It is currently Sat Apr 20, 2024 1:10 am

All times are UTC - 8 hours [ DST ]

Post new topic Reply to topic  [ 1 post ] 
Author Message
 Post subject: Timing according to Endgame Books
Post #1 Posted: Sat Jun 24, 2023 3:15 am 

Posts: 6146
Liked others: 0
Was liked: 788
In ... 71#p278371 Gérard TAILLE asks:

Assume a board P1 U P2 U E with E being an ideal environment. Assume mP1 > mP2 (move value of P1 > move value of P2)
Is it proved that a god play is to wait till T(E) = mP1 in order to play in local position P1?
If not, is it proved that it is correct on condition that no ko can occur in P1 and P2?

Usually, current theory presumes no kos now or later. Some theory assumes an ideal environment while other theory is a bit more flexible allowing any set of simple gotes without follow-ups in the environment. Combinatorial game theory about sentestrat, orthodoxy etc. has had rough approximations about +-T/2, which can be large.

My (partly Bill's) theory in Endgame 4 - Global Move Order and Endgame 5 - Mathematics for the late endgame is exact for some classes of positions. During the early endgame, my theory uses rather tight approximations 2D, where D is the ideal environment's drop. In practice, D is about 1/2 or 1 so my error remains +-1 or +-2 compared to perfect play (which you call god play).

However, such generalised theory is for one local endgame in an environment. You want to study two local endgames in an environment. Such generalised theory does not exist yet.

More specifically, some theorems presume a specific kind of local endgame, such as an arbitrary local gote with one or two simple follow-ups, or a local endgame that is an arbitrary local gote, ambiguous or local sente. Already each of some of their proofs took me up to three weeks and cover up to 11 printing pages in compressed annotation.

Depending on the theory for the early endgame, the conditions differ and include, e.g., one or two of these:

Always start in the environment.

Mgote ? T

Msente ? T1

Gote-sente-difference ? T

My late endgame theory is more sophisticated.

Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 1 post ] 

All times are UTC - 8 hours [ DST ]

Who is online

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group