RobertJasiek wrote:

Bill, you have shown the following two multiples:

You rely on the CGT definitions of local temperatures and mean. Can you explain the relation between the definitions and their application, please?

I'm not sure what you are asking.

**Quote:**

You show application for a local endgame with one player's simple follow-up and without kos. For such, application is straightforward. How about local endgames with more complicated follow-ups and without kos? Is the method exactly the same, except for needing more multiples?

You need a strategy at each decision point. So you end up with several comparisons.

**Quote:**

Can you write down your general method as a procedure applicable to all examples of a class?

Not sure what you are asking. It's a general method for comparing strategies and classifying positions, but more work needs to be done to verify means and temperatures. The method of multiples is inefficient.

**Quote:**

Do we know a priori how many multiples we need at least? How do we find out the minimal necessary number of multiples? (Why) is it always 4 for a local endgame with one player's simple follow-up and without ko?

The minimum is 2^d, where d is the depth of the tree.

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How would you define as a procedure the gote strategy and the sente strategy a) for a local endgame with one player's simple follow-up and without ko and b) for an arbitrary local endgame possibly with follow-ups and without ko?

Each decision point requires a different strategy, so the eventual strategy must say what to do at each node. Finding the best strategy for an arbitrary tree can take a lot of work.

**Quote:**

For a local endgame with both players' follow-ups, how to determine for whom to test a sente strategy? Must a procedure be more complicated by possibly having to test either player's gote strategy and either player's sente strategy?

Yes. In these cases we could eliminate a possible sente strategy for Black, but, OC, that is not always possible. Also, the final node is always a gote, so we don't have to test it for sente.

**Quote:**

Suppose we test one player's gote versus sente strategies with the resulting counts G versus S. Does the more favourable count for the starting player determine the correct strategy?

Each player must have made the same number of plays with each strategy, so that when you double the number of multiples the result will be the same ad infinitum. Also, you must have compared every possible strategy to find out which is correct. But you can compare strategies one by one.

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Is the count of one local endgame the resulting count of the more favourable strategy divided by the number of multiples?

If you have found the correct strategy, yes. But in the arbitrary case the correct strategy can be arbitrarily complex.

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Why is this so explained by the CGT definitions? If we determine a local sente, is the reverse sente gain S - G (with counts calculated in favour of the starting player)? Why is this so explained by the CGT definitions?

Thermography determines mean values and temperatures. These mean values must be the same (for non-ko games) as those found by the method of multiples, by the mean value theorem.

**Quote:**

Suppose we have a local endgame with follow-ups and without ko and have to test both players' gote versus sente strategies with the resulting counts Gb, Sb, Gw and Sw. How to determine the correct strategy, calculate the correct count, explain by the CGT definitions, possibly calculate a reverse sente gain and explain by CGT definitions?

For all cases, how to calculate the move value and explain it by CGT definitions?

In summary, your examples look convincing but how and why can they be generalised as methods?

I think your questions here can be answered by the fact that the method of multiples finds mean values, and temperatures can be derived from them. As for why generalize, why indeed? Thermography is more efficient.