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Dynamic Scoring

Komidashi

Reading about the game of Go, I learned that after a noted player, Honinbo Shusaku, raised the standard of play in the game, interest in competitive Go eventually flagged, because players were so good at defensive play that the first player (in Go, the one using the black stones) almost always won, although only by a small margin.

When komidashi, the practice of adding a small number (such as 4 1/2) to the number of spaces of territory that White controls before comparing the territory each player controls to determine the winner was adopted, then the scene was set for a renewal of interest in Go. This took place after other noted Go players, such as Wu Ch'ing-Yuan (known more popularly in Japan as Go Seigen) developed a new style of play suited to the new environment.

Being aware of the malaise that haunted Chess ever since Steinitz made the understanding of our game of skill more scientific, hope was kindled within me of finding a way to repeat this success story.

Partial Victories

But Chess games are won on the basis of whether or not checkmate takes place; they aren't won by the player who scores the most points. So there's no obvious way to apply a simple offset to the game. Instead, something different is required.

Emmanuel Lasker proposed, sometime around the year 1921, that the following scoring schedule be applied to serious Chess:

Checkmate      10 points -  0 points
Stalemate       8 points -  2 points
Exposed King    6 points -  4 points
Draw            5 points -  5 points

I only recently became aware of his suggestion.

Independently, I thought that it would be reasonable to allow a player to put points on the board for stalemating his opponent, but I also felt that to avoid diminishing the importance of that portion of endgame theory which deals with not blundering away a potential checkmate into a mere stalemate, it was important for stalemate to be a lot less valuable than checkmate.

So I thought that it would be appropriate to split the points 3/5 - 2/5 in the event of stalemate; equivalent to the score suggested by Emanuel Lasker for exposed King above.

Simplified Dynamic Scoring

Since this page was first written, I have re-examined the concept of Dynamic Scoring, and I have changed it in two ways:

I have simplified it considerably, to make it more possible that its adoption might be considered, and

I have adopted the scheme of a material offset which can be changed, more closely analogous to komidashi, and already in use in Korean Chess, so as to allow completely eliminating draws.

First, the score of a game is considered to consist of 100 game points, and the possible endings of a game would be scored as follows:

White score    Black score      Result
 100              0             White checkmates Black
  60             40             White stalemates Black
  52             48             White inflicts perpetual check on Black
  51             49             White wins by material superiority
  50             50             Draw
  49             51             Black wins by material superiority
  45             55             Black inflicts perpetual check on White
  40             60             Black stalemates White
   0            100             Black checkmates White

Material superiority is decided through assigning the following values in material points to the pieces:

90 Queen
50 Rook
32 Bishop
30 Knight
10 Pawn

thus multiplying the most common values by 10, and reflecting approximately the value of 3 1/4 points for the Bishop compared to 3 points for the Pawn as given by some authorities,

and with 4 1/2 material points added to Black's material; and then, the player with the most points worth of material, if that score exceeds that of the other player by 6 points or more, is awarded the victory, with this number subject to adjustment as experience in play is gained. If the difference is less than 6 points, the game is drawn, so a draw is still possible, unlike the case in Korean Chess.

Note that for White, checkmate is worth 5 times as much as stalemate, stalemate is worth 5 times as much as perpetual check, but perpetual check is worth only 2 times as much as material superiority. For Black, the sequence is almost the same, but with one important change: checkmate is worth 5 times as much as stalemate, but stalemate is worth only 2 times as much as perpetual check, because perpetual check is now worth 5 times as much as material superiority.

Thus, Black receives a bonus in material when material superiority is decided, and, in addition, perpetual check as a victory counts for more if won by Black.

When I originally considered a radical simplification of Dynamic Scoring, I omitted perpetual check as a victory condition, and thus used only material superiority, following the idea used in Korean Chess (except that in Korean Chess, a win by material superiority is simply a win like any other, rather than a near-draw). However, Chess has been, and should continue to be, a game in which the attack on the King is the fundamental goal. Given that the problem to be addressed is that the current post-Steinitz perfection of defensive play makes draws very likely, it seemed to me that a victory, much easier to achieve than Stalemate, would have to be counted to both address that problem and retain the centrality of the attack on the King.

But precisely because perpetual check is easier to achieve, it could be close to what the White side, due to the advantage of the first move, can obtain as a forced win; and, hence, at least in that one case, the original Dynamic Scoring scheme of giving different values for White and Black for the lesser victories, it seemed to me, would have to be retained.

In Korean Chess, a Pawn is counted as 2 points, and 1 1/2 points are added to the second player's material balance. Initially, in my system, I counted a Pawn as 10 points, and added 11 1/2 points to the second player's material balance. But then I looked for information, if any was available, on the actual value of White's first move advantage in Chess. I found two recent computer studies; one gave White's advantage as being worth 35 Elo points, and another gave the advantage as 0.14 of a Pawn - but with the additional detail that it was increasing, at the present time, at a rate that would lead to it being 0.23 of a Pawn in 67 years... but the rate of increase was slowing, and, in fact, 0.23 of a Pawn was the asymptotic value of that advantage, the maximum limit that would never quite be reached.

I split the difference between the Korean value of 3/4 of a Pawn and this value of 1/4 of a Pawn, therefore, with the threshhold of a victory by Material Superiority also set so that the game is a draw if material is even, or if White is a Pawn up - but if Black manages to exchange a Knight for a Bishop, with material otherwise even, or if White is a Pawn up and has exchanged a Knight for a Bishop, then it is a win by Material Superiority.

Thus, this leads to two very sensitive trigger points at which the balance of a match could be upset, despite careful defensive play on both sides, to give one player a lead on the scoreboard.

Inspiration from Korean Chess

Since I developed the scheme of Dynamic Scoring, I learned of how, in some Korean Chess tournaments, draws were avoided in tournaments by counting up the material on both sides after an otherwise drawn game, by assigning points to each type of piece.

In Chinese Chess and Korean Chess, the two sides have blue pieces and red pieces; Blue moves first.

A Pawn is worth two points, and 1 1/2 points are added to Red's score in material before the material of the two players is compared.

This, of course, was more exactly analogous to komidashi than what I had done. Why hadn't I thought of it?

But my goal was to encourage exciting attacking play, and so emphasizing the importance of material seemed to be going in the wrong direction. And, since the advantage of the first move in Western Chess is also thought to be less than the value of a Pawn, this doesn't really provide the kind of flexibility that komidashi offered in Go. So it inspired me to tweak Dynamic Scoring, but not to abandon it.

Dynamic Scoring

To institute the kind of scoring system I was looking for, however, I needed a few additional levels of partial victory; not only did I take the historic victory condition of "bare King" as one, I even allowed a player to win by inflicting perpetual check on his opponent.

But there was another element in Dynamic Scoring besides allowing lesser levels of victory, which went back to komidashi. Because White has an advantage from having the first move, the player with the Black pieces is strongly motivated to play defensively. I proposed to address this with the following kind of points schedule:

Score:                                   White - Black

White checkmates Black                     100 -   0
White stalemates Black                      60 -  40
White bares Black's King                    56 -  44
White places Black in perpetual check       52 -  48
Draw                                        50 -  50
Black places White in perpetual check       43 -  57
Black bares White's King                    41 -  59
Black stalemates White                      39 -  61
Black checkmates White                       0 - 100

If victories are won only by means of perpetual check, the scoring system places Black at a large relative advantage; Black can win twice for every seven times White wins that way, and still stand even.

This was intended to encourage Black, despite being disadvantaged, to try to open up the game a little bit, and to encourage White to open it up still more.

Here are the definitions of the partial victories recognized in the current form of the scheme of Dynamic Scoring:

I presume, given the history of Chess, it will also be desired by the Chess-playing community that the player who bares his opponent's King will be required to claim his victory on the turn that he does so, or forfeit this right; it being considered appropriate that a player who fails to correctly estimate his chance to inflict a greater defeat on his opponent should face punishment for that error. I have not explicitly included this rule in my description of the system of Dynamic Scoring, however, as I may be mistaken and also as it is extraneous to the primary objectives of Dynamic Scoring, I prefer to leave the option open as to what the rule on this should be.

And here is the points schedule I propose:

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. 550 450 100 40 5:9
White gives perpetual check. 510 490 20 40 1:5
White has material superiority. 501 499 2 0 1:1
Draw 500 500 0 0 -
Black has material superiority. 499 501 -2 0 1:1
Black gives perpetual check. 450 550 -100 40 5:1
Black bares White's King. 410 590 -180 40 9:5
Black forces stalemate. 390 610 -220 10 11:10
Black forces checkmate. 0 1000 -1000 0 1:1

A more extensive presentation on the subject of Dynamic Scoring is provided in the pages listed below:


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