Some things I think could still be improved or introduced:
I hope nobody feels restricted in editing the article after this rewrite, just because of the work I put in it :-)
It is only a first attempt, and there are many things wrong with it, many area's in which it could be approved. SL is a community effort, so please feel free to completely overhaul, split, merge and rewrite as you see fit!
I will be gone for the weekend, with little or no internet access, so I won't be able to contribute to discussions or answer questions.
+ A fairly effective approach, is to play moves in the order given below: + * If there are endgame moves that are double sente (sente for both), play those. Those with the largest follow up first. + * Otherwise, if there are endgame moves that are sente (for you), play those. Those with the largest follow up first.
* Otherwise, if there are endgame moves that are reverse sente (sente for the opponent) play those. Largest swing value first * Otherwise, if there are endgame moves that are gote (for both), play those. Largest swing value first
now it pretty much resembles my approach to the endgame (reverse sente are a bit underestimated here) so i removed the naive attribute as well. :) however i broke the flow of the text... but i feel a bit uneasy to introduce "a still somewhat naive" approach if all necessary concepts for a better one are already introduced. what do you say?
"Well, for double sente moves we're dividing by zero, which is a strange thing to do, according to mathematics. Effectively we can say that because of the division by zero, the value of a double sente move is infinite. So always play double sente moves immediately!"
Even if I now finally understood the local tally and miai counting (i hope): I found this argument very misleading in Tomoko Ogawa and James Davies "The Endgame" already. If the value is infinite how can i still lose the game?
"If the value is infinite how can i still lose the game?"
You are right. The true answer is that there is no such thing as double sente in terms of value. There is only double sente in the sense that a play by either player leaves a reply that is bigger or more urgent than anything else on the board. Different senses of sente. :)
Because the value of an endgame play using such methods does not represent an actual number of points, but a value which allows ordering the moves.
Instead of dividing the miai value by the local tally, one could multiply them by 60 first, then divide by the local tally, because you like to compare whole numbers. With this system, a 7 point sente move is worth 420 points. How could you lose the game if you get such a move? Because it is not a real value.
If the value of an endgame ko is half a point, then why do games (without komi) always end in a whole number score? And so on ...
Dieter: I tend to forget signing my comments.
Hi Dieter, I try to recognize your IP in future :)
I don't get it. The mathematical point here is division by zero. You don't change this by multiplying with any number before. And i feel like the miai counting wants to be more than just a heuristic to decide the move sequence usually but ends up not being applicable to double sente moves.
The infinite value of double sente moves just indicates that this is a move not to miss. Both players will (or are very likely to) lose the game if they do not answer this move. Whatever system you use to evaluate them, they will be in front. That notion is quite well represented by an infinite value. If we multiply all values by 60, the DS remains at infinity.
The actual value of these moves can of course never be infinity. It suffices to allow a follow-up (so that the tally > 0) which ends up in a big gain for the allowed party. This variation cannot yield infinity, yet it may be big enough to reassure that it should not be allowed.
There is an actual value to such moves: the swing value. But how soon should it be played? Immediately, regardless the swing value and regardless what other move is around. The value indicating its importance is infinite.
The reason for the whole mutual damage chapter - and putting it in the beginning - is that this is simply not true. Toshiro Kageyama makes his awesome insightful example of following the opponent around exactly with this very kind of double sente moves. Don't answer a double sente (instantly) threatening only to reduce your territory by 20 points, if you have a double sente threatening to kill a group worth more / devastating a bigger territory.
We are all aware of this. But this kind of "always answer a double sente or you lose the game" is exactly what makes people follow other people around. I guess it is well enough balanced by mentioning mutual damage half a dozen times. But I feel this is important, it is always about the follow-up.
If the value of an endgame ko is half a point, then why do games (without komi) always end in a whole number score?
That is the nature of the go board. It is also the nature of scoring. Given the seki situation, scores by area scoring differ by at least two points, while scores by territory scoring differ by at least one point.
We count the marked region as 1/2 point for Black, even though in the end the local score in it will be 1 point for Black or none.