Re:Alchian–Allen effect
by tr352 on Tuesday November 13, 2018 @01:42PM
(#18443543)
Similar to an even exchange in chess. If you’re behind it’s a good deal, if you’re ahead it’s bad. Of course evaluating value taking into account positions (and thus determining whether an exchange is really “even”) is not straightforward.
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I don't consider myself a good chess player at all, but I always thought the opposite way: When I'm ahead, I'm willing to whittle down both sides with even trades until they are left with no options and can be checkmated. When I'm behind, an even trade feels scary - I'm looking for a way to catch up.
Am I missing some reason why it would be the opposite?
Yes you're right, I meant the exact opposite.
Re:Alchian–Allen effect
by daxat_staglatz on Tuesday November 13, 2018 @02:14PM
(#18443880)
This seems wrong: an even exchange does not change absolute balance but magnifies relative balance, which you do not want if you're behind.
Let's say your "strength" is simply the sum of the value of your pieces. The losing side has a strength of l and the winning side has a strength of L.
The losing side loses by l-L in absolute terms, or (l-L)/(l+L) in relative terms.
An even exchange of value k makes it go to (l-k)-(L-k) = l-k in absolute terms (no change); and to (l-L)/(l+L-2k) in relative terms. (l-L)/(l+L-2k) < (l-L)/(l+L).
To take an example, if the situation is white : two pawns and black: one pawn, going to white: one pawn and black: nothing is a bad deal for black (the losing side)!