Is a half point komi really fair?

[EdLee]

Proven or not, it does seem like a reasonable assumption.
Play wouldn't be very "perfect" if it led to a loss.

As already pointed out, yes, it would.

More examples:

- It may turn out that even with perfect play, Black will lose in chess. It could be a draw. We still don't know.

- This one our high school math teacher taught us, perhaps more of a warning, because he didn't provide a rigorous proof: as time goes to infinity, the probability of going bankrupt, if you choose to gamble non-stop, is 1.0. Therefore, the only way to "win" is not to play at all.

- Similar line at the end of WarGames.

"Perfect play" only means the best outcome for a player; it does not imply a particular result (win, draw, loss, or no result. )

So the original assumption is huge, and therefore worth questioning.

[hyperpape]

While the idea of a "perfect game" isn't agreed, one version of that idea would be that a game should neither favor the first player nor the second when played by ordinary humans (this can still be achieved in a game that doesn't have the potential for draws). A game like Chess might theoretically be a draw, but practically, it has a significant first player advantage. Among strong players, Black is playing for a draw, White is playing for a win.

Hex and Havannah seem to come close to achieving this based on swap. In Arimaa, one player gets the first move, but the second gains information from seeing the first player's setup.

[Polama]

Give the above statement, the 0.5 point added/subtracted to/from komi is indeed unfair. Because then one side, in spite of playing perfectly, might still lose the game - if the other side also plays perfectly.

I find this discussion very interesting, because I actually have the opposite opinion about fairness in komi. I don't care what perfect play results in: we're not going to play perfectly. I care about the general level of play as black and white in the go playing population.

Specifically, correct komi may very well turn out to be 12. It would be an unintuitive result, but mathematical extremes often are. Who can say where some singularly most effective series of moves will lead, precisely. Were it the case that komi is 12, should we mortals really play with that? Accept that the biggest statistical factor in an even game is nigiri, so that white isn't disadvantaged by the possibility that black achieves perfection in this game? We don't know correct komi so we can't consciously set it if we wanted to, we don't know if it would be fair for humans even if we did have it, so I don't see how 0.5 changes the fairness pragmatically.

[Elom]

When standard komi was first introduced, it was 1.5, then changed later to 2.5, 3.5, 4.5

That's news to me, do you have a source? Or are you just making things up?

http://senseis.xmp.net/?Komi
http://en.m.wikipedia.org/wiki/Komidashi

I was recalling from memory what I read quite a few months to a year ago or so, and mistakenly thought that it said "1.5" . I'm sorry, that was my error.

[Bantari]

In KO tournaments, it is necessary to eliminate draws.

Not to nitpick, but: No, it is not.
Example: Chess has both (frequent) draws and KO tournaments.

In KO tournaments it is "convenient" (for the organizers) to eliminate draws, but it is not necessary. Other provisions can always be made.

[moboy78]

I don't really understand why everyone wants komi to "be fair". Now, it seems to me that the majority of people in the go world agree that having the 0.5 is fine because it makes things easier for tournament sponsors. A lot of people here seem to be saying that if both players played perfectly, then that 0.5 is unfair and just arbitrarily awards the win the person komi happened to favor. Thing is, though, that it is obvious that the losing player didn't play perfectly, or else he/she would've won the match . It's not like the 0.5 was added to the score after the game was finished, both players always know about komi going into a game, and if they can't properly deal with komi then it's to bad for them if they lose.

[yoyoma]

I don't really understand why everyone wants komi to "be fair". Now, it seems to me that the majority of people in the go world agree that having the 0.5 is fine because it makes things easier for tournament sponsors. A lot of people here seem to be saying that if both players played perfectly, then that 0.5 is unfair and just arbitrarily awards the win the person komi happened to favor. Thing is, though, that it is obvious that the losing player didn't play perfectly, or else he/she would've won the match . It's not like the 0.5 was added to the score after the game was finished, both players always know about komi going into a game, and if they can't properly deal with komi then it's to bad for them if they lose.

Why is it obvious the loser didn't play perfectly? I played perfectly, but my opponent played perfectly also. I was behind on move 1 by 0.5 because of the komi, and I was behind by 0.5 at every step until they very end.

[moboy78]

Why is it obvious the loser didn't play perfectly? I played perfectly, but my opponent played perfectly also. I was behind on move 1 by 0.5 because of the komi, and I was behind by 0.5 at every step until they very end.

I fail to see how you can lose the game and still claim to have made perfect moves. That 0.5 is something you have to account for throughout the entire game and if you can't do that then you clearly didn't play good enough moves to win the game. If your moves can't even be called "good enough", then how can they be called perfect?

[oren]

Why is it obvious the loser didn't play perfectly? I played perfectly, but my opponent played perfectly also. I was behind on move 1 by 0.5 because of the komi, and I was behind by 0.5 at every step until they very end.

You lost nigiri.

[MagicMagor]

I fail to see how you can lose the game and still claim to have made perfect moves. That 0.5 is something you have to account for throughout the entire game and if you can't do that then you clearly didn't play good enough moves to win the game.

And what about the other (winning) player? Your reasoning doesn't hold up, because it would mean perfect play is impossible.
With 0.5 komi there is always a winner after the game, regardless of the moves played. If both player played perfect, that means they always made the (objectivly) best move possible, one player still looses because of komi.
By your reasoning, he had not played perfect, because he would have won otherwise, but he played the best moves possible, so there is no room for improvement there, so by definition he played perfect.
Also if the losing player had played, by your definition, perfect he would not have lost, so the other player would have lost, which means he would not have played perfect.
So by your definition it is impossible that both player play perfectly if the komi is 0.5 but it is possible if the komi is even? I'm sorry, but that doesn't sound very convincing.

Back to the actual question at hand. Obviously a komi with 0.5 can't be fair, assuming the actual game is fair. (That means there exist a number X so that a perfect game from both players with komi X will always result in jigo)
But komi is a pretty new concept in go (at least compared to the long history of the game itself) and was/is changed over time. Amateurs don't play perfectly so give or take 0.5 points from komi don't make the game fair or unfair. (Sure some games change winner if you change the komi by 0.5 points, but that isn't to say the komi is unfair) Having a x.5 komi is just a choice made, to eliminate draws.
I think the actual question isn't if it is fair or unfair but if we want draws or not. Some amateur tournaments like draws and mac-mahon tournaments can handle them without problems, so some tournaments already use 6 or 7 komi, without the half point.
But in the pro-scene with KO-tournaments or the best-of-x title games in japan, draws would make everything more complicated. Not impossible to handle, but it would result in extra work. Given how close most pro-games are currently i would assume without the 0.5 komi the chances of having draws is a lot higher than in the typical amateur tournament. And handling draws properly would either mean more games or use some other arbitary chosen tie-breaker, which may in itself also be unfair.

All in all, i think there are good reasons why the x.5 komi is accepted in the pro-scene.

[moboy78]

I fail to see how you can lose the game and still claim to have made perfect moves. That 0.5 is something you have to account for throughout the entire game and if you can't do that then you clearly didn't play good enough moves to win the game.

And what about the other (winning) player? Your reasoning doesn't hold up, because it would mean perfect play is impossible.
With 0.5 komi there is always a winner after the game, regardless of the moves played. If both player played perfect, that means they always made the (objectivly) best move possible, one player still looses because of komi.
By your reasoning, he had not played perfect, because he would have won otherwise, but he played the best moves possible, so there is no room for improvement there, so by definition he played perfect.
Also if the losing player had played, by your definition, perfect he would not have lost, so the other player would have lost, which means he would not have played perfect.
So by your definition it is impossible that both player play perfectly if the komi is 0.5 but it is possible if the komi is even? I'm sorry, but that doesn't sound very convincing.

I think you're misunderstanding what I'm saying. All I was trying to say in the post you quoted was that the loser of a go game where both players understood the value of komi beforehand (regardless of whether or not it is 0 or a non 0 value), then the loser didn't play perfect moves. The reason I'm saying that is because if there is a loser, than the moves the loser played simply weren't as good (i.e. didn't make as many points or didn't attack a group) or better than the moves his/her opponent played. If they were, then that person would have won the match.

I would also like to clarify that my argument (I think) would hold up regardless of whether or not perfect play is possible. You don't need to play perfectly to beat your opponent, you just need to play better moves then him. It is also hard with our current understanding of go to say that there is such a thing as perfect play. By the time endgame rolls around then there is definitely a way to play perfectly, but in the opening it is hard to say that there is such a thing as perfect play. Maybe in the future we will find out that perfect play is possible, but as things are right now I think it would be a bit to presumptuous of us to say that perfect play is possible. But, for the time being, I don't really think that playing perfectly matters for this discussion, since we don't even know if perfect play is possible.

I hope this clarified what it was I was trying to say.

[Sennahoj]

moboy78, saying that perfect play exists is not the same thing as saying that we can compute it: it is quite clear that perfect play exists. (For simplicity assume super ko so the number of possible go games is finite. Then look at the whole tree of all possible games, start at the final positions and just backtrack all the way up to the empty board, recording at each node one of the optimal moves.)

[MagicMagor]

The reason I'm saying that is because if there is a loser, than the moves the loser played simply weren't as good (i.e. didn't make as many points or didn't attack a group) or better than the moves his/her opponent played. If they were, then that person would have won the match.

I understood you, i think you didn't understand my post here.
Since we neither know the perfect komi value or the perfect play, this is all a hypothetical argument. But these are good to find logical flaws in arguments. And if i use this approach on your conclusions, then perfect play is impossible if the komi is x.5

The number of possible board situations is finite and so is the number of possible moves for each player with a given board position. With super ko it is ensured that each sequence of plays does end at some point.
The komi is a theoretic perfect komi x.
We assume that at every position there exist an optimal move for the current player, the move that maximizes his point potential and minimizes the point potential of the opponent. Both players use the same metric to find this best move.
This metric M is dependant on the komi-value x, which is what you stated. Komi has to be taken into account while playing. Depending on M and x, there is game-result R. So M is a function of x leading to a game-result R (Winning margin for black). This can be stated in the following form:
M(x) = R
Now we solve this for x, given R=0 (jigo). This x' is the theoretic perfect komi, under which perfect play results in jigo.

Now lets put x'.5 into the equation. Since the game is sure to end at some point there is a clear result R'. Because of the 0.5 in the komi this R' can not be 0, so there is a clear winner. There are two possibilities:
R < 0 - White wins. By your argument this means black did not play perfectly, that means didn't follow M during the game. But he did, so this is a clear violation of the beginning assumption (both players play perfectly), so this can not be the case.
R > 0 - Black wins. The same argument as for black can be now made for white. So we have clear contradiction. Assuming both players play perfectly and assuming there exist a perfect komi x' which leads to jigo under perfect play, a contradiction occurs by your argument (that loosing = not playing perfect).
I think there are three posibilities how we can solve this contradiction:
M - Can there be a single function, depending on komi, leading to an optimal game-result? Since, like Sennahoj said all games are finite and the number of moves are finite it is possible. It may not be computable, bit it exists. (An optimal game-result would here be the minimum R.)
x' - Does a perfect komi exist, that would lead to jigo under perfect play? I think this is debatable. Since we don't know the whole game-tree it might be possible that at some point a branch can be selected, after which no jigo exists. This however would mean the game is inherent unfair, regardless of the 0.5 komi. I don't like to assume this.
Losing under perfect play is possible if komi includes 0.5. Assuming this is much more natural for me. For one, komi is awarded to white to compensate the advantage of the first move. And since all points are counted as whole numbers i find it hard to see how a player can gain a 0.5 lead, if komi is a whole number. So the advantage of the first move would also have to be a whole number (the lead black gains by playing first).
There a situations where the average value of a move might be a fraction because it takes several moves to gain a single point, but the actual lead is still whole, because either the player gains that point or he doesn't, he can't gain 0.5 points.

So from my point of view - yes a .5-komi is unfair but only if we have arrived at the optimal x'.5 komi. I don't think we have and if we had we would see white winning most of the time in pro games - then it would probably adjusted to x', even if this would mean more work handling jigos in tournaments.

[Bantari]

We assume that at every position there exist an optimal move for the current player, the move that maximizes his point potential and minimizes the point potential of the opponent. Both players use the same metric to find this best move.
This metric M is dependant on the komi-value x, which is what you stated. Komi has to be taken into account while playing.

Not sure I understand this point. If it really means what I think it does, then I think I disagree. I am slightly confused here, heh...

Here is what I have an issue with:

1.
Assuming in every position an optimal play/move exists, which maximizes the player's score and/or minimizes the opponent's score (point potential?), I don't see why it is dependent on komi. Either a move is the largest on the board, or it is not. Either it reduces the most, or it does not. Either it results in the most points gain, or it does not. Komi of 6.5 or 7.5 does not change this. Komi can influence if the largest move is also a winning move, but it cannot change the fact that a move is the largest or not. Just like the current score does not determine the objective value of the move, it just influences if the largest move is also a winning move. Substitute "optimal" or "perfect" for "largest" and you will get my point.

2.
You are correct that in practice "Komi has to be taken into account while playing" - but this is precisely because we do not know the best play. Just like the current score has to be taken into account. It allows us to make strategic decisions of the sort "do I play safely" or "do I need to invade" or some such, based on the fact that we are behind or ahead in the game. It has really nothing to do with the fact if any given candidate move is objectively the most perfect/gainful or not.

Or am I too confused and misunderstand what you trying to say?

[Joelnelsonb]

I don't like the idea of the half point to begin with because it just seems unnatural. I mean, there are no "half-points" on the goban. Theoretically, a specific move might gain a fraction of a point, however, when it's all said and done, there are only complete points ( you can't surround a half of a point).

Furthermore, I never play by area rules so I'm not certain but if I've been told correctly, you still receive points for stones in seki. If this is true, is a draw under area scoring not impossible anyways? Because there are 361 points to be had on the board and if you receive points for dame, then the board can't be split 50-50 (under territory scoring, there may be an odd number of points in dame allowing for a 50-50 split). Thoughts?

Here's the rub (you don't have to read this if you don't appreciate abstract thought): Let's say that komi is unnecessary and that the game is jigo at best play on both sides (best play as defined by me: If God were to sit down at a goban and say "what is the most efficient way that I can place both black and white stones to end up in jigo", His moves would define best play). If this were the case, this means that black, with his first move, has only the potential to make a move that ultimately controls 50% of the board; no more. Now it's white's turn, and the very best move white can possibly make will ultimately lead to controlling the other 50% of the board. This will continue through to the end. Now, because were all humans here (no offense meant if that excludes anyone ), eventually we will make an "inferior" move. That is, a move that ultimately, at best play, leads to controlling less than 50% of the board. For simplicity, let's say 49%. At that moment, for the first time in the game, the opponent now has the opportunity to make a move that ultimately leads to controlling 51% of the board. This is the deep, underlying principle of all proper abstract strategy, zero-sum board games: Only once you're opponent makes a less than perfect move do you have an opportunity to make a winning move.
So, when we talk about komi, the question is: what percentage of the board does white need to start out with in order to achieve a 50-50 split at optimal play. Obviously, this will not be a whole number but will involve a fraction of a point. Therefore, how do you award this "perfect" komi to white without destroying the possibility of jigo and if there's no jigo, the game certainly cannot be called fair for the reasons already discussed. There in lays my question (which obviously has no practical applicability because none of us will ever play perfectly): but! for the sake of getting to think about Go as much a possible, from as many angles as possible , how can it be that in order to make the game fair, white needs a fraction of a point for komi, however, giving white this komi leaves the game un drawable and therefore unfair? It has perplexed me quite a bit as of late. Also, I realize that these are my personal theories; I'm not trying to "teach you guys a thing or two about Go".