Some opening solution

Here is some solution of the game
please avoid such opening since they're totally solved.

Very Small - Open (Totally Solved)

First step for white, move rook to take black's bishop.
1. Rxb4 ..
after take the bishop, there is no defense for d2, knight travel back to d2 make a checkmate.

Actually, black only have 3 valid moves here:
a) Nb2
b) Nc3
c) Rxb4

variation a):
1. .. Nb2
2. Bxb2 #
variation b):
1. .. Nc3
2. Bxb2 ..

after that move, most of black's pieces are blocked, no matter what black move, Bxc3+ then travel is a choice
but sometimes there is no need to make such travel if c3 is not defended by black's rook.

variation ba):
2. .. Rxb4
3. Bxc3 Kc4 (only move)
4. white would won if white does not move the bishop nor knight.
variation bb):
2. .. d2
3.Bxc3 Kd3 (only move)
4. Rxc4#

variation c):
1. .. Rxb4
2. a3 ..
variation c is the major variation, since it have many branches.
firstly, if black don't move rook, you could take the rook by your pawn and got a simple win.
Here, white could perform consecutive moves towards win, but only the strongest defense is shown

variation ca):
2. .. Kc4
3. axb4=Q+ Kxb4
4. Nb2+ Nxb2
5. Bxb2#

the only choice is move rook here. but not move rook to b2 will fail easily, white could only move Bb2+ and then travel the Knight to d2 is enough to win.


variation cb):

2. .. R??
3. Bb2+ ??
4. Knight travels to (T2)d2 directly leads to a win.
variation cc):
2. .. Rb2+
3. Kxb2 Nc3+
4. Nxc3 ..

4. Nxc3 is crucial, without this action, black knight would travel to (T2)b3 and got a softmate. that softmate could not be solved.

white's only legal move is travel Bishop to c4, but it failed to defend (-1LT3)b3.

After Nxc3, the strongest defense is
4. .. d1=Q
5. Nxd1 K??
6. a4=Q#

There might be some non-sense variations, but all of them could be defeated by a knight travel.

Small - Open (partially solved)

1. Rxd4
firstly, black cannot take rook directly, since
1. .. Kxd4
2. Ne2+ K??
3. Ne2 travels to (T1)d2, which leads to a direct win.

Secondly, black cannot perform Rxb2, since Rd4 is really good at defending the b4 and d2 grid. thus white could perform Kxb2

There is a funny variation that make a check to prevent travelling to the two grids, in this case, you should notice you could perform Bxe4+

the branch is quite easy:
Bxe4+ kxe4
Ne2#

Bxe4+ Bxe4
Ne2+ then travel

It seems Rxd4 take lots of advantages here.
But I have not examine all the possibilities.