The Math of Can't Stop

[Agamemnon]

I sat down and ran some of the numbers for the Can't Stop game today, just to do it. The numbers give me hope, but the inane tendency of the dice roller to produce absurdly improbable combinations of numbers does not. I personally thing it has cursed me; as such, I have no intention of playing the game past 150 games. Nonetheless, for those with lots of luck (20 rolls in a row!) and faith, here they are:

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Where:
2 = 12 3 = 11 4 =10
5 = 9 6 = 8
Unless duplication already exists

S = Chance of success on any given roll
L = Chance of going bust on all six rolls

16 / 36 = 44.4% S = 2.95% L 6,7,8
15 / 36 = 41.6% S = 3.97% L 5,6,7
14 / 36 = 38.8% S = 5.25% L 4,6,7 5,6,8
13 / 36 = 35.2% S = 7.40% L 3,6,7 4,6,8 4,5,7 5,6,9
12 / 36 = 33.3% S = 8.80% L 2,6,7 3,6,8 3,5,7 4,5,6 4,7,10
11 / 36 = 30.6% S = 11.17% L 2,5,7 2,6,8 3,4,7 3,5,6 4,6,10 4,5,9
10 / 36 = 27.8% S = 14.17% L 2,4,7 3,5,9 3,4,6 2,5,6 4,5,10 3,7,11
9 / 36 = 25.0% S = 17.80% L 2,3,7 2,5,9 2,4,6 3,4,5 3,6,11
8 / 36 = 22.2% S = 22.18% L 2,3,6 2,7,12 2,4,5 3,4,10 3,5,11
7 / 36 = 19.4% S = 27.4% L 2,3,5 2,6,12, 2,4,10 3,4,11
6 / 36 = 16.7% S = 33.41% L 2,3,4 2,5,12
5 / 36 = 13.9% S = 40.74% L 2,3,11 2,4,12
4 / 36 = 11.11% S = 49.33% L 2,3,12

Ways to Make the Combinations:
5,5,6 (1)
4,5,6 (4)
3,5,6 (8) 4,5,5 (2)
2,5,6 (4) 3,5,5 (2) 3,4,6 (4) 4,4,5 (2)
1,5,6 (4) 2,5,5 (2) 2,4,6 (4) 3,4,5 (6) 3,3,6 (2)
1,4,6 (4) 1,5,5 (2) 2,3,6 (4) 2,4,5 (8) 3,3,5 (2) 3,4,4 (2)
1,3,6 (4) 2,4,4 (2) 2,3,5 (8) 1,4,5 (8) 3,3,4 (2) 2,2,6 (2)
1,2,6 (4) 1,4,4 (2) 1,3,5 (8) 2,3,4 (8) 2,2,5 (2)
1,2,5 (8) 1,1,6 (2) 1,3,4 (8) 2,3,3 (2) 2,2,4 (2)
1,2,4 (4) 1,1,5 (2) 1,3,3 (2) 2,2,3 (8)
1,2,3 (4) 1,1,4 (2)
1,2,2 (2) 1,1,3 (2)
1,1,2 (2)

Percentages by Combinations:
16/36 --> 1 15/36 --> 4 14/36 --> 10 13/36 --> 12
12/36 --> 18 11/36 --> 22 10/36 --> 26 9/36 --> 24
8/36 --> 22 7/36 --> 16 6/36 --> 6 5/36 --> 4
4/36 --> 2

Of 167 possible combinations that can be chosen:
- 1-5% L (16-14): 10% of combinations
- 6-10% L (13-12): 17% of combinations
- 11-20% L (11-9): 43% of combinations
- 21% L or Higher (8-4): 30% of combinations
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So, take it how you like. The central five numbers, as everyone knows, produce the best ones (10% or less chance of "going bust"). Yell at the random dice roller when you don't get more than 4 rolls with a 6,7,8 and your opponent goes for 15-20 rolls with it, though. Just don't blame the game.

[Agamemnon]

One last thing not included: for each probability combination, there is a set number of times you can safely continue (push) before losing all progress (go bust):

16/36: 30 Pushes
15/36: 25 Pushes
14/36: 20 Pushes
13/36: 14 Pushes
12/36: 11 Pushes
11/36: 9 Pushes
10/36: 7 Pushes
9/36: 6 Pushes
8/36: 5 Pushes
7/36: 4 Pushes
6/36: 3 Pushes
5/36: 3 Pushes
4/36: 2 Pushes

If you can figure out your probability on a given turn, this will be one of the more useful guides to a conservative player of the game (as opposed to the "do all of column 6 and 8 on the same turn!" people).

[VolgaChaser]

this math doesn't work

[zfm]

Although I am really interested on the math of Can't Stop, but if it's poorly written, I find it totally boring...