Static Exchange Evaluation

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Wassily Kandinsky - Small Worlds IX [1]

A Static Exchange Evaluation (SEE) examines the consequence of a series of exchanges on a single square after a given move, and calculates the likely evaluation change (material) to be lost or gained, Donald Michie coined the term swap-off value. A positive static exchange indicates a "winning" move. For example, PxQ will always be a win, since the Pawn side can choose to stop the exchange after its Pawn is recaptured, and still be ahead. Some programs optimize the SEE function to only return a losing or equal/winning flag, since they only use SEE to determine if a move is worth searching and do not need the actual value. SEE is useful in move ordering, futility pruning and especially in quiescence search in conjunction with delta pruning, as well to reduce "bad" captures and checks [2] .

Implementation

A didactic recursive implementation of SEE is shown below [3] . In most programs, however, an iterative version is used, as demonstrated in SEE - The Swap Algorithm with bitboards. In CCC, Harm Geert Muller deduced an iterative SEE approach directly from Alpha-Beta [4] .

int see(int square, int side)
{
   value = 0;
   piece = get_smallest_attacker(square, side);
   /* skip if the square isn't attacked anymore by this side */
   if ( piece )
   {
      make_capture(piece, square);
      /* Do not consider captures if they lose material, therefor max zero */
      value = max (0, piece_just_captured() -see(square, other(side)) );
      undo_capture(piece, square);
   }
   return value;
}

This uses a trick, equivalent to negamax in tree search, where the loss for the current side is the gain for the opposite side. This can be seen in the expression piece_just_captured() - see(square); which is the value of the piece captured (piece_just_captured()) minus the gain that the opponent might make after the move by recapturing. If that term becomes negative, one would better choose standing pat rather than to capture, which can be done by a conditional assignment, or by a max function with zero as second argument.

Seeing a Capture

To statically evaluate a capture, that particular capture should be forced, because it might not be the lowest attacker that makes the capture, and must not allow the option of standing pat [5] .

int seeCapture(int from, int to, int side)
{
   value = 0;
   piece = board[from];

   make_capture(piece, to);
   value = piece_just_captured() - see(to, other(side));
   undo_capture(piece, to);
   return value;
}

SOMA

Instead of using a quiescence search, some (early) chess programs aimed to determine the material balance of a position by a static analysis of all possible capture-move sequences. These routines are often referred to as SOMA (Swapping Off Material Analyzer) [6] based on the swap-off algorithm used in the one-ply analyzing "paper machine" SOMA by evolutionary biologist John Maynard Smith, the Smith One-Move Analyzer designed in the early 60s [7] .

See also

Swap-off algorithm

Publications

Forum Posts

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Re: MVV/LVA vs SEE move ordering - more test results by Brian Sheppard, rgcc, August 27, 1995

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Re: I want to SEE by Matthias Gemuh, CCC, December 21, 2001

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External Links

References

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