In this game, I believe the numbers you must aim for are -1–8. This is why:
To make negative five, there is 1 algorithm: 1-6.
To make negative four, there are 2 algorithms: 1-5, 2-6.
To make negative three, there are 3 algorithms: 1-4, 2-5, 3-6.
To make negative two, there are 4 algorithms: 1-3, 2-4, 3-5, 4-6.
To make negative one, there are 5 algorithms: 1-2, 2-3, 3-4, 4-5, 5-6.
To make zero, there are 6 algorithms: 1-1, 2-2, 3-3, 4-4, 5-5, 6-6.
To make one, there are 5 algorithms: 2-1, 3-2, 4-3, 5-4, 6-5.
To make two, there are 5 algorithms: 1+1, 3-1, 4-2, 5-3, 6-4.
To make three, there are 5 algorithms: 1+2, 2+1, 4-1, 5-2, 6-3.
To make four, there are 5 algorithms: 1+3, 3+1, 2+2, 6-2, 5-1.
To make five, there are 5 algorithms: 1+4, 2+3, 3+2, 4+1, 6-1.
To make six, there are 5 algorithms: 1+5, 2+4, 3+3, 4+2, 5+1.
To make seven, there are 6 algorithms: 1+6, 2+5, 3+4, 4+3, 2+5, 6+1.
To make eight, there are 5 algorithms: 2+6, 3+5, 4+4, 5+3, 6+2.
To make nine, there are 4 algorithms: 3+6, 4+5, 5+4, 6+3.
To make ten, there are 3 algorithms: 4+6, 5+5, 6+4.
To make eleven, there are 2 algorithms: 5+6, 6+5.
To make twelve, there is 1 algorithm: 6+6.
Therefore, 12 and -5 were the hardest numbers to achieve, with only one algorithm, and 7 and 0 are the easiest numbers to achieve, with six algorithms.
Using these statements and the board itself, I was able to figure out the following:
The most likely 3 in-a-rows you can get are: 5-6-7, 6-7-8, -1-0-1, 0-1-2.
The most likely 3 in-a-diagonals you can get are: 1-5-9, -2-2-6.
The most likely 3 in-a-columns you can get are: -2-3-8, -3-2-7, -1-4-9, 0-5-10.
All of these methods use at least two of the numbers from -1–8. Also, the methods that are COMPLETELY made up of numbers from -1–8 give you the highest probability of winning. This is why I believe that in this game you must aim for -1–8.