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Worse than Worthless. A discussion of pieces with negative value, and the Nattering Nabobs of Negativity![All Comments] [Add Comment or Rating]
H. G. Muller wrote on Tue, Nov 8, 2016 07:50 AM UTC:

The value of an extra King might also be negative. I once tried the following test (requested by someone on play a FIDE army without Queen against a FIDE army where the Queen was replaced by a second King, under rules of absolute royalty (i.e. none of the royals can be exposed to capture). The result was not significantly different from 50%. So on average the extra King is just as much a liability for getting mated as an asset for (defensive)  tactics.

This is not equally distributed over the game, though. In a Pawn ending, a side with two Kings almost always beats a single King very easily. So in the late end-game the extra King is nearly as good as having an extra minor. That means that it should have a significantly negative value in the middle-game to neutralize its effect overall.