While testing the game during the Beta phase, I've noticed a balance issue, especially regarding the 4x4 and 5x5 boards and also with the Pie Rule active.
On the smalle boards, the game state space is highly constrained. By applying Zermelo's Theorem and backward induction to the opening game tree, the 4x4 and 5x5 board sizes can be easily mathematically solved to guarantee a 100% forced win for Player 1 without Pie Rule, or for Player 2 with Pie Rule.
Because the 4x4 and 5x5 boards are too small to diffuse first-move symmetry, the 4x4 and 5x5 format are inherently broken for competitive matchmaking.
So I would suggest to restrict these board sizes to "Casual Mode/Training Mode" only, preventing them from appearing in competitive Arena queues.
Of course there is also a guaranteed forced win in theory across all board sizes for player 2 (with pie rule active), but on the larger board sizes (6 and 7 fields) human memory limits prevent perfect evaluation, restoring competitive balance.
Anyway, thank you for your hard work on this implementation, and I hope this helps optimize the game for its official release! I really like the concept!
On the smalle boards, the game state space is highly constrained. By applying Zermelo's Theorem and backward induction to the opening game tree, the 4x4 and 5x5 board sizes can be easily mathematically solved to guarantee a 100% forced win for Player 1 without Pie Rule, or for Player 2 with Pie Rule.
Because the 4x4 and 5x5 boards are too small to diffuse first-move symmetry, the 4x4 and 5x5 format are inherently broken for competitive matchmaking.
So I would suggest to restrict these board sizes to "Casual Mode/Training Mode" only, preventing them from appearing in competitive Arena queues.
Of course there is also a guaranteed forced win in theory across all board sizes for player 2 (with pie rule active), but on the larger board sizes (6 and 7 fields) human memory limits prevent perfect evaluation, restoring competitive balance.
Anyway, thank you for your hard work on this implementation, and I hope this helps optimize the game for its official release! I really like the concept!