rows
|
columns
|
tiles
|
Result
|
1x1
or 1x2 or 2x1
|
1 or 2
|
No moves are
possible. The only
question is what color of piece initially occupies each of the 1 or 2
squares.
|
2
|
2
|
4
|
Draw - score 2-2.
|
3
|
6
|
A 5-0 win for red: 1. b1 or 1.
b2. Any other red move causes red to lose, as blue can then play 1...b1
or 1...b2 from his remaining piece.
|
4
|
8
|
Blue
wins. 1.a1c1 leads to 1...a2c2 (blue wins), while 1.a1c2 leads
to 1...a2c1 (blue wins). The longer games are 1.a2 d1b2, followed by
any red move, then blue winning by shutout, or 1.b2 d1b1, followed by
any red move, then blue winning by shutout.
|
5
|
10
|
Red
wins. 1.a1c1 or 1.a1c2 results in blue winning on move 1. But
1.b1, followed by any blue move leads to a red win on move 2. 1.b2 has
the same effect - red wins on move 2.
|
6
|
12
|
Red
wins - best line (found after 10
plies of search) gives an 8-4
win as follows: 1.b1 e1 2.c1 d1
3.b1d2 e2 4.c2 0 5.b1 0 6.b2, or 1.b2 e1 2.c1 d1 3.b2d2 e2 4.c2 0 5.b1
0 6.b2
|
7
|
14
|
1.a1c1 loses to blue 6-8 (15-ply
search). Same goes for 1.a1c2. The best lines are 1.a1c1 b1 2.f1 d1
3.e1 d2 4.e2 c2 5.f2 a1 6.0 b2 (blue wins 8-6), and 1.a1c2 b1 f1
2.d1 e1 3.d2 e2 4.c1 f2 5.a1 0 6.b2 (blue wins 8-6). Unfortunately for
red, the moves 1.b1 and 1.b2 also lose (16-ply
search). Blue can respond with either 1...f1 or 1...f2 in each case.
The four best lines are:
- 1.b1 f1 2.b2 e1 3.a1c1 e1c2 4.a1 e1 5.b1d1 f1d2 6.b1 e2 7.0
f1 8.0 f2 (Blue wins 8-6),
- 1.b1 f2 2.b2 e1 3.a1c1 e1c2 4.a1 e1 5.b1d1 f2d2 6.b1 e2 7.0
f1 8.0 f2 (Blue wins 8-6),
- 1.b2 f1 2.b1 e1 3.a1c1 e1c2 4.a1 e1 5.b1d1 f1d2 6.b1 e2 7.0
f1 8.0 f2 (Blue wins 8-6),
- 1.b2 f2 2.b1 e1 3.a1c1 e1c2 4.a1 e1 5.b1d1 f2d2 6.b1 e2 7.0
f1 8.0 f2 (Blue wins 8-6).
Searching further (17+ plies) may reveal quicker or more punishing wins
for blue, but blue will still win. I don't care to search further.
|
3
|
3
|
9
|
Another 5-0 win for red: 1. b2.
Any other red move loses, resulting in 1...b2.
|
4
|
12
|
A win for red: 1.a1c2, followed
by any blue move results in there being a shutout move for red on move
2.
|
5
|
15
|
Unclear
at present, but likely solvable with about
22 plies of search. All three initial red hop moves to row 'c'
lose on turn one to blue. However, the other four moves all show
similar strength after searching ahead 10 additional plies: +2 for each
of 1.a2, 1.b1 and 1.a1b3, and +3 for 1.b2.
|
4
|
4
|
16
|
Another win for red, similar to
the one in the 4x3 board: 1.a1c1, followed by any blue move results in
there being a shutout move for red on move 2. |
5
|
20
|
Yet another similar two-move win
for red: 1.a1b3,
followed by any blue move results in there
being a
shutout move for red on move 2. |
5
|
5
|
25
|
Unclear
at present. So far,
1.a1c1 and 1.a1c2 can be shown to lose for red: 1...d2 is the response
to each, resulting in a winning shutout move for blue on each of his
second turns. However, interesting yet solid defences exist for 1.a1c3,
and if 1.a1c3 can be defended, it is unlikely that 1.a2 or 1.b2 will
fail red.
|