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Some say the value of the komi has a relationship with the value of the first move.
Some don't see it this way (or just don't understand it).
This page is to facilitate this discussion on the relationship between value of the first move and komi.
Feel free to add, but please:
The starting points are taken from different pages on sensei's library
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Consider a game where Black passes as first move. So White plays first, and the game starts just as if White were Black, with the difference that White still has the komi advantage. This can be interpreted as if White played a game with reversed komi; the advantage he has is 2*komi (the komi he has + the komi that Black does not have)
We can assume that by passing, Black lost an amount of points equal to the value of the first move, which is about 14 points according to professionals.[7]
It is then normal that the value of komi be equal to half the value of a move in the opening.
Continuing the theory : I'm 6k, so I think the average value of my moves is about 1 point behind that of professionals’ moves (15 stones is about 200 points, and a game is about 200 moves long). Well then I guess the komi that professionals set is half a point too much for me ! Well I don't know about you, but in that case, I prefer playing as White, with a decisive advantage of half a point !
Velobici: IMHO its not that amateurs play moves that are 1 point (or N points) less efficient than professionals. Consequently, over 200 moves end up 200 points amateurs are 200 points behind. Rather, amateurs play some moves that are professional level and some that are just horrible. The just horrible moves (errors) are the ones that mark us as amateurs. By reducing the magnitude of our errors, we improve...still we make moves that are somewhat less horrible in the midst of moves that are professional level. Once we stop making horrible moves, all our moves are professional level and we play like Jie Li.
That is obviously correct as such, but you can still say that statistically 6k loses about 1 point per move, so the calculation above makes sense. Theoretically he may not lose any points for the first move (say, he plays 3-4), but we could think of the statistical one point loss coming from the fact that he doesn't know how to use the stone properly later in the game. Still continuing the thought you could say that if correct komi for 9d is 7, then for 30k it would be about 6. Which implies that in practise the same komi is actually good enough for players of all strengths. Of course, statistics from games would be a better way to prove this.
If someone thinks that fair komi is exactly the same for all players, then it may be interesting to note that, for nearly random players (who know only enough not to fill their own eyes), fair komi is actually very close to 0. This is easy enough to test with a computer program.
It is generally considered that 17 stones is a fair handicap between two equal players where black can kill all white stones. This indicates each stone is worth 361/17 or about 21 points so that komi would be 10.5. It is to be admitted that this is not proof for 1 stone, but it is indicative.
anonymous: You're trying to prove 0 equals 1 (Komi = Komi + 1) ?
So probably 0 doesn't equal 1 after all.
PlatinumDragon: Suppose to be here, but I made one huge post earlier.
anonymous: You state "Komi = First move + 0.5" according to the rules. I think "Komi = First-Move / 2 + 0.5" however.
Normally both players play biggest moves, going to smaller moves to the end of the game. The game stops if the value of the move has decreased to zero. (Of course sente moves can be played in between by both players, so the value of the moves itself will not be an decreasing line). As the number of moves is greater than the value of the first (and biggest) move, there are a lot of moves with the same value. The number of moves is either odd or even. If it is odd, the black player will get the last move of the series (of same value moves) and White has to play a move worth one point less. On average, half the series will have an odd number of moves, so White loses one point for every second series. The komi value will correct this. As the number of series equals the value of the first move, the komi should be Value-First-Move divided by 2.
edit: forget the above. If white starts a lower value series, Black will be the one losing a point going to start the next level next. So on average both players will loose the same amount of points by going to lower value moves series.
I still don't agree with PlatinumDragon, as I think the second move has roughly the value value as the first move. Maybe the komi isn't just related to some points directly. Black has the chance to start to game the way he likes, and white gets some points in return. The result will be a game where both players do have about 50% chance to win.
PlatinumDragon: Komi should be first move - second move, to give white the compensation for going second. If first move = second move, komi = 0 because going first has no advantage, so without an advantage, there does not need any compensation. There is already a 50/50 chance if first move = second move, so we don't need komi.
anonymous: I think the values of the first two moves are equal. Things start to differ once more stones are played, subtly influencing each other. So komi cannot be value first move - value second move.
PlatinumDragon: The best way to put it is
Actually, if you make a rule that Black must pass on the 3rd move, White might take advantage on the 2nd move by making a contact play to black's 1 stone, then capitalizing on the 4th stone. (meaning White would win by more than komi) ~srn347
(in short) Komi between weaker opponents sdk, ddk should be lower, they play not the best move so a high komi gives White an easier game.
PlatinumDragon: In my opinion, you will not need komi until players can play consistent moves. Consistent moves gives consistent results. In such way, there is a different komi for each opponent. As you get stronger, komi will move towards true komi eventually. Rock/Paper/Scissors occurs when the players' moves are consistent with the strategy but not consistent with the point value i.e. the moves are not consistent.
PlatinumDragon: The value of first move is 361 (area), 360 (territory) because if there is no more play, then the game is scored and you have the whole board. The value of a move changes when more moves are added, and the average value (end game value) of a move is what books use even though the immediate value of a move is what players want to know, as the immediate value affects the player's choice more usually. It is logical to say the first move is the whole board because this is its immediate value. Players should therefore see both the immediate value and the dynamic values of a move. Not seeing the dynamic values of a move means that you are not reading, but know that each turn you read ahead gives you one moku advantage or 50 ELO points.
anonymous: With an empty board, all points are dame and White is ahead by the komi. So the value of the first move should be 180. Normally both players put a stone in a corner and the complete layout is balanced again. So the value of the second move will be 180 too.
symplicity: On the contrary, when playing a real game, people essentially never want to know the "immediate" value of the move, as you defined it - the score difference that would result if the game were stopped immediately and scored (never mind the ambiguity of scoring a non-terminal position!). This notion of value has pretty much no impact on a player's choice of move. You are free to define the "value" of a move however you like, and people have done so. This is why there are two major notions of "value" floating around, deiri and miai. However, the test of such a definition is its utility in play and positional analysis. The idea of an "immediate value" is not useful for either purpose.
PlatinumDragon: It seems that the average or final value (similar to miai value) and the opportunity cost (similar to deiri value) are closer values that players look for as players would want to look for the value when scoring will occur. How much something is worth at the end is important to the decision making. The immediate value is not a dynamic value and therefore cannot be useful for positional analysis, or finding its usage. Only dynamic values are possible. Miai and Deiri values are finite dynamic values that can only look at local areas, but are more effective in positional analysis. If there is a better dynamic value, then it will be something related with deeper reading.
PlatinumDragon: It is more logical to say that the value of all moves added together has net total of 361 (Area) or less (Territory). The value of midgame moves are about 30 moku, significantly larger than first move, but players don't complain about it as much. The value of the dame moves is one (Area), zero (Territory). The average value increases towards 40 or so before they decrease. The value of a move changes with the addition of more moves, so the only value you can get is its average value and not the impact it has during the occurrence of the move which is usually many times larger.
[7] Bill disputes this, see his note on the main page: Komi#7.