[PERF] games.py O(n²) fork detection algorithms

[galpt]

Issue

In cog/games.py#L302-L337, the check_fork_opportunities() and check_block_fork() functions have nested loops resulting in O(n²) complexity:

def check_fork_opportunities(self):
    for idx in empty:  # O(n) where n is empty cells
        self.board[idx] = bot_mark
        for i in range(self.size * self.size):  # O(n) nested!
            # ...

Why This Is a Problem

For a 5x5 board with 25 cells, this results in 625 iterations per strategy check. With multiple strategy checks (check_immediate_win, check_block_player, check_fork_opportunities, check_block_fork), this adds up.

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How to Fix

Consider caching board state analysis or pre-computing valid move positions. However, for typical board sizes (3x3, 5x5), this is likely not a major concern unless boards get much larger.

If boards are small, you could add a comment explaining the complexity is acceptable for the use case, or refactor to avoid repeated nested iterations.

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Severity

Medium - Potential performance issue for larger boards

[galpt]

[STILL PRESENT] O(n^2) nested loop algorithm in check_fork_opportunities and check_block_fork. On larger boards performs thousands of check_winner calls per strategy evaluation.