Topic: counting group tax on a real board.
The “group tax” seems natural and elegant, but I have read it was abandoned because it was harder to count that way. I know from experience that this can be true when you try to count the “Chinese way”, because there is an added complication. The total eye space for example reduces the total stones on the board down from the predictable 361. Many people prefer “Japanese” counting, which they say is simpler/faster, but isn’t the following method just as simple as “Japanese counting”, even with group tax, while you are effectively counting the stones difference and hence doing away with all the Japanese complications. (From what I read, this is close to or perhaps the same as what happened in the Chinese Tang dynasty: History of Go rules, PDF.)
If you make sure both sides have played the same amount of stones to the board (like AGA rules: passing gives the opponent a prisoner, all prisoners are returned to the board in the end as usual), then you end with the same amount of stones for both players on the board. You can then ignore all those stones in the counting, because you want the difference between the opponents. This difference now only lies in the remaining open but enclosed spaces (territory).
Then use additional stones to fill in all the minimum necessary eyes (two stones per group). Then count the remaining open spaces (territory) for both players, and compare the result to find the winner.
Example:
Black: 24 total stones + territory (“area”). 1 groups, 2 eyes, 22 total stones minus eyes, 8 surrounded empty points (“territory”), 6 surrounded empty points minus the eyes.
White: 25 total stones + territory (“area”). 2 groups, 4 eyes, 21 total stones minus eyes, 9 surrounded empty points (“territory”), 5 surrounded points minus the eyes.
In both methods, Black wins by +1 stone. The benefit is that it is easier to count to 5 and 6 and compute the 1 difference, than it may be to count to 24, subtract that from the 49 (board size), then subtract 2 eyes from 24 = 22 (Black), and subtract 49 - 24 - 4 = 21 (White), and subtract 22 - 21 = 1. The underlying reason may be that there are more stones than empty spaces, and/or that it is easier to rearrange the empty spaces.
In currently popular rules, White wins by 1 (eyes are counted as points).
Do dame need to be played to the end ? In the historical PDF linked above, The History of Go Rules by Chen Zuyuan 陈祖源 © 2011, page 10:
As a result White would lose by 9. But the result is still 8, as in present Japanese rules. How can that be? A reasonable assumption is: If Black makes the last move, in order to have equal stones for each side, Black will remove his last stone. Once territory counting is adopted, dame are naturally not played.
This I have now tested twice, and (I am sorry to say) it does not seem to work out this way, but rather it works as the AGA rules seem to prescribe. If black takes the last dame point, then white will play a pass stone, and then both the absolute stone count (counting all stones and territory), and only the territory (because the stones are equal) give the same result (with or without the group tax, which has no impact on this matter). From the perspective of the absolute stone count, this makes sense: the last dame is a point, and there is no more benefit for white in its last move. To not play that dame point for black, means to loose that point. When white plays the pass stone, that difference becomes accurately codified into the remaining territory for both. If black omits merely as a counting short cut, white’s territory is one larger than it should have been, even though that black stone itself later gets ignored in the counting.
This leaves the question of why they didn’t play the dame points. Perhaps the one who started the game first, then withdrawing his last useful move was a form of komi, since komi points back then where not awarded. It restores a balance, so that each side plays an equal amount of useful moves. It seems courteous for the one who played first, to in the end not force the other to have to give up a pass stone (or play inside their own territory), when there is no longer a useful move. If the goal is to allow the player who played second in the beginning the benefit of getting the last useful dame playing move if he gets it, then you could omit playing not only the last dame point but more or all of them, since the score doesn’t change when both players fill in a dame point. If the scoring is done by putting back in the pass stones (prisoners) and count the territory (enclosed empty space), to prevent confusion these empty dame points could be randomly filled in.
(Corrections welcomed.)