[5/6] Add Late Move Reductions (LMR) and Principal Variation Search (PVS)

[luccabb]

Summary

• Add Late Move Reductions (LMR) to reduce search depth for late quiet moves
• Add Principal Variation Search (PVS) for faster searches with good move ordering

Details

Late Move Reductions (LMR)

Reduce search depth for moves that are unlikely to be the best:

Conditions:

• Depth >= 3 (need sufficient depth to reduce)
• Move index >= 3 (first few moves get full depth)
• Not in check (check positions are critical)
• Quiet move (no capture, no check, no promotion)

Implementation:

reduction = 1  # Reduce by 1 ply
board_score = negamax(depth - 1 - reduction, ...)
if board_score > alpha:
    board_score = negamax(depth - 1, ...)  # Re-search at full depth

Principal Variation Search (PVS)

Optimize search based on the assumption that the first move is best:

Implementation:

• First move: full alpha-beta window search
• Later moves: zero window search first (faster)
• If zero window beats alpha, re-search with full window

if move_index == 0:
    score = negamax(alpha=-beta, beta=-alpha)  # Full window
else:
    score = negamax(alpha=-alpha-1, beta=-alpha)  # Zero window
    if score > alpha:
        score = negamax(alpha=-beta, beta=-alpha)  # Re-search

Test plan

• All 64 unit tests pass
• Verified LMR only applies to late quiet moves
• Verified PVS re-searches when needed

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