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This cube error cost us the match in Novi
Posted By: Bob Koca
Date: Sunday, 19 July 2015, at 1:49 a.m.
In Response To: This cube error cost us the match in Novi (phil simborg)
It is the second game of a doubles match so you probably have time for a significant amount of calculations. Since the cube is large the choice is particularly important. Since at least 4 points are at stake the remaining match cannot have very many games. Thus, if in doubt it is worth it to use a lot of this time and if your choice at the moment is to take then strategically you should use nearly all of the time until you are sure.
With the race so short a lot of the formulas breakdown a bit. But with race so short it can often just be calculated. I would do this by looking at chance I win on my first roll (easy and quick), second roll (easy with pen and paper but needing to keep track of things while doing further calculations might make it difficult, and a bit time consuming) and third roll (very difficult but likely to be very very small).
To win on first roll we need 55 or 66 after opponent did not get 55 or 66. Our 2 wins in 36 games gets multiplied by 34/36 giving us about 1.9 wins.
To win on second roll we must get off in exactly two rolls. I will count how often that happens in 36 games. To keep track of things I do this by first doing the non doubles and then multiplying by 2, and then adding in the doubles. A quicker version of this could be done by doing some quicker approximations and then doing more carefully if needed.
I will mentally think the following:
65: 34
64: 31 more to 65
63: 23 more to 88
Comment: It is worthwhile to know these 34,31, 23... values beforehand without needing to figure them out OTB.
62: 19 more to 107
61: 14 more to 121
54: 27 more to 148
53: 17 more to 165
52: 13 more to 178
51: 10 more to 188
43: 14 more to 202
42: 10 more to 212
41: 8 more to 220
32: 8 more to 228
31: 6 more to 234
21: 4 more to 238.
238 X 2 = 476.
66, 55: add 0 since would be off in 1 turn and we already accounted for those wins.
44 and 33: add 36 each up to 548
22: 19 more to 567
11: 6 more to 573
COMMENT: Some grouping is possible. For example do 31 and 11 together but makes it harder to keep track of what has been done so far.
573 times in 1296 you take exactly two turns.
I think it is easier to put this in terms of 36 instead. 16 x 36 = 576 so I will think just under 16 times out of 36.
For us to win in exactly 2 turns we need our opponent to take at least 3 turns.
Note that 66, 55, 44, 33, 65, 64, 54 all give no chance for this.
Here I like to start with the small numbers getting the larger contributions out of the way first.
21: gives 23 bad rolls.
31: 31 more for 54
41: 17 more for 71
51: 13 more for 84
61: 13 more for 97
23: 17 more for 114
24: 13 more for 127
25: 5 more for 132
26: 5 more for 137
34: 31 more for 168
35: 10 more for 178
36: 10 more for 188
45,46, 56: no more.
188 x 2 = 376.
11: 22 more for 398
22: 2 more for 400
400 times out 1296 our opponent takes at least 3 turns to bearoff. 11 x 36 = 396 so this is slightly more than 11 out of 36 times.
Our chance to win in exactly 2 rolls is about 16 x 11 out of 1296. 176 games out of 1296 is just under 5 games in 36.
We are already up to about 6.9 games. 6 games out of 36 is 16.7%. No need to continue. Easy take.
If this seemed daunting, note that it is a skill that definitely can be improved with practice.

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