I believebelieved it is a draw. (but may well be missing something)
CORRECTION: I believe white wins
Observations:
Any 2 non-interacting pairs on equal distance:
The winner should only play responsively
- if the opponent moves away: move the same distance toward the moved piece to push it back
- if the opponent moves closer: move the other pair the same amount closer
Board 2: the second player wins The winner should only play responsively on that board; it can be ignored
- if the opponent moves closer: make a rectangle again
- if the opponent moves away: treat it as 2 non-interacting pairs on equal distance
(without further proof) This makes the puzzle equal to winning on the following 3 boards:
Analysis:
Board 1 starts with distances {6,4,1}
- As soon as 2 distances are the same, one can win by reducing the third to 0
- A first player win is ->{5,4,1}->{3,2,1}
Board 2 wins by using the horse-block: h2, a2 (or?); b2
Board 3: black starting loses, but white starting is a draw!
CORRECTION!
I forgot a pair; the lone distances should not be {6,4,1} but {6,4,3,1}
This is a losing position:
- making first double looses (opponent makes second double and plays symmetrically)
- making 3210 wins (opponent must make double)
- making third<4 looses (opponent makes 3210)
- since >3 may not be made <=3 6431 is equivalent to 2031 and first player looses
Corrected strategy:
For white to win, since 1 and 3 are losing, it can prioritize board 2 and move the rook h4-h2 for a losing position there. The third board is a win for white if black starts; because black does not have the room to retreat (to fore a draw) like in the old strategy.
a87 h6 a6 h7 a7 a6 g7 h5! h7 h6 h8 h7 a7 b7, and black cannot move to a9 to gain initiative.
Old Strategy:
For white to force a draw:
If white prioritizes board one and black board 2 we can end up as below, with white to move.
On board 3 follows repeatedly:
hb6, a8; a6, a87; a5, a6; h6, g6; h4 h76; h5 h7; h6 a6;
(or a similar infinite sequence)
