Go is actually a finite two-person game of perfect information and cannot end in a draw. Then by Zermelo's theorem, it is exactly one of the two has winning strategy, either Black or White.
So my question is which one? the Black or the White?
Update: Despite of the game is too large to calculate directly, my (roughly) idea is to prove inductively, from $3 \times 3$, $4 \times 4$ until $19 \times 19$. If for any $n$, one player(suppose black) has winning strategy, then it seems a conclusion that the player(black) has winning strategy.
Update: It seems the result is also rely on the scoring rule.
So another idea is to consider scoring rules, since the more compensation the White earned, the higher probability the winning strategy White has. Different results may be yielded within area scoring and territory scoring.
Best Answer
Mini-go results up to 5x6, 4x7, and 3x9 are known, see Solving Go for Rectangular Boards. In general, the first player has the advantage, and can be expected to win by a certain number of points under optimal play. Optimal play on the 3x7 board is extremely different than optimal play on the 3x9 board.
If the Komi is above/below the optimal points, then the first player will lose/win. Minor changes in rules, such as japanese/chinese scoring, superko rules, and so on, can change the optimal play.
Optimal plays for 6x6 and 5x7 are currently unknown, and are believed to be 4 and 9 points for black. However, these have not yet been exhaustively proven.
Based on known results so far, there is no inductive process that can be applied to these results.