Fair komi without ties

[Bill Spight]

EDIT:
For the board below, does the two circled points counted as black's area in area scoring if the game end as-is? If they are counted, then there will be less concern of "pass/take button first then has to play move again even if opponent passed too"

$$
$$-----------
$$|...XCBO..|
$$|....XOO..|
$$|....XO...|
$$|....XO...|
$$|....XO...|
$$|...XXO...|
$$|...XOOO..|
$$|...XO....|
$$|...XXO...|
$$-----------

Click Here To Show Diagram Code

[go]$$
$$-----------
$$|...XCBO..|
$$|....XOO..|
$$|....XO...|
$$|....XO...|
$$|....XO...|
$$|...XXO...|
$$|...XOOO..|
$$|...XO....|
$$|...XXO...|
$$-----------[/go]

Yes, would count as one point for Black.

I don't see how this situation would arise, however, or who would have taken the button.

EDIT2:I constucted a case where play-after-pass/button will always happen.

$$ W first
$$-----------
$$|.OX..X...|
$$|.OXXXX...|
$$|.OOOOX...|
$$|....OX...|
$$|OOOOOXXXX|
$$|XXXXXOOOO|
$$|XOO.XO...|
$$|COO.XO.O.|
$$|XXXXXO...|
$$-----------

Click Here To Show Diagram Code

[go]$$ W first
$$-----------
$$|.OX..X...|
$$|.OXXXX...|
$$|.OOOOX...|
$$|....OX...|
$$|OOOOOXXXX|
$$|XXXXXOOOO|
$$|XOO.XO...|
$$|COO.XO.O.|
$$|XXXXXO...|
$$-----------[/go]

is a one-way dame. Very good! I think that the Mind Sports rules would allow White to reopen play and fill that point, however. Even though they use a pass to implement the button.

[luigi]

Except for regarding taking the button as a pass, the Mind Sports rules get it right. Psychologically, using a card or token that someone takes may be best, but you can simply have a player announce that they are taking the button instead of playing a stone on the board. If that person is White, then Black subtracts one point from his final score. Instead of a komi of 7, have Black give a komi of 6½. Giving the lower komi compensates for subtracting one point from Black's score about half the time.

I'm really interested in this topic but have a hard time wrapping my head around it. Could you please provide a clear answer as to whether the following rulesets are fully equivalent to each other, without exception?:

A: Area scoring. No suicide. Positional superko. Button not considered a pass, worth 0.5 points for whoever takes it. Komi 7.
B: Area scoring. No suicide. Positional superko. Button not considered a pass, worth 1 point for White and 0 points for Black. Komi 6.5.

[moha]

The basic idea of button go is to unite area and territory scoring by being a hybrid of the two.
(...)
White can take the button and then fight and win the ko. The result is then ½ pt. less for Black instead of ½ pt. more. One may consider this an undesirable side effect of Button go, but it is an exceptional case, not a common one.
(...)
Anyway, button go is a hybrid of area and territory scoring, and there are pluses and minuses to that.

Nice summary.

To be honest I'm not a fan of the button (complications for little benefit, since the result is still not as nice as Japanese). But I think I see where it's problems originate from. From a fairness perspective, shouldn't it go like this? (complementing my earlier list )

Code: Select all

"Fair" button  :  Less stones played wins ties, B wins if still tie

This seems to be the intended meaning, has a reason and sounds fair. And seems to fix my position as well.

[Bill Spight]

Could you please provide a clear answer as to whether the following rulesets are fully equivalent to each other, without exception?:

A: Area scoring. No suicide. Positional superko. Button not considered a pass, worth 0.5 points for whoever takes it. Komi 7.
B: Area scoring. No suicide. Positional superko. Button not considered a pass, worth 1 point for White and 0 points for Black. Komi 6.5.

First, the status of the button matters to positional superko. All board positions before the button is taken are different from all board positions after the button is taken. So when the button is taken we can forget all positions earlier than the current position. They cannot be replicated.

With a 7 point komi we have the following button, represented as a game.

Code: Select all

            B
           / \
          ½  -½

From the button, B, Black can move to a position worth ½ pt. or White can move to a position worth -½ pt., i.e., ½ pt. for White. Now let's add the komi to those results.

Code: Select all

            B
           / \
        -6½  -7½

So the combination of button and komi means that Black can take the button for an effective komi of 6½, while White can take the button for an effective komi of 7½.

With a 6½ point komi we have the following button, represented as a game.

Code: Select all

            B
           / \
          0  -1

From the button, B, Black can move to a position worth 0 or White can move to a position worth -1 pt., i.e., 1 pt. for White. Now let's add the komi to those results.

Code: Select all

            B
           / \
        -6½  -7½

All same same.

[luigi]

All same same.

Cool, thanks.

[billyswong]

To be honest I'm not a fan of the button (complications for little benefit, since the result is still not as nice as Japanese). But I think I see where it's problems originate from. From a fairness perspective, shouldn't it go like this? (complementing my earlier list )

Code: Select all

"Fair" button  :  Less stones played wins ties, B wins if still tie

This seems to be the intended meaning, has a reason and sounds fair. And seems to fix my position as well.

Advantage: This method keeps a game playing sequence the same of before introducing such rule. Button go introduce a new move which maybe inserted before all stones have played out, making the scoring 'impure'.
Disadvantage: 'Play it out when there is life/death dispute' is no longer 100% neutral to game result, thus losing a major advantage of area scoring. Button go preserves that.

[moha]

Code: Select all

"Fair" button  :  Less stones played wins ties, B wins if still tie

This seems to be the intended meaning, has a reason and sounds fair. And seems to fix my position as well.

Advantage: This method keeps a game playing sequence the same of before introducing such rule. Button go introduce a new move which maybe inserted before all stones have played out, making the scoring 'impure'.
Disadvantage: 'Play it out when there is life/death dispute' is no longer 100% neutral to game result, thus losing a major advantage of area scoring. Button go preserves that.

You are right, though we surely don't want to count stones played for dispute removal. So maybe a more elaborate wording like "less stones played (before first two passes) wins ties, b wins if still tie".

EDIT: this could still reward delaying onesided dame (like other variants)...

Exact wording aside, what seems nice is this (like "first passer wins" idea) is just a tiebreak. Using less stones for achieving a jigo can be acknowledged (where such is necessary) as a slightly better performance - but the difference does not amount to a half point in go terms. Even having B winning the remaining ties has some logic, since he worked for overcoming those 7 points, while W got a komi that is a bit too high for nonperfect players.

Nonetheless, I still prefer the last one on my earlier list.

[Bill Spight]

On the fairness of the button with area scoring

In its basic form, where the "taking the button" is simply a move that gains ½ pt., which either player can play, then button go is plainly fair. The average value of the button is 0, and favors neither player. Nor does it alter the mean value of any position, although, OC, it affects the final score.

At present, altering the final score with the button seems to make games more fair, since a 7½ pt. komi favors White, while a 5½ pt. komi favors Black. Button go with a 7 pt. komi probably produces results closer to 50:50.

However, there are occasions where there is some strategy to taking the button, as moha's example indicates. While I don't think that either White or Black is more likely to face such a situation, it does give an advantage to the player who is more familiar with the button.

[moha]

But does fairness only mean not favoring either player? Then "dicethrow" as tiebreak is fair too, unless you also care whom ties are awarded to. By "fair" I also meant no undeserved or quasi-random advantage - wasn't a good choice of word probably.

Consistency is what I miss in my example (W+ or B+ based on leftover threats). Having no special button strategy would also be nice, not changing move sequences too much - a clean tiebreak.

At present, altering the final score with the button seems to make games more fair, since a 7½ pt. komi favors White, while a 5½ pt. komi favors Black. Button go with a 7 pt. komi probably produces results closer to 50:50.

I wonder what stats simple komi 7 would produce. Go quest is the only place I know where it is regularly used, for it's small boards. But even in 9x9 I find it nice to have a jigo from time to time.

[Bill Spight]

But does fairness only mean not favoring either player? Then "dicethrow" as tiebreak is fair too, unless you also care whom ties are awarded to. By "fair" I also meant no undeserved or quasi-random advantage - wasn't a good choice of word probably.

Button go takes away the advantage of getting the last dame by area scoring. Under button go with a komi of 7 pts., if Black makes 7 pts. of territory, White will normally play the last dame (if there is one) and Black will also get the button. Her button go score will be ½ pt., while her area score will be 0. But if Black makes only 6 pts. of territory, Black will normally get the last dame and White will get the button. Black's area score will still be 0, but her button go score will be -½ pt. As we know, there is skill involved (by both players) in whether Black gets 6 or 7 pts. of territory. That skill is reflected in the button go score, not the area score. If there is any quasi-random advantage under normal conditions, it is not in button go.

[moha]

Most go rules behave nicely under normal conditions.

[luigi]

In fact, I have objected to ending play with two consecutive passes for over 20 years. Yasunaga, many years ago, proposed a three pass rule, and Ing has a four pass rule. But I think that the Mind Sports rules end play with two consecutive passes, and count "taking the button" as a pass. I am afraid that I am swimming against the tide.

I had a suspicion that three and four pass rules where passing lifts ko bans would be problematic. And sure enough, Ikeda's analysis of the issue shows that it introduces cycles, defeating the purpose of the superko rule. He summarizes his position as follows:

In short, the super-ko rule is one of the fundamental rules of go, and making exceptions to it can lead to troubles that are hard to foresee. If you feel that [those] run counter to tradition and you make exceptions to the super-ko rule to accommodate them, you had better be ready to prove by logic that your exceptions do not cause trouble. It will not be enough to say that no cases have been found in which the exception leads to peculiar results. That argument will always leave doubts about the rules.

My opinion is that go has three fundamental rules which should be common to all rulesets and to which no exceptions should be allowed. These are:

(1) The rule of alternate play (where play means playing a stone on the board or passing)
(2) The capturing rule
(3) The super-ko rule

These issues don't apply to the button, of course. But I think you should reconsider your opinion on three and four pass rules.

[Bill Spight]

In fact, I have objected to ending play with two consecutive passes for over 20 years. Yasunaga, many years ago, proposed a three pass rule, and Ing has a four pass rule. But I think that the Mind Sports rules end play with two consecutive passes, and count "taking the button" as a pass. I am afraid that I am swimming against the tide.

I had a suspicion that three and four pass rules where passing lifts ko bans would be problematic. And sure enough, Ikeda's analysis of the issue shows that it introduces cycles, defeating the purpose of the superko rule. He summarizes his position as follows:

In short, the super-ko rule is one of the fundamental rules of go, and making exceptions to it can lead to troubles that are hard to foresee. If you feel that [those] run counter to tradition and you make exceptions to the super-ko rule to accommodate them, you had better be ready to prove by logic that your exceptions do not cause trouble. It will not be enough to say that no cases have been found in which the exception leads to peculiar results. That argument will always leave doubts about the rules.

My opinion is that go has three fundamental rules which should be common to all rulesets and to which no exceptions should be allowed. These are:

(1) The rule of alternate play (where play means playing a stone on the board or passing)
(2) The capturing rule
(3) The super-ko rule

These issues don't apply to the button, of course. But I think you should reconsider your opinion on three and four pass rules.

Ing rules and Spight rules have 3 or 4 pass ko rules that do not rely upon no exceptions having been found. Ing rules are problematic in that the distinction between fighting and disturbing kos is not clear. But both rules avoid infinte repetition, despite allowing passes to lift ko or superko bans. Just because Ikeda did not see how to do that does not mean that it couldn't be done.

[pookpooi]

I ask Macelee to generated latest komi stats, big thanks!

31564 games of 6.5 komi: black 15972 50.60% (50.58%), white 15592 49.40% (49.38%)
19037 games of 7.5 kimi: black 9025 47.41% (47.38%), white 10012 52.59% (52.56%)
Percentages in brackets are calculated from total games including void results, mostly triple ko
Generated from Go4Go database on 2017-11-24.

It's mostly similar to the previous data. However now we have data from different time we can have stats of the latest two years, reflecting how well pro adapt to the new komi rule right now.

Stats from games from January 8 2016 to November 24 2017
6836 games of 6.5 komi: black 3465 50.69%, white 3371 49.31%
4027 games of 7.5 kimi: black 1898 47.13%, white 2129 52.87%

It's very, very little change but pro seems to getting better playing as black in 6.5 komi and getting better playing as white in 7.5 komi, thus worsening the situation.

[luigi]

I've been thinking that, if the button were to be officially used to fine-tune komi for optimal balance under area scoring (thus inserting 7 komi with button as an additional option between 7.5 komi and 5.5 komi), it would be inconsistent to have it lift ko and superko bans. That is, unless a 0-point button with such a capability were used with fractional komi. And, since I see that as an unnecessary complication, I have to see it that way with a half-point button as well...

Also, positional superko is already a compromise. It doesn't take into account which player is to move in a repeated position because the hassle of checking for that outweighs its benefits, and checking for repetitions is already a hassle. Thus, since only the position of the stones on the board is considered, the state of the button should be left out as well. I think it's consistent with the spirit of keeping things simple that motivates positional superko.

Another perk of this simplified button is that, unless I'm missing something, it makes komi 7 plus button under area scoring fully equivalent to 6.5 komi under Ikeda's Territory Rules I and Area Rules III.