Komi and the total number of moves to equalize

On one hand, I’m new to go, so forgive the naiveness. On the other hand, I’m not new to logical thinking, as I teach computer science, and then I like to find and learn about the reasoning behind games decisions.

Go is my new vacation project, to start the year and bring something new and fun to my students, to help them program computers. I always look for inspirations in games, and Go for sure is very inspirational, specially after alphago.

That intro is just to give context and to say hello to all, as this is my first post. Thanks for the wonderful website.

Now to the question: on the British GO rules ( https://www.britgo.org/files/rules/GoQuickRef.pdf ) you can see that White is obliged to be the last to pass so the game can end. (rule number 10: even if it means 3 pass in a row!).

This is to make the number of moves equal throughout the whole game.

Since KOMI is to compensate for black moving first, I wonder what is the point of it, since the total of moves are equal.

I know in chess White has a “initiative” for being first and here are the statistics for an amount of 600k professional games:

White wins   37.35%
Black wins   27.41%
Drawn        35.23%

That alone could be used to calculate how many points in chess White and Black would be fighting for, but they still ignore and use 1 for victory and 0.5 for draw (and of course 0 for losing).

I wonder if in Go we also couldn’t ignore KOMI? Also, I’m curious if there are statistics (for only games of strong professional players) to understand what is the percentage of win/lose for Black (playing first, opposed to chess) and White?

Thanks a lot for the kind discussion.

Dr. Bèco

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Komi is to compensate for the first move advantage. Even when both players play an equal number of strategically meaningful moves, the first move advantage still remains. Just like in chess, having the initiative gives a significant advantage.

An overly simplified model of a game of go is like taking turns at choosing from a pie that has been cut into uneven pieces. Even if there are an even number of pieces (and hence both players get to take the same number of pieces), the player going first has the advantage of always being able to take a piece that is at least as large (or potentially larger than) the other player’s next piece.

The “white passes last” rule is merely a book-keeping convenience in order to say that both players have either played or passed an equal number of times. The pass stones used in the British go rules (which by the way are essentially equivalent to the American Go Association rules) are also merely a book-keeping convenience in order to use territory counting methods to get a result equivalent to area scoring.

You can drop the need for white passing last, counting prisoners, and counting pass stones, if you just use area counting to determine the score. See:
https://senseis.xmp.net/?EquivalenceScoringExample

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I wouldn’t say that the first move advantage is ignored in chess. Rather instead, it is balanced out by playing matches of multiple games, where the players alternate at playing as white and black.

Komi is actually a relatively modern convention (in common use for less than 100 years). However, long before that, the first move advantage had been recognized. Hence, to get a balanced match, players would play a series of games alternating between playing black and white.

Some of these multi-game series would even use an adaptive handicapping procedure if one player starts to dominate the match (e.g., the stronger player would switch to playing first in only 1 out of 3 games, and eventually to playing second in all games, if they still keep winning, which would be quite embarrassing for their opponent).

These statistics certainly exist, although I’m not familiar with their exact numbers. I’m sure that others that are better informed will chime in with relevant data.

Over the decades, komi was gradually adjusted to its current levels based on observations of whether a bias still seemed to exist. In very recent times, strong AI play and analysis seems to support that the fair value of komi may be around 6 or 7 (which would perhaps also depend on the specific nuances of the rules adopted).

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There is waltheri which collects pro games (and recently also games played by AlphaGo). If you restrict to modern games (the last 20 years), then it shows a 50 percent chance for black to win. Including older games from the previous century raises this to 51.6, and restricting it to only very new games, most of which are played by computers, lowers it to around 48.5 percent.

My interpretation is that human play has a slight advantage for black, but strong AI disagrees and shows a slight advantage for white.

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Also, if you’re interested in game theory of Go, then Mathematical Go: Chilling Gets the Last Point by Elwyn Berlekamp and David Wolfe is a must-read.

A related thing that might be fun to know, is that John Conway’s surreal numbers were inspired by endgame positions of Go.

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The difficulty for go is, that it’s difficult to predict how a different Komi would affect the progress of a game. Games ended by resignation could have carried on, since a win would be possible with the other Komi while lost with the set Komi, or if the game ended with a score, the players would play differently (more save/aggressive) for a different score target (Komi).

If we ignore Komi, black has a big advantage. A quick and crude analysis with KataGo (an AI) suggests a winrate of 75% for black.
In an tournament, you need many games to average out blacks advantage. With 2 hours up to several days per game, this will take a while.

The reason could be, that some human games are played with 6.5 Komi, while AI plays 7.5 exclusive.

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We can ignore komi, and for preventing draws messing up cup-type tournaments, we can let white claim the win if he/she manages to draw against blacks first move advantage.

This is called “one stone handicap” ^___^

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Until about 1950, almost all games were played without komi. This was kind of alright, since the nominally weaker player took Black. But it was accepted even in the 19th century that the first move advantage was significant, and White usually employed a particular active style to combat it.

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Tournament komi first came in at something tiny like 2.5, then it gradually rose up to the present 6.5. It’s worth noting that the shift from 5.5 to 6.5 happened in the 1990s, well before AI had any say. Today, superhuman AIs seem to consider 6 komi to be correct, but that would allow draws which would make tournament directing harder.

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I thought that the evidence from strong AI suggests that it may be 7, and that is for area scoring rules, in particular.

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Which superhuman AI can play with 6 komi? I know of KataGo. Most AIs are trained with 7.5 and fail to play with anything else.

KataGo predicts an almost even game for an empty board with 7Komi

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With all due respect, I think everyone may be misunderstanding what drbeco was suggesting when he asked whether komi could be ignored (in the context of the chess statistics he was talking about). I think he means one could substitute fractional scoring in place of komi. In other words, a win by white would be worth 1 and a win by black would reflect whatever the statistical difference is in the win rate. To take an arbitrary number: if the difference were 5%, then a black win would be worth 0.95. This wouldn’t be useful for individual games, but it might be better for large tournaments or a long series of games where the players play both colors an equal number of times.

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I don’t see a point in removing a rule which makes every game almost fair. As far as I can see, one need to play many games to get more of such a rule than a tiebreaker. In addition to Komi, it could be an interesting addition.

If I understand it right white would get (1/3 • 1/0.37)=0.9 points for a win, black (1/3 • 1/0.27=)1.23 points, and in case of a draw each player gets (1/2 • 1/3 • 1/0.35=)0.48 points.

For 2 games with alternating colours, the possible outcomes could be:

white black fractional points classic scoring chance to happen
win win 2.13 2 0.102
draw win 1.71 1.5 0.097
win draw 1.38 1.5 0.131
loss win 1.23 1 0.075
draw draw 0.96 1 0.124
win loss 0.9 1 0.140
loss draw 0.48 0.5 0.096
draw loss 0.48 0.5 0.132
loss loss 0 0 0.102

So for 2 games it serves as a tiebreaker. Maybe it would even need different points for draw as black and draw as white, to get the order for loss+draw right (if black can force a draw it should be worth more than white losing the advantage).

If this scoring system should be more than a mere tiebreaker, you have to play more games. I’ve trouble to find a method to estimate how many games are needed (depending on win rates of black and white) to get a difference between both scoring methods that’s more than a tiebreaker or luck.

I can understand that nobody wants to burn his hands by trying to implement the new scoring method in a tournament. If you implement it, you will get many complains about seemingly unfair results. 3 wins as black are (almost) worth more than 4 wins as white (if you add additional decimal places). Even if it wouldn’t already be a problem with how many decimal places you use, it still makes 4 wins worse than 3, which by itself will lead to many complains (by the players who won 4 games as white).

For go without Komi, black has an estimated win rate of 75%, so a win for black would be worth 0.44 points, while white (wr < 25%) gets at least 1.33 points for a win, so 3 wins for black are worth as much as 1 win for white. So each player should probably play at least 3 games per colour (better more, since the player getting white against the weakest opponent (the biggest rank difference) has the greatest chance to win the 1.33 points).

Most amateur go tournaments I’m aware of have played 5 games (less than the estimated 6 games). With 2 hours per game tournaments get much longer with each additional round. That’s even worse for professional games with 4h+ (up to multiple days) per game.

I don’t think this is doable for go.

As an additional problem, we cannot transfer the statistics to other Komi values. If we change Komi, we have to start over again collecting new data (the old pre Komi games are probably obsolete, since strategy has changed in the last decades). Whit just AI analysis, it could be possible to estimate good values though.

But I would rather keep (integer) Komi, to keep each individual game as fair as possible. To give different points based on the remaining first move advantage could be an addition.

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