Is a half point komi really fair?

[Boidhre]

A question though, do you think it'd be a good idea to set komi according to perfect play?

[lava12005]

Regarding the 'perfect komi':

Taking the definition of Perfect Play from Wikipedia:
In game theory, perfect play is the behavior or strategy of a player that leads to the best possible outcome for that player regardless of the response by the opponent.

Regardless of the komi, the perfect play starting from a certain board position will always be the same.
Even when the perfect play from that position always leads to a losing game the idea is to minimize the loses (there can be more than 1 move as a perfect move that will lead to the same final point).
This is because the komi is only translating the final outcome uniformly.

If we assume all games has finite moves due to whatever reason (such as superko, no pass, etc to simplify) then the total number of possible games becomes finite.
Now by 'backward chaining' from a certain final position we can get the best outcome (say maximizing black point - white point for black) and therefore the best move from 1 move before the end of game.
Repeating the process for all final position one can get the best outcome from the starting of the game. (this is valid from finite tree)
When this outcome say is 10 (black points - white points) then you get the 'perfect komi' which is always an integer.
Whereby with this value of komi and 2 perfect players they will always force the game to draw. (it can be more than 1 possible games that can lead to this draw I suppose)

A question though, do you think it'd be a good idea to set komi according to perfect play?

Hence, comes the more philosophical question as Boidhre asked.
If the 'perfect komi' of above is used then the game somehow becomes fair to the perfect players.
But does this needs to be used? or is this the same fair criteria to be used?
Is this the value that people are trying to guess using the 'statistical data'?

The second thought is that the statistical data might be pretty far from 'perfect komi' (as previously noted that things can go pretty weird in extreme math)
If we limit the search through statistical komi where all the games is taken from player at best of 10k then the value itself might change (due to more chaotic game)
And hence the komi to be used between two 10k players playing might need to be bigger to be 'fair'. (50% chance of winning at least from the statistics of all games ever been played at this level)

But anyway 0.5 will not really change the result especially for a SDK like me, so no worry on fairness..
Apologize for my craziness..

[Boidhre]

If we limit the search through statistical komi where all the games is taken from player at best of 10k then the value itself might change (due to more chaotic game)
And hence the komi to be used between two 10k players playing might need to be bigger to be 'fair'. (50% chance of winning at least from the statistics of all games ever been played at this level)

I would have said smaller, komi presumes you know how to use the advantage of first move and more chaos and big losses makes the value of komi less important if they're equally distributed between black and white, I think the weaker the players are the less it affects game result who goes first. I'd love to see data on this though.

[wineandgolover]

Y'all think too much.

For the time being perfect play is unknowable. I am perfectly content with setting Komi at a level that results in a 50% win level with good, but not perfect play.

If 5.5 yielded a 55% win ratio for black, then it is too low. If 6.5 yielded a 55% win ratio for white, then I'd be content setting at 6.0.

If a new fuseki was discovered that gave black a twelve point advantage, then adjust Komi until that fuseki is refuted.

Sometimes good enough is good enough. The quest for perfection can be our undoing.

[Mike Novack]

"no half point in go"

I think that this is simply a misunderstanding of the purpose of the half point. It is simply to prevent a tie result. Perhaps it would help if you considered a komi of 6.5 is equivalent to a komi of 6 plus the rule "in case of tie, white wins". Making the komi itself 6.5 eliminates the need for the additional rule. Similarly, in even games, the komi of half a point is simply a rule "in case of tie, white wins". Makes it simpler, just "the player with the most points (including komi) wins". No need for a special rule "in case of a tie count ......."

[Uberdude]

If you don't like half points how about playing with komi equal to 2π, that's a nice round number.

[Bill Spight]

Actually, there are half points in go. That is, positions that really should count as X + 0.5 points by territory scoring. A move in the position is worth less than filling a dame; in fact, it loses 1/2 point. For instance, in one net play White can move to a position worth 1 point for Black, while in one net play Black can move to a position worth 0. The theoretical value of that position is 1/2 point for Black.

I know that such positions exist, because I have constructed them. Some may have occurred in actual play without being noticed.

[Bill Spight]

If you don't like half points how about playing with komi equal to 2π, that's a nice round number.

Come on! π are square.

[Mike Novack]

Actually, there are half points in go. That is, positions that really should count as X + 0.5 points by territory scoring. A move in the position is worth less than filling a dame; in fact, it loses 1/2 point.......

But that is something different, the "value" of a position. Or the "quantum" points of go. Before the position is played out it can indeed have a fractional value. If we ask "what is the value of some end game position" we have a value if black gets to make the first move and a (different) value if white gets to make the move but at this point we do not know who will have sente when remaining endgame points are down to the size that might attract play here. So we judge the position to be X points with X possibly a fractional value.

But at the time the game is over and being scored, that uncertainty has been resolved, one way or the other, won't be a fraction of a point.

[Bill Spight]

Actually, there are half points in go. That is, positions that really should count as X + 0.5 points by territory scoring. A move in the position is worth less than filling a dame; in fact, it loses 1/2 point.......

But that is something different, the "value" of a position. Or the "quantum" points of go. Before the position is played out it can indeed have a fractional value. If we ask "what is the value of some end game position" we have a value if black gets to make the first move and a (different) value if white gets to make the move but at this point we do not know who will have sente when remaining endgame points are down to the size that might attract play here. So we judge the position to be X points with X possibly a fractional value.

But at the time the game is over and being scored, that uncertainty has been resolved, one way or the other, won't be a fraction of a point.

The proper time, in theory, to score a game at territory scoring is when the last dame has been filled and there are no plays that gain points. But what if a play loses 1/2 point for each player? Sure, you can have rules that award an integer score to the position. The J89 rules do. But should they?

[Joelnelsonb]

I'm not quite understanding how you claim that fraction points exist. To reiterate, if you use 20 stones to surround 10 points of territory, one way to say it is that each move was worth a half of a point, another way would be to say that each move shared the weight of 10 points. At any rate, by the time you score the board, you will never count up a fraction of a point. But I don't think that's what you meant anyways.

[Bill Spight]

I'm not quite understanding how you claim that fraction points exist. To reiterate, if you use 20 stones to surround 10 points of territory, one way to say it is that each move was worth a half of a point, another way would be to say that each move shared the weight of 10 points. At any rate, by the time you score the board, you will never count up a fraction of a point. But I don't think that's what you meant anyways.

What I mean is this. We may have a board position where neither player wishes to play using territory scoring, because a play makes a loss. That is the normal place to stop play and score the game. The traditional scoring method is to count territory. But there is another way, which we can use to settle disputes, and that is to play an encore in which the player who passes hands over a pass stone as a prisoner and each player makes the same number of plays or passes. Since filling in your own territory costs one point, as does playing a stone inside your opponent's territory, this method preserves integer scores. (Not that it preserves Japanese or Korean scores, but there are rules under which it does preserve scores.)

But there are positions where neither player wishes to play using territory scoring, because a play makes a loss, but where each player wishes to play in the encore described above. The reason is that the loss by territory scoring of making a play is less than 1 point. A play is worth less than filling a dame but more than filling territory. Therefore it loses less than 1 point of territory, and the territory score should have a fractional point.

Here is an example of such a position.

(;GM[1]SZ[19]CA[ISO8859-1]FF[4]AP[GOWrite:2.3.46]ST[2]PB[ ]C[*** Assuming no other ko threats on the board and that the outer stones are alive, this corner combination has a theoretical value of 1/2 for White.

Let us evaluate this position using play with pass stones, so that the player who plays first does not play last.]AW[ba][ca][da][cb][ad][bd][cd][dd][ed][fd][fc][fb][fa][qa][qb][pb][ob][oc][od][rc][qd][rd][sd][qe][re][rf][sf]GN[ ]PW[ ]FG[259:]AB[ea][eb][ec][dc][cc][bc][bb][ac][ra][rb][sb][qc][pc][pd][pe][pf][qf][qg][rg][sg]PM[2]
(
;W[aa]
;C[*** Black passes, handing over a pass stone, and then the players agree to stop play. Result\: 1 point for White.]B[tt]
)
(
;B[aa]
;W[ab]
;B[sc]
;W[db]
;B[se]
;TW[aa][ac:ec][bb][ea:eb]TB[qd:sd][qe:re][rc][rf:sf][sa]C[*** White passes, handing over a pass stone, and then the players agree to stop play.

White is 1 point ahead on the board, so with the pass stone the result is 0]W[tt]
)

)

In the encore each player gains 1/2 point on average by playing first so that the value of the starting position is 1/2 point for White. And that is the theoretical territory score for that position.

[Unusedname]

I just skimmed the thread and I don't think anyone said it but I'm pretty sure the answer is:

Is black going first really fair?

[yoyoma]

I was also confused by Bill's claim that half points exist, but now I realize that it's his opinion on what the rules should be, not what they actually are. Unless you use Bill's rules (button go).

[Bill Spight]

I was also confused by Bill's claim that half points exist, but now I realize that it's his opinion on what the rules should be, not what they actually are. Unless you use Bill's rules (button go).

It's not as strong a claim as that. If the rules do not allow fractional scores, that's that. But once the idea of button go was around, then I constructed a button on the board.

Suppose that there was a button such that if White took it it would subtract one point from his score, but if Black took it it would leave his score unchanged, and that a player could not pass before the button was taken. Such a button would be worth 1/2 point to Black. That button would be miai with the position shown. That justifies a theoretical value of 1/2 point for White for that position. You can make a similar demonstration of the value of Three Points without Capturing.