Drawn Games via "Margin" or "Random" Komi

General Go Discussion
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Looking up an old comment from an earlier thread for another unrelated discussion reminded me of some thoughts that I had about draws in the game of go. This post is just to further discuss that and some extensions.

In the following, score is defined as black’s points minus white’s points.

Standard Komi Practices

The most common practice these days is to use a non-integer komi, which makes a tie impossible.

For a typical komi of 6.5 points:

  • Black Wins, if score > 7
  • White Wins, if score < 7

However, an alternative (that is even mandated in the New Zealand rules) is to use integer komi that allows for possible ties.

For an integer komi of 7 points:

  • Black Wins, if score > 7
  • Draw, if score = 7
  • White Wins, if score < 7

However, even with integer komi, draws may still be somewhat uncommon, and reaching one requires the game to proceed along a delicate balance, where one point mistakes can flip between winning, losing, or drawing.

Margin Komi

Margin Komi is an extension of the standard komi practices that introduces a non-negative margin to widen the range of scoring outcomes that results in a draw, i.e., if the score is within the margin value around komi, then the game is a draw.

For a Margin Komi of 6.5 ± 3 points:

  • Black Wins, if score > 9
  • Draw, if score = 4, 5, 6, 7, 8, 9
  • White Wins, if score < 4

For a Margin Komi of 7 ± 2 points:

  • Black Wins, if score > 9
  • Draw, if score = 5, 6, 7, 8, 9
  • White Wins, if score < 5

Naturally, a margin of ± 0 reduces to the original standard komi practices.

Maybe the terminology could be improved. Perhaps, it would be more clear to respectively call the above examples something like “4 - 9” or “5-to-9” margin komi, in order to explicitly state the range of scores that are declared draws.

However, even with margin komi, one could have a game end with a delicate balance. If the score is close to the boundary of the margin, again a one point mistake can swing between a draw and a win (or loss). This leads us to the next idea, where the shift in outcomes is smoothed out with randomness … :open_mouth:

Random Komi

Okay, so this is a crazy idea that is going to be controversial, since it introduces an element of chance into the mechanics of the game. I’m not suggesting that this should become standard, but just putting it out there as a crazy variant to consider.

Instead of a fixed komi value, we could instead pick a random distribution for the komi parameter, which is only randomly selected after the score is determined. This could also be combined with the use of a margin to increase the draw probability.

For a Random Komi of “Uniform over {5, 6, 7, 8, 9} with a margin of ± 3”, the final outcome will be random depending on the score, with probabilities given by:

  • If score > 12, then Black Wins 100%
  • If score = 12, then Black Wins 80%, Draw 20%
  • If score = 11, then Black Wins 60%, Draw 40%
  • If score = 10, then Black Wins 40%, Draw 60%
  • If score = 9, then Black Wins 20%, Draw 80%
  • If score = 6, 7, or 8, then Draw 100%
  • If score = 5, then Draw 80%, White Wins 20%
  • If score = 4, then Draw 60%, White Wins 40%
  • If score = 3, then Draw 40%, White Wins 60%
  • If score = 2, then Draw 20%, White Wins 80%
  • If score < 2, then White Wins 100%

Why have draws at all? Why make them more common?

In an older post, I discuss how games/sports where draws are common are philosophically different than games where draws are impossible or at least very rare. If draws are common, then they should indicate that neither side has significantly outplayed the other to decisively earn the win, but if draws are very rare or impossible, then winning could happen by very thin margins, simply since one side ultimately must.

Why mess with adding randomness?

That part is just a thought experiment and a wacky idea.

Note: I am not suggesting that we adopt margins or randomness as standard practice. Rather, I’m just putting these ideas out there, maybe for consideration as variants. since these ideas significantly alter the game.

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I hope your ‘wacky’ Random komi idea doesn’t distract from a very interesting Margin komi idea.

The margin may seem arbitrary but it doesn’t need to be. I would find it very appealing if the margin were set such that statistically, a win indicated that a change in handicap (of one stone) is more likely to produce a well matched game than a rematch with the same arrangement.

Does that make sense?

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I have no comment on increasing possibility of draw (could be a good custom rule), but introducing any kind of randomness into a perfect information game is a terrible idea +_+
I mean, people play this game precisely because there’s no randomness.

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I play abstract games in general, because there is no randomness. I enjoy skill based games to my uttermost core :smiling_face_with_three_hearts:

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I hadn’t given much thought as to how to properly choose an appropriate margin parameter, and I had imagined that it would be a debatable topic that would be much harder to settle than komi.

I like your suggestion that it could be statistically based on the ranking system somehow. I think there are many different ways to formally approach this, but let me outline some rough thoughts on one particular approach that I think seems to be in line with what you suggest.

First, let’s begin with considering games between players of equal rank. Also, for the sake of argument, let’s hypothetically assume that 7 is the theoretically correct komi that results in a fair game. With an integer komi of 7, draws are possible, but are still uncommon. For example, with two players of equal skill, they might only draw 2% of the time, and each win 49% of the time. Of course, these are not the actual statistics that would be seen in real games (I’m just guessing and using these as a hypothetical placeholder). Further, these statistics might also depend on the rank of the players. Maybe it’s a 2% draw rate between two 5 kyu players, while maybe two 5 dan players would yield a 5% draw rate (again, hypothetical numbers), since the stronger players would be more apt to play the correct moves that keeps a game balanced on the draw. For two perfect players, the draw rate should be 100% (if 7 is the correct value komi and we’re using rules that avoid “no result” outcomes).

So, with two equal strength players, adding a margin should increase the draw probability, but at what point should we set it? Maybe it should be wide enough such that a third of the games (between evenly matched opponents) should end in draws? Maybe half of the games should end in draws? Unlike komi, which can be hypothetically defined on the basis of perfect play, the appropriate value for the margin would have to determined based on some imperfect skill level of human play.

Building off of @Kosh’s suggestion:

It seems that one possible way to tune the komi margin would be to pick the value such that for two players with ratings that indicate a half rank difference in skill, the stronger of them is just as likely to win as draw. For example, maybe the stronger player would win (hypothetically) 38% of the time, draw 38% of the time, and lose 24% of the time. Thus, we would have:

  1. When two players of equal strength play each other, drawing would be the most likely outcome.
  2. When two players differing in one full rank play each other, the stronger play winning is the most likely outcome.
  3. The tipping point occurs when the players are only half a rank apart.

Philosophically, this is based on the idea that a draw should be evidence that two players are equally strong, and a win should be evidence that two players are at least one rank in skill apart.

However, a complication is that I believe that how the margin will impact outcome statistics will also depend on the absolute skill of the players, instead of just their relative skill difference.

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I don’t expect a lot of people to like the idea of random komi, which may even offend some purely on philosophical grounds. In fact, I don’t think I would really want to play with random komi myself. However, I’m just putting it out there as a wacky variant, since it was a natural extension (maybe some might say an “unnatural abomination”) to consider as a thought experiment after discussing margin komi.

Nonetheless, let me try to further justify my random komi abomination …

  • Playing with integer komi makes draws a possibility, but they are still quite rare, since there is no margin of error when playing out a drawn game. I would liken it to walking along a knife-edge ridge, with plunging cliffs on either-side. A one-point mistake by either player ruins the draw (unless another mistake is later made).
  • Margin komi makes draws more likely, since now there is some wiggle room for a wider path, allowing some mistakes to be made while preserving the draw. However, now the game is like a plateau, which still might take a path that is close to one of the edges, where one of the players cannot afford one-point mistakes to avoid falling off a cliff (losing from a drawn position).
  • Random komi (plus a margin), which I illustrate with an updated example in the first post, has the effect of turning the cliff edges of the plateau into sloping hills. There can still be room in middle for the game to certainly be a draw (e.g., scores of 6, 7, 8 are 100% draws), and the extremes will still be certain wins (e.g., scores > 12 are 100% black wins, and scores < 2 are 100% white wins), but in between, the outcome transitions gradually (in a probabilistic way). At worst, a one-point mistake might shift the outcome away from the player’s favor by a 20% chance.

I fully concede that, for some, margin/random komi might ruin the excitement of go. Yet still, some others might prefer the more peaceful play and outcomes that margin/random komi encourages.