!!!SOLVED!!!
I had some spare time and decided to use it to completely solve this game. I know I have no life. I am marking positions in the game by marking the number of spaces between a spartan and a goblin. So the starting position is S 666 (lol). Then I will write either win or lose for whoever created the position (not the next player to move). So every move you should create one of these winning positions. After that I will explain why it is a winning or losing position. Also note that it is pointless to move backwards because your opponent can just create the same position. I will start with simple positions so I can refer to them with the more complex positions. The only way positions change is by reducing one of the three numbers.
(A plus after a number means any number of spaces that is higher will have the same result)
Simple positions with at least one spartan and goblin adjacent to each other.
So 000 is a win. As your opponent moves backwards you just recreate 000 until he loses.
001+ is a lose because your opponent can create the 000 position
011 is a win because your opponent must eventually create the losing 001 position
012+ lose opponent makes 011
022 win opponent makes 012 or 002
023+ lose opponent makes 022 (noticing a pattern yet?)
033 win opponent makes 023, 013, or 003
034+ lose opponent makes 033
044 win (hopefully you noticed by now)
045+ lose
055 win
056 lose
066 win (this is the reason your first move is limited to three spaces)
So you should only move your piece adjacent to the opponents if the other two are the same distance from their goblin.
More complex positions. X can be any number 0-6 but must be the same as other X. (i.e, 2XX can be 233, 002, and 266, but not 246.)
0XX win this was proven in simple positions
1+XX lose because your opponent will make it 0XX
123 win opponent must eventually create 1+XX
124+ lose opponent will make 123
133+ lose opponent will make 123 (or 033 in the case of 133)
145 win opponent must create 1+XX, 124+, or 133+
146 lose because 145
156 lose because 145
234+ lose because 123
245 lose because 145
246 win because opponent cannot change this to a winning position
256 lose because 246
345 lose because 145
346 lose because 246
356 win because opponent cannot turn the game in his favor
456 lose because 356
Now it is finally time to find the best opening, because both you and your opponent can only move three spaces on the first move these positions are different. S before a position means no one has moved yet it is the START. The only starting position is S 666. O before a position means only one player has moved and the opponent is still bound by only moving three spaces.
O 366 is a lose. A good opponent will quickly make it a 066 position.
O 566 is a lose. It will be turned into a 356 position.
O 466 is a WIN. The opponents options are 166, 266, 346, 446, or 456. All of these are losing positions. Note that if the Goblins weren't restricted by only being able to move three spaces they could win by 066 or 246
So If you play perfectly you can always win. Just keep moving to winning positions.
I attempted to solve this just to see if I could and then thought I should share my findings. I doubt anybody will read the whole thing but I'm putting it here anyways. If you did read the whole thing and still don't understand that is my fault. I did the best I could to explain but understand it is still very confusing.