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Subject: Question about static exchange evaluation

Author: Larry Coon

Date: 09:13:26 11/12/98


(Long question follows -- sorry.)

I know I saw SEE talked about recently, but I couldn't
locate the discussion here, on rgcc or anybody's web
page (I don't remember where I saw it).  Can somebody
tell me if I'm thinking about this the right way?

I'll start with a contrived position:
1kq5/3n2p1/5p2/8/6N1/5R2/5RK1 w

Would a SEE do the following?
  1. Find all attackers on the square in question (f5).
  2. For each side, order the attackers in value, lowest
     to highest.  Include the piece that is initially
     captured to start off the exchange.  Put them into
     two....whatever, I'll say stacks just to make it
     easy to talk about.  The lowest valued pieces will
     be at the top of the stack.  Only the values of the
     pieces need to be pushed onto the stack.
  3. Start with a "trade balance" of zero.
  4. Pop the next value for the side NOT to move (black's
     stack if it's white's move) and SUBTRACT it from
     the trade balance, then do the same for the other
     stack.  (This works because at least in my program
     opposing pieces have opposite signs).
  5. When all values have been popped off either one of
     the stacks, then the exchange is over and the trade
     balance lets you know where you stand.
  6. However, neither side has to follow the exchange
     through to its completion.  So if either of the
     following happen:
         a. You pop the next value of "your" stack and
            subtract it from the trade balance and it ends
            up negative (for white, positive for black)
         b. You do the same for the opponent's stack and
            the result is positive (if black is the
            opponent, otherwise negative)
     Then you can assume that the side to move will not
     continue the exchange, exit the loop now, and the
     current trade balance will be the final balance.

So in my example position, the stacks would look like
(top of stack to the left):
   white:  3,  5,  5
   black: -1, -1, -3, -9

And the process would be as follows:
   Step   stack   value   balance
   ----   -----   -----   -------
     0                       0
     1      b      -1        1
     2      w       3       -2
     3      b      -1       -1  *
     4      w       5       -6  **
     5      b      -3       -3
     6      w       5       -8
     7      b      -9        1

So at the point I marked *, the value is negative
with black to move and the loop can actually stop
here.  Black doesn't have to play NxR, and he's
won the exchange.  Therefore, the initial capture
is bad for white.

However, if black DOES play NxR the following move
takes him to an even better position (**).  Maybe
I keep track of "most positive after an odd-numbered
step" and "most negative after an even numbered
step"?  Then the "most negative" would be the
assumed jumping-out point for black, and the "most
positive" would be the jumping-out point for white.

Or is it like beta-cutoff in alpha-beta where you
don't care how big the cutoff is, as long as you
find -a- cutoff?  So in this case, it doesn't
matter if the next exchange takes black from -1 to
-6, because the -1 by itself means the initial
capture is bad for white.

I think I'm missing something obvious here about
the essence of this problem.  Can anybody help?

Thanks,

Larry Coon



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