I started answering in the math way, but 2 answers already appeared.
So for the fun of it here it is "the long way around":
0 = chain not possible
1 = chain formed
X = cannot have this combination
[0,0]||[0,1]||[0,2]||[0,3]||[0,4]||[0,5]||[0,6]||[1,1]||[1,2]||[1,3]||[1,4]||[1,5]||[1,6]||[2,2]||[2,3]||[2,4]||[2,5]||[2,6]||[3,3]||[3,4]||[3,5]||[3,6]||[4,4]||[4,5]||[4,6]||[5,5]||[5,6]||[6,6]
[0,0]| X |
[0,1]| 0 || X |
[0,2]| 0 || 0 || X |
[0,3]| 0 || 0 || 0 || X |
[0,4]| 1 || 0 || 1 || 0 || X |
[0,5]| X || X || X || X || X || X |
[0,6]| 0 || 0 || 0 || 0 || 0 || X || X |
[1,1]| 0 || 0 || 0 || 0 || 0 || X || 0 || X |
[1,2]| 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || X |
[1,3]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || X |
[1,4]| 0 || 1 || 0 || 0 || 1 || X || 0 || 0 || 1 || 0 || X |
[1,5]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || X |
[1,6]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || X |
[2,2]| 0 || 0 || 0 || 0 || 1 || X || 0 || X || 0 || 0 || 0 || 0 || 0 || X |
[2,3]| 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || 0 || 0 || 1 || 1 || 0 || 0 || X |
[2,4]| 1 || 1 || 1 || 1 || 1 || X || 1 || 0 || 0 || 0 || 1 || 0 || 0 || 1 || 0 || X |
[2,5]| X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X |
[2,6]| 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || X |
[3,3]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || X |
[3,4]| 0 || 0 || 0 || 1 || 1 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || 1 || X || 0 || 0 || X |
[3,5]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || X |
[3,6]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || X |
[4,4]| X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X || X |
[4,5]| 0 || 0 || 1 || 0 || 1 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || X || X |
[4,6]| 0 || 0 || 0 || 0 || 1 || X || 1 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || 0 || 0 || 0 || X || 0 || X |
[5,5]| 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 1 || X || 0 || 0 || 0 || 0 || 0 || X || 0/1 || 0 || X |
[5,6]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || X |
[6,6]| 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || 0 || X || 0 || 0 || 0 || 0 || X |
[0,0]||[0,1]||[0,2]||[0,3]||[0,4]||[0,5]||[0,6]||[1,1]||[1,2]||[1,3]||[1,4]||[1,5]||[1,6]||[2,2]||[2,3]||[2,4]||[2,5]||[2,6]||[3,3]||[3,4]||[3,5]||[3,6]||[4,4]||[4,5]||[4,6]||[5,5]||[5,6]||[6,6]
There are $24*25 / 2$ combinations in total
Now just count the 1. I got:
- 31 if you allow forks. In this case the chance is $31/300 = 0.1033$. So 10.33%
- 30 if you don't allow forks. In this case the chance is $30/300 = 0.10$. So 10%
[2, 5], [5, 5], [5, 0]
,[2, 5], [5, 5], [5, 4], [4, 4]
$\endgroup$[5, 2] [2, 4] [4, 4] [4, 0] [0, 5]
would fork on the middle[4, 4]
, but only extends in one direction. Is that a valid line? $\endgroup$[5, 2] [2, 4] [4, 4] [4, 0] [0, 5]
is valid $\endgroup$