Button go has a similar effect as the Taiwan rules, which count area, but do not count the point for Black if he plays the last Japanese dame, and to Ikeda's Area Rules III, which adjust the score if White passes first. In most instances, Button go reconciles area and territory scoring.
Button go is played with a token called the button, which is worth 1/2 point. (Barry says that we now have a good use for those broken White stones. ;-)) Area scoring is used. At his turn a player may take the button instead of making a board play or passing. Taking the button lifts any restriction on taking a ko or superko.
To see the usual effect of the button, suppose that each player has the same territory score, a jigo. Because the number of points on the go board is odd, normally Black will fill the last dame, which will give him a 1 point win under area scoring. In Button go, White will then take the button, and the final score will be a 1/2 point win for Black.
Now let's compare that with the case when Black wins by 1 point by territory scoring. Then normally White will fill the last dame, and the result by area scoring is also a 1 point win. In Button go Black will then take the button, and the final score will be a 1 1/2 point win for Black. Usually the score in Button go is 1/2 point more for Black than the territory score.
Territory scoring is sharper than area scoring in that, as here, it differentiates cases that area scoring does not. With area scoring the winner can more often make sloppy plays and still win. Like the Taiwan rules, button go also makes these differentiations, and makes for a sharper game.
Area scoring requires less complex rules than territory scoring, but territory scoring makes for a sharper game. Button go is a practical way to enjoy the benefits of both.
Note: In using the Chinese style of determining the final result, 180.75 is subtracted from Black's score, because 361.5 points are at stake.
The Count: What I would find interesting is to know whether button go rewards "good play" in any sense over area scoring. Being "sharper" is not a reason in itself, I believe. Is it not an arbitrary distinction to give the first passer an extra half point? We could instead use a rule where whoever occupies the 6-8 point gets an extra half point. It would be just as "sharp". Does territory scoring make it so that there are ways of determining in the endgame which plays you must make before other ones, whereas you might be able to play one weaker play first in area scoring and still get the same score? If the answer is "yes", I'm sure it's a well known fact, but I haven't seen it stated in Territory and Area Scoring.
Bill: Consider this situation, where the rest of the board is settled.
Net local area score: 0.
With button go White takes the button, for a net score of -0.5.
Sloppy play is punished.
The Count: I don't know if this is a faux-pas, but I am writing a new reply above my old one (which is of course now below). Sloppy play is not punished in general; this is definitely not the advantage of playing with a button or playing with territory rules. Fortunately, I can use the same example as above to show what is going on. First, let us realise exactly what happened above. Black played a move that is easily considered the wrong one (even though, with no other moves left on the board it happened not to matter). If you play with the button, Black would lose one extra point for his bad play. Now consider the following.
White to play. The correct play is of course at a. If White made the mistake of playing at b, she would lose two points. If you play with the button, White would only lose one point (compared to the best play). White's sloppy play is being rewarded!
To create an even simpler example, imagine there is one dame left on the board and it is Black to play. Black could mistakenly pass, losing two points. If there is a button, Black would mistakenly take the button and only lose one point.
Nonetheless, I am still in favour of the button. I think the answer probably lies in button go reflecting how bad a bad play is in the score more. I don't want to think about it now though.
Bill: You make an interesting point, Count. :-) However, I disagree with your description of it. Sloppy play is not being rewarded, it is being punished. It is just not being punished as much as it would be without the button.
The point about the sharpness of button go is that, characteristically, there are fewer correct plays among the options available than there are without the button.
(Below is my old reply.)
The Count: I didn't see how the punishment of this terrible move could extent to that of subtly-bad pre-yose moves, but after a lot of thought, now I think I do. Basically, you should always be aiming to finish with sente in any local part of the board, all things (the count) being equal. This is "good play". If it just so happens that you end up not being able to use your sente, you get a half point in compensation.
The Count: Here is an example I came up with while thinking about these things. Black to move, what is the best play? And with White first?
Bill: This is a very nice example. Thank you. :-)
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