 109) (108.3,112.3)
97 : (105, 108) (107.2,111.2)
96 : (104, 107) (106.0,110.0)
95 : (103, 106) (104.8,108.8)
94 : (102, 105) (103.7,107.7)
93 : (101, 104) (102.5,106.5)
92 : (100, 103) (101.3,105.3)
91 : (99, 102) (100.2,104.2)
90 : (97, 100) (99.0,103.0)
89 : (96, 99) (97.8,101.8)
88 : (95, 98) (96.7,100.7)
87 : (94, 97) (95.5,99.5)
86 : (93, 96) (94.3,98.3)
85 : (92, 95) (93.2,97.2)
84 : (91, 94) (92.0,96.0)
83 : (90, 93) (90.8,94.8)
82 : (89, 92) (89.7,93.7)
81 : (88, 91) (88.5,92.5)
80 : (86, 89) (87.3,91.3)
79 : (85, 88) (86.2,90.2)
78 : (84, 87) (85.0,89.0)
77 : (83, 86) (83.8,87.8)
76 : (82, 85) (82.7,86.7)
75 : (81, 84) (81.5,85.5)
74 : (80, 83) (80.3,84.3)
73 : (79, 82) (79.2,83.2)
72 : (78, 81) (78.0,82.0)
71 : (77, 80) (76.8,80.8)
70 : (75, 78) (75.7,79.7)
69 : (74, 77) (74.5,78.5)
68 : (73, 76) (73.3,77.3)
67 : (72, 75) (72.2,76.2)
66 : (71, 74) (71.0,75.0)
65 : (70, 73) (69.8,73.8)
64 : (69, 72) (68.7,72.7)
63 : (68, 71) (67.5,71.5)
62 : (67, 70) (66.3,70.3)
61 : (66, 69) (65.2,69.2)
60 : (64, 67) (64.0,68.0)
59 : (63, 66) (62.8,66.8)
58 : (62, 65) (61.7,65.7)
57 : (61, 64) (60.5,64.5)
56 : (60, 63) (59.3,63.3)
55 : (59, 62) (58.2,62.2)
54 : (58, 61) (57.0,61.0)
53 : (56, 59) (55.8,59.8)
52 : (55, 58) (54.7,58.7)
51 : (54, 57) (53.5,57.5)
50 : (53, 56) (52.3,56.3)
49 : (52, 55) (51.2,55.2)
48 : (51, 54) (50.0,54.0)
47 : (50, 53) (48.8,52.8)
46 : (48, 51) (47.7,51.7)
45 : (47, 50) (46.5,50.5)
44 : (46, 49) (45.3,49.3)
43 : (45, 48) (44.2,48.2)
42 : (44, 47) (43.0,47.0)
41 : (43, 46) (41.8,45.8)
40 : (42, 45) (40.7,44.7)
39 : (40, 43) (39.5,43.5)
38 : (39, 42) (38.3,42.3)
37 : (38, 41) (37.2,41.2)
36 : (37, 40) (36.0,40.0)
35 : (36, 39) (34.8,38.8)
34 : (35, 38) (33.7,37.7)
33 : (34, 37) (32.5,36.5)
32 : (32, 35) (31.3,35.3)
31 : (31, 34) (30.2,34.2)
30 : (30, 33) (29.0,33.0)
29 : (29, 32) (27.8,31.8)
28 : (28, 31) (26.7,30.7)
27 : (27, 30) (25.5,29.5)
26 : (26, 29) (24.3,28.3)
25 : (24, 27) (23.2,27.2)
24 : (23, 26) (22.0,26.0)
23 : (22, 25) (20.8,24.8)
22 : (21, 24) (19.7,23.7)
21 : (20, 23) (18.5,22.5)
20 : (19, 22) (17.3,21.3)
19 : (18, 21) (16.2,20.2)
18 : (16, 19) (15.0,19.0)
17 : (15, 18) (13.8,17.8)
16 : (14, 17) (12.7,16.7)
15 : (13, 16) (11.5,15.5)
14 : (12, 15) (10.3,14.3)
13 : (11, 14) (9.2,13.2)
12 : (10, 13) (8.0,12.0)
11 : (8, 11) (6.8,10.8)
10 : (7, 10) (5.7,9.7)
9 : (6, 9) (4.5,8.5)
8 : (5, 8) (3.3,7.3)
7 : (4, 7) (2.2,6.2)
6 : (3, 6) (1.0,5.0)
5 : (2, 5) (-0.2,3.8)
4 : (0, 3) (-1.3,2.7)


** Process exited - Return Code: 0 **
Press Enter to exit terminal

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"ah...Clem" <ah_clem@ymail.com> writes:

Here's the doubling windows as calculated by my little python script.

At first I was confused by the fractional part digits 0, 2, 3, 5, 7, and
8 caused by rounding to one digit. After all, we are dealing with
6ths. Rounding to two or three digits would make this more obvious. On
the other hand, you will never have a non-integer pip count (not even
after adjustments), so you can round accordingly: 109.5 to 113.5 gives
the same cube decisions as 110 to 113.

Having said this, I do not care about the (re)doubling window, only
about the cube decision. The window is just a means to this end.

Best regards

Axel

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On 9/27/2022 3:56 PM, Axel Reichert wrote:

"ah...Clem" <ah_clem@ymail.com> writes:

Here's the doubling windows as calculated by my little python script.

At first I was confused by the fractional part digits 0, 2, 3, 5, 7, and
8 caused by rounding to one digit. After all, we are dealing with
6ths. Rounding to two or three digits would make this more obvious. On
the other hand, you will never have a non-integer pip count (not even
after adjustments), so you can round accordingly: 109.5 to 113.5 gives
the same cube decisions as 110 to 113.

Having said this, I do not care about the (re)doubling window, only
about the cube decision. The window is just a means to this end.

Presenting it this way is more concise since there's one entry for each pipcount for the player on roll. I only went up to 99 and stopped at 5
since I rarely see race cubes for pipcounts in the three digits.

My first crack at the problem computed the decision and only outputted
the pipcounts where the two metrics differed, but that made for multiple entries for each pipcount.

I've included it below, but I think the earlier list is more
illuminating. Agree, that the doubling window is just a means to an
ends, but it's a simple way to think about the problem.

The columns are On-roll pipcount, opponent pipcount, Trice verdict,
Isight verdict, Trice window, Isight window.

90 - 97 D/T ND/T (97, 100) (99.0,103.0)
90 - 98 D/T ND/T (97, 100) (99.0,103.0)
90 - 101 D/P D/T (97, 100) (99.0,103.0)
90 - 102 D/P D/T (97, 100) (99.0,103.0)
90 - 103 D/P D/T (97, 100) (99.0,103.0)
89 - 96 D/T ND/T (96, 99) (97.8,101.8)
89 - 97 D/T ND/T (96, 99) (97.8,101.8)
89 - 100 D/P D/T (96, 99) (97.8,101.8)
89 - 101 D/P D/T (96, 99) (97.8,101.8)
88 - 95 D/T ND/T (95, 98) (96.7,100.7)
88 - 96 D/T ND/T (95, 98) (96.7,100.7)
88 - 99 D/P D/T (95, 98) (96.7,100.7)
88 - 100 D/P D/T (95, 98) (96.7,100.7)
87 - 94 D/T ND/T (94, 97) (95.5,99.5)
87 - 95 D/T ND/T (94, 97) (95.5,99.5)
87 - 98 D/P D/T (94, 97) (95.5,99.5)
87 - 99 D/P D/T (94, 97) (95.5,99.5)
86 - 93 D/T ND/T (93, 96) (94.3,98.3)
86 - 94 D/T ND/T (93, 96) (94.3,98.3)
86 - 97 D/P D/T (93, 96) (94.3,98.3)
86 - 98 D/P D/T (93, 96) (94.3,98.3)
85 - 92 D/T ND/T (92, 95) (93.2,97.2)
85 - 93 D/T ND/T (92, 95) (93.2,97.2)
85 - 96 D/P D/T (92, 95) (93.2,97.2)
85 - 97 D/P D/T (92, 95) (93.2,97.2)
84 - 91 D/T ND/T (91, 94) (92.0,96.0)
84 - 95 D/P D/T (91, 94) (92.0,96.0)
84 - 96 D/P D/T (91, 94) (92.0,96.0)
83 - 90 D/T ND/T (90, 93) (90.8,94.8)
83 - 94 D/P D/T (90, 93) (90.8,94.8)
82 - 89 D/T ND/T (89, 92) (89.7,93.7)
82 - 93 D/P D/T (89, 92) (89.7,93.7)
81 - 88 D/T ND/T (88, 91) (88.5,92.5)
81 - 92 D/P D/T (88, 91) (88.5,92.5)
80 - 86 D/T ND/T (86, 89) (87.3,91.3)
80 - 87 D/T ND/T (86, 89) (87.3,91.3)
80 - 90 D/P D/T (86, 89) (87.3,91.3)
80 - 91 D/P D/T (86, 89) (87.3,91.3)
79 - 85 D/T ND/T (85, 88) (86.2,90.2)
79 - 86 D/T ND/T (85, 88) (86.2,90.2)
79 - 89 D/P D/T (85, 88) (86.2,90.2)
79 - 90 D/P D/T (85, 88) (86.2,90.2)
78 - 84 D/T ND/T (84, 87) (85.0,89.0)
78 - 88 D/P D/T (84, 87) (85.0,89.0)
78 - 89 D/P D/T (84, 87) (85.0,89.0)
77 - 83 D/T ND/T (83, 86) (83.8,87.8)
77 - 87 D/P D/T (83, 86) (83.8,87.8)
76 - 82 D/T ND/T (82, 85) (82.7,86.7)
76 - 86 D/P D/T (82, 85) (82.7,86.7)
75 - 81 D/T ND/T (81, 84) (81.5,85.5)
75 - 85 D/P D/T (81, 84) (81.5,85.5)
74 - 80 D/T ND/T (80, 83) (80.3,84.3)
74 - 84 D/P D/T (80, 83) (80.3,84.3)
73 - 79 D/T ND/T (79, 82) (79.2,83.2)
73 - 83 D/P D/T (79, 82) (79.2,83.2)
72 - 82 D/P D/T (78, 81) (78.0,82.0)
70 - 75 D/T ND/T (75, 78) (75.7,79.7)
70 - 79 D/P D/T (75, 78) (75.7,79.7)
69 - 74 D/T ND/T (74, 77) (74.5,78.5)
69 - 78 D/P D/T (74, 77) (74.5,78.5)
68 - 73 D/T ND/T (73, 76) (73.3,77.3)
68 - 77 D/P D/T (73, 76) (73.3,77.3)
67 - 72 D/T ND/T (72, 75) (72.2,76.2)
67 - 76 D/P D/T (72, 75) (72.2,76.2)
66 - 75 D/P D/T (71, 74) (71.0,75.0)
60 - 68 D/P D/T (64, 67) (64.0,68.0)
54 - 57 ND/T D/T (58, 61) (57.0,61.0)
48 - 50 ND/T D/T (51, 54) (50.0,54.0)
47 - 49 ND/T D/T (50, 53) (48.8,52.8)
47 - 53 D/T D/P (50, 53) (48.8,52.8)
42 - 43 ND/T D/T (44, 47) (43.0,47.0)
41 - 42 ND/T D/T (43, 46) (41.8,45.8)
41 - 46 D/T D/P (43, 46) (41.8,45.8)
40 - 41 ND/T D/T (42, 45) (40.7,44.7)
40 - 45 D/T D/P (42, 45) (40.7,44.7)
36 - 36 ND/T D/T (37, 40) (36.0,40.0)
35 - 35 ND/T D/T (36, 39) (34.8,38.8)
35 - 39 D/T D/P (36, 39) (34.8,38.8)
34 - 34 ND/T D/T (35, 38) (33.7,37.7)
34 - 38 D/T D/P (35, 38) (33.7,37.7)
33 - 33 ND/T D/T (34, 37) (32.5,36.5)
33 - 37 D/T D/P (34, 37) (32.5,36.5)
29 - 32 D/T D/P (29, 32) (27.8,31.8)
28 - 31 D/T D/P (28, 31) (26.7,30.7)
27 - 30 D/T D/P (27, 30) (25.5,29.5)
26 - 29 D/T D/P (26, 29) (24.3,28.3)
23 - 25 D/T D/P (22, 25) (20.8,24.8)
22 - 24 D/T D/P (21, 24) (19.7,23.7)
21 - 23 D/T D/P (20, 23) (18.5,22.5)
20 - 22 D/T D/P (19, 22) (17.3,21.3)
19 - 21 D/T D/P (18, 21) (16.2,20.2)
17 - 18 D/T D/P (15, 18) (13.8,17.8)
16 - 17 D/T D/P (14, 17) (12.7,16.7)
15 - 16 D/T D/P (13, 16) (11.5,15.5)
14 - 15 D/T D/P (12, 15) (10.3,14.3)
13 - 14 D/T D/P (11, 14) (9.2,13.2)
12 - 13 D/T D/P (10, 13) (8.0,12.0)
11 - 11 D/T D/P (8, 11) (6.8,10.8)
10 - 10 D/T D/P (7, 10) (5.7,9.7)
9 - 9 D/T D/P (6, 9) (4.5,8.5)
8 - 8 D/T D/P (5, 8) (3.3,7.3)
7 - 7 D/T D/P (4, 7) (2.2,6.2)
6 - 6 D/T D/P (3, 6) (1.0,5.0)
5 - 5 D/T D/P (2, 5) (-0.2,3.8)
Diffcount: 104


** Process exited - Return Code: 0 **
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