[ttepsldv] Breakthrough

Breakthrough is an elegant game with simple rules that can be played on a chess board.  Both sides start with only with pawns (typically 16 each on the first two ranks).  First to promote, wins.

Capture like chess pawns, only diagonally.  No two-step initial move (consequently no en passant).  The one critical difference: pawns can also move diagonally forward as well as forward one square.

Invented by Troyka.

For avoiding death by opening theory like Chess960, consider only starting with only 13 pieces each (on 2 ranks): Binomial(16,13). or 16 pieces (on 3 ranks): B(24,16)  or restrict to exactly 2 pawns per file: 3^8.

What board shapes (not necessarily rectangular) is the game guaranteed not to end in a draw?  Consider general graphs: probably need directed acyclic graphs.