This sounds great and it is so sad that such books are not available in English and not found easily in ordinary Japanese bookstores, AFA my small experience of trying to find and buy such books in Japan tells.



Now this again disappoints me because, from your earlier descriptions, I could not conclude that what was being done was close to equating influence and territory. It all sounded only like very rough symbolic approximations of the kind "A ponnuki is worth 30 points.".



Simply counting stones can be very useful for assessing efficiency or mobility. Equating territory requires more though. E.g., a Territory Efficiency is not a direct expression of territory. So, until I learn more, I am sceptical whether that book's technique is as imprecise and often wrong as the "Extend n+1 spaces from a wall n stones high." or is at least about as precise as the territory sum I form from 0-territory and 1-territory. Several years ago, I started from the proverb (because that was what I knew) and tried to make exceptions for aji in the wall but it merely became nasty without noteworthy extra use. For Joseki 1 Fundamentals, then I came up with the more useful principle for widths of standard extensions. Now I wonder whether the book you mention did present something general, often correct and still reasonably easily applicable.

My models of thickness in Joseki 2 Strategy do not have any problem with walls having useless stones or bending around corners because the models are independent of shape. Instead they depend on reading variations. Is your described book's method equally general and mighty?



It is easy to use such phrases but the crucial question is: Is the underlying theory good?



I need to be convinced. Was it wheels or rough immovable rocks?



Now we are getting closer, I hope. - So was it he to have invented miai counting? For sure, that is a very useful concept. - How, from your memory, did he try to equate thickness and territory?



I don't buy that. Maybe quite some pros don't want to apply theory like miai counting. However, then it is their fault of not using Sakauchi's (contribution to) theory to become stronger. If indeed Sakauchi did invent (some) such things, then he is responsible also for some improvement of those pros learning from his ideas.



While, in practice and in view of too short thinking times, 4.5 might be good enough and 4 and 11/16 more precise than one can calculate as a player during one's game, rounding to "almost 5" is the player's fault and he should improve his endgame. Similarly his ko dame abilities.



Apparently he was correct!? Maybe except for yet another level of precision a la Conway's and Guy's infinitesemals.



Sounds promising if he offered general principles for making such equations.



- I am well aware that my English is by far not as good as my German.
- People trying to correct my English have a tendency desire to replace precision of contents by fluency of ordinary style. This I cannot accept where I need to be precise. There precision takes priority over style.
- Proofreaders are saying that my English has improved up to a comment that it would be flawless. This I can't believe because I tend to be as critical as my average proofreader.
- Do you have general suggestions for improving my English other than demanding to lose precision?



I supposed so because I could not believe that Asians would have discovered as little as is reported in English. Concerning topics related to thickness - territory comparisons, what of the following from Joseki 2 Strategy was discovered before?

- territory efficiency
- mobility difference
- unsettled group average with successive local plays by one player
- estimating the value of early corner moves by means of formations created by one player's successive local plays
- territory equals influence in case of an equal number of played black and white stones
- value of an extension facing empty space on the outside
- assessing excess influence stones by one player's successive local plays
- n-territory

1. Has anyone ever sat down and looked at a representative sample of professional endgames looking for how often mathematical approaches would improve their play? I do not mean cases where the professionals make blunders, but where professional counting is imprecise enough to make a 1 point difference. It would still be interesting to know how often professional play deviates from mathematically correct play even where the values in question do not change the score by a point, but changing the final score by a point is obviously more important.

Such experiments would tell us a bit about how important these contributions are to go theory.

2. "Correct" is a tricky word in these contexts. There need be nothing incorrect about an estimate of "a bit more than six", it only lacks in precision. We should also distinguish between "factually incorrect" and "a bad method." Even a factually incorrect estimate may arise from the best method to use for reasons of time-pressure, diminishing returns for learning a new method, etc.

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Occupy Babel!

Interesting question. I do not think though that mathematically precise endgame can be done earlier than the very late endgame. before we need approximations for the mathematically touched calculations, which might assess a precise local value but cannot always fit the global collection of values together yet. With that restriction, your question is still very valid, of course.

Another question is about learning and teaching endgame below top pro level. There, AFA I have heard, the (basic) theory helps those using it. I think though that almost nobody uses infinitesemals... yet. The majority of endgame books I have seen were imprecise to wrong with the fractions. It is ok (for me) if they don't become more precise than 1/2 or 1/3 but they shouldn't just round everything to natural numbers or calculate +1/2 when -1/2 is correct.