I proved that shogi is a first player win or a draw if:
1. Both P-26 G-32[^1] (a) and P-76 G-32[^2] (b) are perfect plays for the second
player.
2. Either G-68 P-84 (a') or G-68 P-34 (b') is a perfect play for the second
player.
Corollary: In both (a') and (b'), by playing G-78, the first player can be
equivalent to the second player in (a) and (b), respectively.
Assume that shogi is a second player win. Then both (a) and (b) are second
player wins. However, by the Corollary, the first player can be equivalent to
the second player in either (a) or (b). It then follows that shogi is a first
player win. Contradiction.
This is called the strategy-stealing argument. To put it simply, if the first
player can "pass," then they never lose.
Although neither assumption can be proven, this suggests that the claim that
shogi is a first player non-loss may be related to these claims about opening
theory. Most modern shogi engines would support both assumptions. However,
especially in (b) of Assumption 1, it may be controversial whether the second
move G-32 is optimal or not.
By the contrapositive, if shogi is a second player win, then at least one of the
following must be true:
1. P-26 G-32 is not a perfect play for the second player.
2. P-76 G-32 is not a perfect play for the second player.
3. Both G-68 P-84 and G-68 P-34 are not perfect plays for the second player.