Should go rules be changed to allow for komi 7 and a draw?

[xiaodai]

After analysing many games with Katago, I realise that komi 7 leads to 50%/50% win rate instead of a slightly higher win rate for white with 7.5 komi.

Japanese published some stats saying that 6.5 leads to roughly even win rate. But I think a middle ground is 7 komi allowing for a draw.

So what about the best of 3 series? Many of them will be draws? I think we need to introduce one more game in those cases since it's possible to draw using 3 ko rule anyway. Although 3 kos are much rarer.

[lightvector]

For area scoring, I'm a fan of 7 komi + button. This means you get clean and simple rules, the fairest possible komi as far as we can tell, and still don't get draws.

If you still have to use Japanese rules then 6.5 komi is fairer than 7 as far as we can tell, and is drawless, so it's already good as-is at 6.5.

[Harleqin]

For area scoring, I'm a fan of 7 komi + button. This means you get clean and simple rules, the fairest possible komi as far as we can tell, and still don't get draws.

If you still have to use Japanese rules then 6.5 komi is fairer than 7 as far as we can tell, and is drawless, so it's already good as-is at 6.5.

I agree, but as far as I see, 7 komi + button has a result granularity of 1 (any integer result is possible with no probability difference by parity), so draws are just as possible as in explicit territory scoring. I think button go is equivalent to territory scoring with points in seki, and one-sided dame are also territory.

One question for the asker: which rules do you mean? Japanese, Korean, Chinese, AGA, France, Britain, EGF, WMSG, New Zealand (which already has area scoring and 7 komi, btw.), some specific server…

[luigi]

as far as I see, 7 komi + button has a result granularity of 1 (any integer result is possible with no probability difference by parity), so draws are just as possible as in explicit territory scoring.

The button breaks ties, though.

[lightvector]

Yep, 7 komi plus a half-point button gives gives you a result on ..., -1.5, -0.5, 0.5, 1.5, 2.5, ... so no draws (at least by scoring), and you do get a 1-point granularity without having to depend on odd-dame sekis.

[Harleqin]

Ah, OK, my understanding of button was “if white makes the last move, she gains one point’.

[jlt]

Whatever the rules, if the two players are perfect and no draw is allowed, one of them wins for sure.

However, tournament time constraints do not always allow to play tiebreaks.

[Bill Spight]

Ah, OK, my understanding of button was “if white makes the last move, she gains one point’.

There are basically three ways to implement the button at area scoring, by having a play that is not on the board that may be represented like this, using slash notation.

1) {½ |-½} ; The button may be a token worth ½ point to the player that takes it.

2) {0 | -1} ; The button is worth 1 pt. to White, 0 to Black.

3) {1 | 0} ; The button is worth 1 pt. to Black, 0 to White.

At territory scoring, these become

1) {-½ | ½} ; The player that takes the button loses ½ pt.

2) {-1 | 0} ; If Black takes the button she loses 1 pt.

3) {0 | 1} ; If White takes the button he loses 1 pt.

Options 2) and 3) allow ties with integer komi.

[lightvector]

Ah, OK, my understanding of button was “if white makes the last move, she gains one point’.

Ah, that makes sense. So the thing is, these three are exactly identical:

A: 7 komi, the button is worth 0.5 points to the player who spends a move to take it.
B: 6.5 komi, if white spends a move to take the button, white gains a point.
C: 7.5 komi, if black spends a move to take the button, black gains a point.

At least for me, even though these are literally identical in all cases, I intuitively find stating it as in B and C to be weirdly asymmetric and confusing. Stating it as in A makes it more obvious that the button is simply a move with a particular value, and that when the game is as close as possible, it functions as a tiebreaker to the player able to end in sente for normal board plays (or who is a ko-monster with enough threats to take the button before finishing a final ko). It also generalizes better to coupon Go / environmental Go: https://senseis.xmp.net/?EnvironmentalGo.

Note that we use "spends a move to take the button" rather than a formulation that talks about who "is the first to pass". The button should ideally not be considered to be a pass, because it may lead to some oddities rarely in some rules if the action of taking the button, a move that actually has value, is conflated with "I have nothing to do and wish to end the game", and also the act of taking the button should also be considered to change the game state so that it makes retaking a ko afterwards to be legal. For similar reasons "spends a move to take the button" is probably better than a formulation that talks about who "makes the last move". To avoid pathologies, you probably want the button to behave as much as possible like an ordinary extra possible move on the board that is gote and worth 0.5 points to the player who can take it.

[lightvector]

(Slightly unfortunately, KataGo's formulation of the button does call it a "pass", this is out of need to be compatible with the existing SGF and GTP formats and avoid having to invent new notation that SGF parsers or GTP controllers will not understand. It is careful to specify however that this "pass" does not count towards the two that are needed for game end, and that it affects the game state for determining repetition for ko/superko).

[jann]

A button still makes the game unfair, a minimax win for either player. For strong bots that undeserved half point is important, so OP's problem (non-50% winrate) is not addressed.

[Bill Spight]

A button still makes the game unfair, a minimax win for either player. For strong bots that undeserved half point is important, so OP's problem (non-50% winrate) is not addressed.

Actually, the {½ | -½} button with 7 pt. komi does address the winrate question. xiaodai finds that a 7 pt. komi (with area scoring, it appears) yields a statistical winrate closer to 50% than a 7½ pt. komi. Adding the {½ | -½} button to the 7 pt. komi should also yield a winrate closer to 50% than the 7½ pt. komi, since sometimes Black will get the button and sometimes White will.

[lightvector]

Or to address the objection more directly - @jann - yes with a button the game theoretically is still a win for one of the players, and therefore for game-theoretic-optimal players it would be unfair. However, even with super-strong AI that can give 3 whole handicap stones to many human pros and sometimes win, we are still so far from game-theoretic-optimal that it doesn't matter.

For example, you can see this with Japanese rules - if I recall correctly, there are some statistics that suggest 6.5 komi is very close to fair for humans, and amazingly, this continues to hold true well into superhuman levels. For KataGo, 6.5 komi is still judged to be about the fairest possible komi for Japanese-like rules, more fair than 6 or 7 even though 6 or 7 allow draws and 6.5 does not. Supposing the game theoretic optimal on-the-board score by black was in fact one of +6 or +7, it's so closely a tossup which one it is that awarding a draw for either one is less fair in practice than being drawless and having black win one and white win one.

[Bill Spight]

Or to address the objection more directly - @jann - yes with a button the game theoretically is still a win for one of the players, and therefore for game-theoretic-optimal players it would be unfair. However, even with super-strong AI that can give 3 whole handicap stones to many human pros and sometimes win, we are still so far from game-theoretic-optimal that it doesn't matter.

For example, you can see this with Japanese rules - if I recall correctly, there are some statistics that suggest 6.5 komi is very close to fair for humans, and amazingly, this continues to hold true well into superhuman levels. For KataGo, 6.5 komi is still judged to be about the fairest possible komi for Japanese-like rules, more fair than 6 or 7 even though 6 or 7 allow draws and 6.5 does not.

And, as indicated above, a 6.5 komi may be implemented with a 6 point komi with the {-1 | 0} button, which allows jigo. The {-1 | 0} button may be implemented by having Black give up a pass stone if Black makes the first pass.

Usually, if the net territory is 6 points for Black at the end of play, White will make the first pass. The result will be jigo. Or if the net territory is 7 points for Black, usually Black will make the first pass and hand over a pass stone. In that case the result will also be jigo.

[Pio2001]

If I'm not mistaken, according to stats, in AGA rule, a komi of 6.5 slightly favours Black, while 7.5 slightly favours White.
The odds are within 48% / 52% .

However, as jlt said, some tournaments will have to be redesigned : championships that are supposed to lead to a unique winner, qualifying tournaments for a limited number of places, and single or double elimination tournaments.

Button go is an altogether different topic, as it introduces a new major category of rules in addition to area style rules (Chinese, New Zealand, AGA, Ing...) and territory style rules (Japanese, Korean...) : the button style rules (area plus button, territory plus button), with new strategic concepts related to the button.