AlamBios: Suggestions for the Handicapped System (2009-01-01 01:35) [#5445]

Handicapped system enables players of different strength to have interesting and competitive games. I notice that KGS system uses the “~” mark to identify players who seldom play with players of lower ranking. Probably the KGS website would like to encourage players of higher ranking to play with the lower ranking players. The following suggestions may help to achieve this aim. (1) Concept of Handicapped Stone-Equivalent

Since each player plays in turn, in an even game, the black player has one more stone (including the stones being captured) on the board after making his move. Both players will have the same number of stones (including the stones being captured) after the white player makes his move.  That is, the black player will have one stone more only for “half of the game”.  Therefore, the black player has “half-a-stone” advantage.  In an even game, this “half-a-stone” advantage is compensated by komi.  (It is important to note that the advantage is only “half-a-stone”, NOT “one stone”.)
In a 2-stone handicapped game, there will be 2 more black stones on the board (including the stones being captured) for half of the game.  In the other half of the game, there will only be one more black stone (including the stones being captured) after the white player makes his move.  That is, on average, the black player has a “one and a half stones” (1.5 stone) advantage (Note: Again, it is important to note that it is “1.5 stones”, and NOT “2 stones”).
Similarly, in a 3-stone handicapped game, the black player has an advantage of “2.5 stones” (NOT 3 stones).  Let us use the term “handicapped stone-equivalent” to represent the actual advantage of the black player.  From the above discussion, the “handicapped stone-equivalent” is always half a stone less than the actual number of handicapped stones.

(2) Handicapped games between players of one rank difference

Under the existing system, for games between players with one rank difference, the number of handicapped stone is one.  This is done by using a komi of 0.5 instead of the “normal komi” of 6.5.
As discussed in the previous section, this means that the black player does not have to compensate the white player for the “0.5 handicapped stone-equivalent” advantage.

(3) Handicapped games between players of more than one rank difference

Under the existing system, the number of handicapped stones is the same as the difference in ranking. (E.g. a 9d player will give 9 handicapped stones to a 1k player).
Consider the following example.  If a 4d player is to play with a 3d player, he will give the 3d player “0.5 handicapped stone-equivalent” advantage.  When a 3d player plays with a 2d player, he will also give the 2d player “0.5 handicapped stone-equivalent” advantage.  When a 2d player plays with a 1d player, he will give the 1d player the same “0.5 handicapped stone-equivalent” advantage.  Logically, when a 4d player plays with a 1d player, one will naturally assume that he will give 3 times the “0.5 handicapped stone-equivalent” advantage, that is, “1.5 handicapped stone-equivalent” advantage.
As discussed in the section of (1), handicapped stone-equivalent is half a stone less than the actual number of handicapped stones.  Therefore, “1.5 handicapped stone-equivalent” corresponds to 2 handicapped stones.  That is, the 4d player should give “2 handicapped stones” to the 1d player.  However, under the existing system, the 4d player has to give “3 handicapped stones” to the 1d player.  That is, the 4d player gives one extra stone to the 1d player.
This extra advantage will become bigger when the ranking difference is higher.  For example, when a 9d player plays with a 1k player, he should give 9 times “0.5 handicapped stone-equivalent” to the 1k player.  That is “4.5 handicapped stone-equivalent”.  This means that the 9d player should give “5 handicapped stones” to the 1k player.  However, under the existing system, the 9d player has to give “9 handicapped stones” to the 1k player.  That is, the 9d player has to give “4 extra handicapped stones”.
Except in “very fast” games where the lower rank player tends to make more serious mistakes, it would be quite difficult, if not impossible, for a 9d player to beat a 1k player in “9 handicapped stones” games.

(4) Suggested Handicapped System

I would suggest using the handicapped stone-equivalent for players with “one rank” difference (that is, 0.5 handicapped stone-equivalent) as the basis for handicapped games.  The handicapped stone-equivalent for a handicapped game is determined by multiplying the “0.5 handicapped stone-equivalent” with “the difference in rank”.
For example, if the difference in rank is 4 (such as a 5d against a 1d), the handicapped stone-equivalent is 0.5 times 4, that is, 2.  However, as explained above, the handicapped stone-equivalent is always 0.5 stone less than the actual number of handicapped stones.  This means that the handicapped stone-equivalent corresponds to a particular actual number of handicapped stones is always not a whole number.  For a 3-stone handicapped game, the handicapped stone-equivalent is 2.5 while that of a 2-stone handicapped game is 1.5.
In the case of a 5d against a 1d where the handicapped stone equivalent is 2, we can get around this problem by having a 3-stone handicapped game.  The normal komi (say, 6.5) will then be used to compensate the 5d player for the extra 0.5 handicapped stone-equivalent given to the black player.
The following formula, for determining the number of handicapped stones (H) and komi, can be used to implement the above suggestions:

H = (Difference in ranking)/2 + 0.5 (with the following rules): Rule 1: When H is a whole number, the komi is 0.5 Rule 2: When H is not a whole number, it has to be “rounded up” to a whole number and the komi is 6.5. Illustrations: (a) Even game

The difference in ranking is 0.  Therefore, H = 0/2 + 0.5 = 0.5.  Since this is not a whole number, it has to be rounded up to 1.  That is, the black player plays first with a komi of 6.5.

(b) 5d against 2d

The difference in ranking is 3.  Therefore, H = 3/2 + 0.5 = 2.  Since this is a whole number, the number of handicapped stones is 2 and the komi is 0.5.

The objective of the above suggestions is to let players of higher rank feel that they are not disadvantaged in handicapped games, so that they will be more willingly to play with lower rank players.