Optimal play and Komi
Optimal play is play where both players play the best move available all the time.
Also some (like Willemien) have the idea that optimal play should lead to a jigo score. And that the komi should be so that this becomes true. (so the relation is reversed not komi defines optimal play but optimal play defines the komi)
In normal Go on a 19x19 Goban the problem is that it is unknown what optimal play is and it will probably stay that way in the near future. Therefore komi cannot be defined in this way. (the whole game needs to be played optimal and we just cannot prove that a first move at the 3-4 point is better/equal/worse than a move at the 3-5 point)
On smaller boards like 7x7 it can be provisionally done. (see 7x7 best play) and therefore it can be (provisionally) proved the komi for 7x7 should be 9.
In most rulesets the Komi is not a natural number but something with a fraction just so that the result never can be jigo. Is this the right theoretical perspective?
Willemien's motivation against a fractional komi is the following: If you lose when you play your optimal you will lose. you will lose anyway. So what is good about optimal play?
Herman: Yes, I agree. The good thing about fractional komi is that it does not allow jigo. The bad thing about fractional komi is that it does not allow jigo, even when both players play perfectly :-)
Jay?: Possibly this is not yet an issue.
Slarty: The "best move" was not defined. Presumably it means a move that maximizes the final score difference (B-W for black, W-B for white) provided that the opponent responds with a best move.
Then if you lose despite optimal play, you have at least achieved the smallest loss, even though on that day komi would be obviously broken. One thing to be said for fractional komi, before that day: it pushes players to play for the win and perhaps deviate from optimal play in interesting ways.
Anonymous: I still have my doubts about this.
To define komi in terms of optimal play, we need to define optimal play independent of komi. The idea described above is that 'best' means best final point difference. This would indeed define optimal play independent of komi, except for cycles.
Some rules say a cycle is no result (mushoubu), which is different from a tie (jigo). What do we do with those? Even where it is ruled jigo, suppose at one point, one player can force a cycle, and therefore jigo. If they are otherwise winning, optimal play is not to force a cycle. If they are otherwise losing, optimal play is to force a cycle. But whether they are winning or losing will depend on komi. So optimal play still depends on komi.
It's said that small boards have already been solved anyway. But perhaps they're just too small to set up the forced cycles that might occur with optimal play on larger boards.
billyswong: Since we can use super ko rule to prohibit cycles, I don't see much reason to think for cycles for the optimal play. If anyone want to argue that super ko rule aren't used commonly in many tournaments today nor games in older days, "optimal play", as I understand, is about looking for the safest move in the eye of God, which is not necessarily the best play for most actual game play in modern or past either.
If optimal play is to be defined as the best play to maximize the chance of winning the game, then optimal play will be either opponent dependent, or exist only for one colour. In the days of jigo counted as a draw, games were played in 0 komi. Optimal play for black can always win and not jigo a zero komi game. (Unless optimal play for white can force black into choosing either a rule-allowed cycle or facing loss, which sounds fairly unlikely.) In the modern days games are always specified a fractional komi or assign jigo as a win to one of the colours. The best play for the disadvantaged colour in the eye of God, will need to predict what level of mistakes his opponent will make and deviate from the safest play correspondingly.