It’s a little mysterious to me why Robert’s calculation is met with such snarkiness, but thinking back, that's how Bantari communicates almost always. Clearly Robert is not claiming to have solved go, so the method cannot answer every question --- rather it's a simple heuristic, which assigns a number to a particular type of local situation. (So in this sense it’s probably similar to the influence calculation Bill alluded to --- I mean similar in spirit, they might be measuring different things.)

I personally find Robert’s proposed measure quite natural, but of course it’s coarse grained (the proposed "reasonable" range of 1.5 to 3.5 is pretty wide). So it’s unlikely to resolve questions about details, as Knotwilg points out:

There are various different kinds josekis; not all of them simply share territory versus influence. Therefore, josekis without one-sided other (dis)advantages can have a value range 1.5 to 3.5. Values outside this range must be compensated by a clear other advantage for the player having the disadvantageous value. E.g., a value around 4 to 4.5 can occur if a player makes much territory in the corner but the opponent prevents his easy access to the adjacent sides; there are a couple of such josekis.

Without a clear local explanation for a player's value advantage, a locally one-sided result can still be acceptable in the case of particularly fitting global circumstances for the opponent.

Robert: Thank you for the detailed reply, but you still haven't convinced me. In themselves the points you make are reasonable. Part of the problem is that you consistently change the other person's context to stress your own.

For example, yes, your system can be said to build up in blocks from a base. But it's still circular in that it depends on pro assessments via a feedback loop. If by some fluke pro thinking changed, you would have to change your system. There is nothing that I see in your system that would enable you to say to a pro, you are wrong because... I say "by some fluke", but if we consider the changes in go in the 20th century, we can say that there has been a gradual change in thinking in favour of central thickness, as players have got used to using it better. This has already changed the significance of many joseki evaluations. Current changes in go thinking seem likely to change evaluations further. I expect pros will rely on their own methods, not yours, to make them.

Secondly, yes, your system can be applied quickly on a single position even by a human, but this is practical only in leisurely home study. In a game context, if an opponent plays a new move, you have to look at several, maybe many, lines and evaluate each one independently. I don't believe your system can cope with that. Furthermore, pros do cope with this situation often and seem more often than not to come up with a good reply, so clearly they do have a system of their own that works.

The problem with applying numbers can be illustrated by looking at the stock market. Many numerical systems are touted - the Japanese started the ball rolling a very long time ago with their candlestick theory - but isn't it strange how all these tipster companies ask you to let them use your money instead of their own.

Essentially, complex things like go and stocks remain impervious to numbers and are best studied in a hermeneutic way. (Or best of all, get inside information - in go terms, pro advice). And in that context, the old chestnut from medicine applies, in which new students are told by the professor that half of all the "science" they will learn in the next few years will turn out to be wrong. He then adds: "The only problem is that we don't yet know which half."

For the creation of my method, I have used mainly dictionary / game database josekis as input to detect the existing joseki value types and calibrate the bounds ca. 1.5 and ca. 3.5. Now, the method does not need fresh, circular input. However, it is possible to view the bounds and the first move value as parameters, which can be re-evaluated from time to time. I think this is all that needs observation. If you want to include this process of re-evaluation in future, you can perceive some circularity but I perceive it as possibly repeated input with possibly adjusted parameters.

In a game context with various candidate joseki-like sequences, I can apply my method easily. It is possible that you can't do it yet; I recommend regular practice.

I dislike the stock market analogy because it is chaotical. Go is a perfect information game. This has a very different behaviour: the same positions always have the same best next moves (if one is able to understand which they are). In a stock market, the same initial situation can result in different continued market developments.

You think you know me?

As a matter of fact, my posts alternate freely between the scathing wit underlining thoughtless remarks from others and wise informative style presenting well though-out arguments on my part, virtually dripping with wisdom - if you only open your eyes wide enough to see it. Heh...

As for Robert, we do have a long history, and the hatchet not always can stay buried, no matter how I try. My failure, doubtless, so I concede this point to you.

But ultimately, I really have a very high respect for him and his work, regardless on how I need him now and then, and I think he knows it.

These days, the people I don't respect I don't talk to - and when you search through my posts you might notice a few prominent names I stopped responding to a long time ago, no matter what weird stuff they write.

Bottom line: I consdier RJ one of the most valuable poster on this forum, and MVP if you will, one of maybe 3 or 4 people I consider to be such MVPs. And I have said so both publicly and personally to him in the past, not only on this forum.

Hope this clears the situation for you.

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- Bantari
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WARNING: This post might contain Opinions!!

I think you're giving Robert both too little and too much credit.

The calculation he gives implies that for "joseki" positions the ratio of territory to "influence stones" is 1.5-3.5. Setting aside the ratio for a moment, he is looking at the relative efficiency of the player's stones. I've certainly seen pro commentaries indicating that efficiency is of paramount concern when pros evaluate a new sequence. He's also noting empirically that an "influence stone" is worth 2-3 points of cash territory. Again, it sounds plausible.

The method looks fine as far as it goes, but the problem is identifying those influence stones. That's largely a matter of opinion, at which point you have to ask why bother with the mathematics if it only substitutes opinions at one level with opinions at another?

I think the method seems most reasonable for strongish kyu players, who will have demonstrably inefficient stones that can be identified during a post-game analysis. It's just another tool in the kit, although whether it's a Swiss army knife or a specialty tool remains to be seen.

It's more than plausible. It's been backed up by at least a couple of pros, although a little indirectly. Writers like Abe Yoshiteru have usually been concerned with measuring thickness alone in the opening or early middle game, and not just with josekis, and use methods they often describe as wielding a sword. In their calculations an extension from the wall is normally assumed (this is the sword sweep), and this typically heightens the value of each stone in the wall to closer to 4 (also increasing as the size of the wall increases, which seems reasonable). But so long as an extension stone is eventually possible, its absence can be factored in and the value of the wall reduced accordingly to more like 3 per stone. They also make remarks about which wall stones are valid: bumps, gaps and second-line stones are typically discounted. This method works also round corners. There are also refinements such as very big walls needing not just their "magic sword" extension but also a "magic dirk" extension (the analogy used is the samurai's two swords).

In other words, putting a numerical value on influence is not new. But I have never been able to establish that pros use it themselves. I half-suspect it's a device they've come up with only to teach amateurs. But then again, surely they must assess influence, and it may seem there's not much else to go on apart from a numerical estimate. The only alternative I've deduced is that they simply assess the efficiency of each play (a kind of tewari-lite), and FWIW I've seen far more evidence of that than for using numbers. However, if they do decide a move is inefficient, they quite often say it loses 1 point or 2 points, or whatever, so in that sense numbers come into it.

pwaldron, I have not repeated the full method here but only given hints that it includes more cases. A joseki belongs to one of the value types 'ideal equaly' (stone difference, territory count T and influence stone difference I are all 0; this triple indicates a joseki; dividing T by I is unnecessary and would not work), 'small values', 'ordinary sharing of territory and influence' (with ratio values from 1.5 to 3.5), 'territory disadvantage combined with other advantage' (two cases, of which one is a ratio <1.5, the other is of course I = 0), 'territory advantage combined with other disadvantage' (ratio >3.5).

Identified are those influence stones with significant outside influence. The outside is given clearly by perception. Stones with significant outside influence are, with a bit of experience of thinking about these details, reasonably easily identified.
- In the simplest case, they are the outside live stones.
- If influence is generated by thickness so that this generation is given by a shape of which influence-generating stones are not situated on the outside but have clear impact on the outside, then all such essential, non-superfluous stones are counted (consider, e.g., a thick small nadare shape)
- Ignore those influence stones whose influence is dominated by other same-colour influence stones. E.g., first and second line stones of a high wall.
- Ignore those influence stones being "covered" by strong opposing stones.
I will work out and publish this aspect of positional judgement more carefully later.

It can sometimes happen that one is not sure whether one wants to perceive a stone as "half" an influence stones. Round to either adjacent integer. The method tolerates such approximation. If the result is near to a bound of the standard ratio range, it does not matter because the bounds are circa-values. Of course, nevertheless one may look for compensating other strategic advantages.