[6/6] Add futility pruning

[luccabb]

Summary

• Skip quiet moves at low depths when static evaluation is far below alpha
• Margin-based pruning: depth 1 = 100cp, depth 2 = 200cp

Details

Futility Pruning

If the static evaluation plus a safety margin is still below alpha, quiet moves
are unlikely to improve the position enough to beat alpha. We skip them.

Implementation:

if depth <= 2 and not in_check:
    static_eval = self.eval_board(board)
    futility_margin = 100 * depth  # 100cp at depth 1, 200cp at depth 2
    can_futility_prune = static_eval + futility_margin < alpha

# In move loop:
if can_futility_prune and move_index > 0 and is_quiet_move:
    continue  # Skip this move

Safety Conditions

Pruning is conservative to avoid missing important moves:

• Only at low depths (1-2 ply)
• Never when in check
• Never prune captures, checks, or promotions
• Never prune the first move
• Margin allows for reasonable positional improvement

Why it Works

At low depths near leaf nodes:

• Quiet moves have limited potential to swing evaluation
• If we're already losing by > margin, a quiet move won't save us
• Captures/checks are still searched (tactical opportunities)

Test plan

• All 64 unit tests pass
• Verified pruning only happens for quiet moves at low depth

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🤖 Generated with Claude Code

[github-actions]

🔬 Stockfish Benchmark Results

vs Stockfish Skill Level 3

Metric	Wins	Losses	Draws	Total	Win %
Overall	0	100	0	100	0%
As White	0	50	0	50	0%
As Black	0	50	0	50	0%

vs Stockfish Skill Level 4

Metric	Wins	Losses	Draws	Total	Win %
Overall	1	99	0	100	1.0%
As White	0	50	0	50	0%
As Black	1	49	0	50	2.0%

vs Stockfish Skill Level 5

Metric	Wins	Losses	Draws	Total	Win %
Overall	0	100	0	100	0%
As White	0	50	0	50	0%
As Black	0	50	0	50	0%

Configuration

• 5 chunks × 20 rounds × 3 skill levels = 300 total games
• Each opening played with colors reversed (-repeat) for fairness
• Moonfish: 60s per move
• Stockfish: 60+5 time control