Odds in Can't Stop

Can't Stop, by Parker Brothers is a cute little dice game. Sadly, it's out of print, but copies can be found here and there.

The idea is that one rolls four dice, splits them into two pairs, and can keep going if one of three "good" numbers appears as the sum of any of the two pairs. If there's no way to make a good number, one's turn is over and all progress is lost.

The chance of rolling a single given sum on four dice is:

Roll #hit%hit
2 171 13.2
3 302 23.3
4 461 35.6
5 580 44.8
6 727 56.1
7 834 64.4
8 727 56.1
9 580 44.8
10 461 35.6
11 302 23.3
12 171 13.2

The next two tables are the odds of rolling one of three specific numbers; the first is sorted by likelihood of success; the second by number.

%hitRolls
92.0 6, 7, 8
91.4 6, 7, 9
91.4 5, 7, 8
91.1 6, 8,10
91.1 4, 6, 8
90.3 6, 7,10
90.3 4, 7, 8
89.5 6, 8, 9
89.5 5, 6, 8
89.3 6, 7,11
89.3 5, 7,10
89.3 4, 7, 9
89.3 3, 7, 8
89.0 6, 7,12
89.0 2, 7, 8
88.7 7, 8, 9
88.7 5, 6, 7
88.6 7, 8,10
88.6 4, 6, 7
88.3 6, 8,12
88.3 4, 8,10
88.3 4, 6,10
88.3 2, 6, 8
87.7 4, 7,10
86.7 5, 8, 9
86.7 5, 6, 9
86.5 7, 8,11
86.5 3, 6, 7
86.4 7, 8,12
86.4 5, 8,10
86.4 4, 6, 9
86.4 2, 6, 7
86.3 5, 6,10
86.3 4, 8, 9
85.3 6, 8,11
85.3 5, 7, 9
85.3 3, 6, 8
84.8 7, 9,10
84.8 4, 5, 7
84.6 6, 9,10
84.6 4, 5, 8
84.3 5, 7,11
84.3 3, 7, 9
83.6 5, 7,12
83.6 5, 6,11
83.6 4, 7,11
83.6 3, 8, 9
83.6 3, 7,10
83.6 2, 7, 9
83.3 5, 8,12
83.3 4, 7,12
83.3 4, 6,11
83.3 3, 8,10
83.3 2, 7,10
83.3 2, 6, 9
82.9 6, 9,12
82.9 2, 5, 8
82.6 5, 8,11
82.6 3, 6, 9
82.3 5, 6,12
82.3 4, 9,10
82.3 4, 8,11
82.3 4, 5,10
82.3 3, 6,10
82.3 2, 8, 9
81.6 6,10,12
81.6 4, 6,12
81.6 2, 8,10
81.6 2, 4, 8
81.1 4, 8,12
81.1 2, 6,10
80.9 7, 9,12
80.9 2, 5, 7
80.8 6, 9,11
80.8 3, 5, 8
80.7 7,10,12
80.7 2, 4, 7
79.9 5, 9,10
79.9 4, 5, 9
79.6 8, 9,10
79.6 6,10,11
79.6 4, 5, 6
79.6 3, 4, 8
79.1 7,10,11
79.1 3, 4, 7
78.7 7, 9,11
78.7 3, 5, 7
78.1 2, 7,12
77.9 5,10,11
77.9 4, 5,11
77.9 3, 9,10
77.9 3, 7,12
77.9 3, 4, 9
77.9 2, 7,11
77.6 5, 9,11
77.6 3, 7,11
77.6 3, 5, 9
77.1 8, 9,11
77.1 3, 5, 6
77.0 8, 9,12
77.0 2, 5, 6
76.0 5, 9,12
76.0 2, 5, 9
75.8 8,10,12
75.8 4, 9,11
75.8 3, 8,11
75.8 3, 6,11
75.8 3, 5,10
75.8 2, 4, 6
75.6 6,11,12
75.6 5,10,12
75.6 4,10,11
75.6 4, 9,12
75.6 3, 8,12
75.6 3, 4,10
75.6 2, 6,11
75.6 2, 5,10
75.6 2, 4, 9
75.6 2, 3, 8
75.2 7,11,12
75.2 2, 3, 7
74.2 8,10,11
74.2 3, 4, 6
73.8 4,10,12
73.8 2, 8,12
73.8 2, 6,12
73.8 2, 4,10
73.6 3, 6,12
73.6 2, 8,11
71.2 5,11,12
71.2 3, 9,12
71.2 2, 5,11
71.2 2, 3, 9
71.0 4, 5,12
71.0 3, 9,11
71.0 3, 5,11
71.0 2, 9,10
68.4 8,11,12
68.4 2, 3, 6
66.9 9,10,11
66.9 3, 4, 5
65.7 9,10,12
65.7 3,10,11
65.7 3, 4,11
65.7 2, 4, 5
63.7 3, 5,12
63.7 2, 9,11
63.4 4,11,12
63.4 3,10,12
63.4 2, 9,12
63.4 2, 5,12
63.4 2, 4,11
63.4 2, 3,10
58.4 9,11,12
58.4 2, 3, 5
57.9 3, 4,12
57.9 2,10,11
55.2 2,10,12
55.2 2, 4,12
52.5 3,11,12
52.5 2, 3,11
52.210,11,12
52.2 2, 3, 4
43.8 2,11,12
43.8 2, 3,12
%hitRolls
52.2 2, 3, 4
58.4 2, 3, 5
68.4 2, 3, 6
75.2 2, 3, 7
75.6 2, 3, 8
71.2 2, 3, 9
63.4 2, 3,10
52.5 2, 3,11
43.8 2, 3,12
65.7 2, 4, 5
75.8 2, 4, 6
80.7 2, 4, 7
81.6 2, 4, 8
75.6 2, 4, 9
73.8 2, 4,10
63.4 2, 4,11
55.2 2, 4,12
77.0 2, 5, 6
80.9 2, 5, 7
82.9 2, 5, 8
76.0 2, 5, 9
75.6 2, 5,10
71.2 2, 5,11
63.4 2, 5,12
86.4 2, 6, 7
88.3 2, 6, 8
83.3 2, 6, 9
81.1 2, 6,10
75.6 2, 6,11
73.8 2, 6,12
89.0 2, 7, 8
83.6 2, 7, 9
83.3 2, 7,10
77.9 2, 7,11
78.1 2, 7,12
82.3 2, 8, 9
81.6 2, 8,10
73.6 2, 8,11
73.8 2, 8,12
71.0 2, 9,10
63.7 2, 9,11
63.4 2, 9,12
57.9 2,10,11
55.2 2,10,12
43.8 2,11,12
66.9 3, 4, 5
74.2 3, 4, 6
79.1 3, 4, 7
79.6 3, 4, 8
77.9 3, 4, 9
75.6 3, 4,10
65.7 3, 4,11
57.9 3, 4,12
77.1 3, 5, 6
78.7 3, 5, 7
80.8 3, 5, 8
77.6 3, 5, 9
75.8 3, 5,10
71.0 3, 5,11
63.7 3, 5,12
86.5 3, 6, 7
85.3 3, 6, 8
82.6 3, 6, 9
82.3 3, 6,10
75.8 3, 6,11
73.6 3, 6,12
89.3 3, 7, 8
84.3 3, 7, 9
83.6 3, 7,10
77.6 3, 7,11
77.9 3, 7,12
83.6 3, 8, 9
83.3 3, 8,10
75.8 3, 8,11
75.6 3, 8,12
77.9 3, 9,10
71.0 3, 9,11
71.2 3, 9,12
65.7 3,10,11
63.4 3,10,12
52.5 3,11,12
79.6 4, 5, 6
84.8 4, 5, 7
84.6 4, 5, 8
79.9 4, 5, 9
82.3 4, 5,10
77.9 4, 5,11
71.0 4, 5,12
88.6 4, 6, 7
91.1 4, 6, 8
86.4 4, 6, 9
88.3 4, 6,10
83.3 4, 6,11
81.6 4, 6,12
90.3 4, 7, 8
89.3 4, 7, 9
87.7 4, 7,10
83.6 4, 7,11
83.3 4, 7,12
86.3 4, 8, 9
88.3 4, 8,10
82.3 4, 8,11
81.1 4, 8,12
82.3 4, 9,10
75.8 4, 9,11
75.6 4, 9,12
75.6 4,10,11
73.8 4,10,12
63.4 4,11,12
88.7 5, 6, 7
89.5 5, 6, 8
86.7 5, 6, 9
86.3 5, 6,10
83.6 5, 6,11
82.3 5, 6,12
91.4 5, 7, 8
85.3 5, 7, 9
89.3 5, 7,10
84.3 5, 7,11
83.6 5, 7,12
86.7 5, 8, 9
86.4 5, 8,10
82.6 5, 8,11
83.3 5, 8,12
79.9 5, 9,10
77.6 5, 9,11
76.0 5, 9,12
77.9 5,10,11
75.6 5,10,12
71.2 5,11,12
92.0 6, 7, 8
91.4 6, 7, 9
90.3 6, 7,10
89.3 6, 7,11
89.0 6, 7,12
89.5 6, 8, 9
91.1 6, 8,10
85.3 6, 8,11
88.3 6, 8,12
84.6 6, 9,10
80.8 6, 9,11
82.9 6, 9,12
79.6 6,10,11
81.6 6,10,12
75.6 6,11,12
88.7 7, 8, 9
88.6 7, 8,10
86.5 7, 8,11
86.4 7, 8,12
84.8 7, 9,10
78.7 7, 9,11
80.9 7, 9,12
79.1 7,10,11
80.7 7,10,12
75.2 7,11,12
79.6 8, 9,10
77.1 8, 9,11
77.0 8, 9,12
74.2 8,10,11
75.8 8,10,12
68.4 8,11,12
66.9 9,10,11
65.7 9,10,12
58.4 9,11,12
52.210,11,12
Jeff Goldsmith, jeff@tintin.jpl.nasa.gov, Jan. 11, 1999