RobertJasiek wrote:Bill, many thanks for your, as usual, very helpful explanations!
De nada.
Now, I realise that I must separate analysis and values of unchilled and chilled game carefully. MGE chilling is thrice as difficult as I feared: 1) understanding the unchilled game, 2) the chilled game and 3) how the findings for the chilled game provide information for the unchilled game.
Chilled go is a simplification of territory scoring, just as some forms of territory scoring, such as Spight or Lasker-Maas or Ikeda scoring may be regarded as simplifications of area scoring. And, with some exceptions, correct play in chilled go is also correct play by territory scoring, just as, with some exceptions, correct play by territory scoring is also correct play by area scoring. The exceptions, OC, have to do with ko.
So chilled go without kos is a simpler game than territory scoring, and that simplicity can help with analysis and with finding correct play. However, there are plays that are incorrect in chilled go but are still correct by territory scoring. Examples abound, even in pro play. Why not? They have read the game out, anyway. Chilled go also has something that territory go does not have, and that is a variety of infinitesimals. A dame is an infinitesimal, and you can construct others, but in modern territory go infinitesimals can be ignored. In chilled go they can be crucial to winning.
If you know CGT, you already know a good bit about infinitesimals, which you can immediately apply to chilled go. But most go players do not know CGT, and so chilling does not have that advantage for them. Go players do know that getting the last play can be important, but are generally clueless about how to go about doing that, except by reading the game out.
Now, in chilled go play stops once we reach a number, which may be a fraction. This may be useful to go players, because it means that, except in ko situations, once the global temperature drops below 1, they can generally stop reading and round the unchilled result up or down to the nearest integer, depending on who has the play. It is true that some positions with temperature below 1 are tricky, but that bridge can usually be crossed later.
Although I am awaiting your remaining answers, here is yet another question: you wrote that temperature theory was easier than CGT chilling but can linear algebra (no, not thermographs, which I perceive yet another layer of complication) representing temperature equations solve everything that MGE solves with chilling?
Well, naive temperature theory, which says to make the hottest play, is easier than working out unfamiliar infinitesimals, but is more prone to error. Any time you rely upon mean values you introduce the possibility of error. Finding the mean value and temperature of a game is, as I have noted, a form of defuzzification, with the temperature as the maximum error when there are no kos. So using algebra with mean values and temperatures may improve on the naive theory, but will still produce errors. Chilling makes getting exact solutions easier.
