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Without material advantage as a victory condition, the points schedule for Dynamic Scoring looked something like this:

Game Outcome Points for White Points for Black Difference Offset favoring Black Ratio of Differences
White forces checkmate. 100 0 100 0 1:1
White forces stalemate. 60 40 20 1 10:11
White bares Black's King. 56 44 12 3 2:3
White gives perpetual check. 52 48 4 5 2:7
Draw 50 50 0 0 -
Black gives perpetual check. 43 57 -14 5 7:2
Black bares White's King. 41 59 -18 3 3:2
Black forces stalemate. 39 61 -22 1 11:10
Black forces checkmate. 0 100 -100 0 1:1

Although I don't know ahead of time if White has an advantage large enough that the player with the White pieces could tend to win often by perpetual check, or if both players can prevent victories by the other player even by perpetual check, not just checkmate, if they choose to play defensively - I have reason to hope this will encourage players to play exciting attacking chess.

If White's advantage is such as to allow White to force perpetual check, but not enough to allow White to force checkmate, then the equilibrium point of the game is between a point at which Black wins and White wins are counted equally, checkmate, and a point at which Black wins are given a large premium over White wins. So while both players might find a different balance between an open game and a closed game ideal, they would still be driven to attempt to adjust the game within the area in which victories of one type or another take place, rather than seeking to play so defensively that only draws, or victories by material superiority, take place.

If White's advantage is smaller, it is still the case that Black, at least, is encouraged to play less defensively by the promise of a large bonus he can manage to win by perpetual check. If he has enough of a realistic chance to win by bare King or stalemate, that the lower bonuses relative to White at these levels can be accepted, since these victories pay off much more than those below them, it's reasonable for Black to try for them as well, even if it is even more so for White.

Black is motivated to try for wins that are accessible by the large bonuses given to Black for the smaller victories, and White is motivated to take further risks and open the game up into territory where the handicap given to Black by the scoring system is less significant. Both players are, during the course of any individual game, strongly motivated to work for the largest victory that they can grasp as well, but this would be equally true if Black only received the same credit for each type of victory as White: the asymmetry of the scoring system affects the basic strategic planning that happens before the game starts, such as the choice of openings to use.

Thus, the intent is to construct a scoring system that is robust in the face of the actual expected outcome of a game of Chess being unknown; one that will, under a wide range of circumstances, drive the kind of behavior from those playing in major Chess events that is desired.

Incidentally, adjusting the points schedule to increase the gap between perpetual check and material superiority originally made it significantly more difficult to assign scores to the minor victories by Black so as to provide a system of incentives representing the principles of Dynamic Scoring. This problem, though, was largely alleviated when I realized that a large gap between bare King and perpetual check, and a small gap between stalemate and bare King, rather than the reverse, was desirable.

Even so, it may be interesting to see the more regular schedule of points we could obtain if we avoid that step, such as the following:

Game Outcome Points for White Points for Black Difference Offset favoring Black Ratio of Differences
White forces checkmate. 1000 0 1000 0 1:1
White forces stalemate. 600 400 200 10 10:11
White bares Black's King. 525 475 50 25 1:2
White gives perpetual check. 505 495 10 20 1:5
White has material superiority. 501 499 2 1 1:2
Draw 500 500 0 0 -
Black has material superiority. 498 502 -4 1 2:1
Black gives perpetual check. 475 525 -50 20 5:1
Black bares White's King. 450 550 -100 25 2:1
Black forces stalemate. 390 610 -220 10 11:10
Black forces checkmate. 0 1000 -1000 0 1:1

And another wrinkle is added: a 2:1 advantage for Black for a victory by material superiority, to given an incentive for Black to cooperate in opening up the game at least a little even when his prospects of achieving a perpetual check are low.

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