Zwischenzugzwang wrote on 05/19/12 at 14:15:12:


It will be available within the next several weeks.  When it is, it will speak for itself.

With a repertoire that is at all deep, the corresponding tree diagram is simply too big to be useful.  I'm working with tree data for a chess website project, and we're talking about 50 or more generations of ancestry.  That's a massive tree by the time you get to the lower levels, even with the repertoire restricted to one's chosen variations.

A nice feature of the internet is that it solves some of the problems it creates! 

http://postimage.org/image/g0ykj3bsf/ (4.a3)

http://postimage.org/image/etttid0fj/ (4.e3)

The links above should give you access to two trees, Queen's Indian with (1.d4 Nf6 2.c4 e6 3.Nf3 b6) 4.a3 (Petrosjan) and 4.e3, both from Black's point of view (more or less according to Greet's "Play the Queen's Indian") (sorry, the trees are in German, but that shouldn't cause big difficulties: "K" = King, "D" = Queen, "T" = Rook, "L" = Bishop, "S" = Knight). The trees are generated with yEd, free accessible over the internet.

One can (hopefully) see that the 4.e3-system (the tree is not finished yet) is much more messy than the Petrosjan, which contains only a limited amount of move order issues (the variations [4.a3 Ba6] 5.e3, 5.Nbd2 and 5.Qc2 Bb7 6.Nbd2 can transpose into each other).

Over time I've developed a sort of coding, some features are: Squares indicate positions within the variation, where there is a branching, whereas circles are sort of final positions of a variation. The colour of the circles code the evaluation of the resulting position. A continous line indicates the lines as I have them in the accompanying Chessbase file, an interrupted line is an alternative move order. Dotted lines are moves that have been played, but quite rarely, so I don't follow them any further.

The lines (or edges of the tree) contain (obviously) the moves and, below that, some figures in parentheses below. These indicate the relative frequency of the moves. Take e.g. the starting position of the Petrosjan-Variation after 4.a3 Bb7: The "2,981" under the knot is the number of times this particular position has been reached, according to Mega 2012 (+ some updates). Now I've given this hole variation a "value" of 1000 / 3 = 333 "points". This figure is somehow arbitrarily chosen: The bigger that "value", the more detailed (and complex) the tree will be in the end. These 333 points are distributed to the possible 5^th moves of White. By far the most common 5^th move in this position is 5.Qc2, played 2,210 times, another move is 5.e3, played 376 times. Distributing the value of 333 to all those 6 moves indicated in the tree in relation to their frequencies yields a value of 247 for 5.Qc2 and 42 for 5.e3 (5.b3 has been played 32 times, which yields a value of 4, which I consider being too low, so I stop here). The total of the values equals 334 (you can check that), the difference to the starting value of 333 is due to rounding inaccuracies.

This way of computing the "values" of the positions is followed through the whole tree. As a general rule, I stop a variation when its value is down to appr. 10 (that is, when the likelihood of this particular position to occur is 10 / 333 = 3%). (I still follow them up if they lead to transpositions.) This way I control the size of my repertoire: Using a "starting value" of 333 and a "stop value" of 10 yields appr. 33 variations (it might be maybe 30 or 37, as in some cases you want to stop earlier, when the variation is not forced at all and rather requires understanding, or you want to stop later, when there are some tactics you don't want to leave out). After having mastered this repertoire, you might think about going into more details, and revise the whole tree, this time with a higher starting value.

Of course, there are many options to do those statistics: You might consider only the games of the last 10 years, or those within a certain "strenght range", or ... . You can also take the preferences of your opponents into account (as far as you know them). 

So what are the advantages and disadvantages of this approach? Of course, it takes quite some time to generate the trees. On the other side it enables you to focus on the most likely variations. Going through several opening books this way, I found that it often happens that the author is going into considerable detail in some positions, whereas the tree tells you that it's very unlikely to reach those positions, so just skip them! It also enables you to keep track of move order issues and be forewarned. This approach can also help to master your repertoire: Say there are two or more quite similar positions which require a different approach (= a different move from you), and you always confuse those positions. With the tree, it's easy to pin down those positions (for example, if you're doing opening training with CPT, as I do) and have a deeper look at them to finally understand what makes those positions different.

I hope this post gives you some ideas how to work with trees (at least to make the "fundamental decision" (i) "Hmm, that sounds interesting, I'll give it a try" or (ii) "Oh no!!!!"). 

Any questions, critics and suggestions are welcome!

Best regards,

Zwischenzugzwang

I would love to show a picture of one or two of them, but how to append a .pdf- or a .gif-file? Can anybody explain that to me? (I didn't find the online help very helpful here.)

Best regards,

Zwischenzugzwang

I fully agree with you. You feed ChessBase with a data file of games, and it can calculate this tree data file from it (.ctg), so I miss the next step of showing the structure of this ctg-file in a sort of tree diagram. Some things could be so easy!

That's true. But with the tree neatly printed out on a (large) piece of paper, the overview is much, much better.

As my QGDEx tree project is slowly approaching it's final stages, some quantification is possible: Actually, the tree has 126 knots and 131 edges. There will still be some changes, but I guess I will end up with between 130 and 140 knots. I would estimate that a new tree to be 'digestable' should have much less than 100 knots, so maybe 50 ... 60 would be a reasonable figure. That means that I will cut down the tree by about 50%.

The better the tree is learned and it's branches understood, the less memory capacity it requires for a given amount of data. That means that after becoming familiar with the reduced (50 knots) tree (by playing games, analyzing, memorizing, ...) the next step would be to add some of the previously deleted branches and therefore include them in your repertoire. The whole process of 'digesting' would then be repeated, until you find your tree is detailed enough for being an effective weapon against your opponents.

That might make not a lot of sense for some of you yet (although I hope, it does!), but next week I'll hopefully be able to show some pictures which might make clearer what I'm talking about. At least this 'tree approach' could be a tool for answering that eternal question any time you open a new book you want to learn an opening from: "How much of that stuff do I have to memorize?" One 'simple' answer could be: 50 knots for club level, 120 knots for 'master' level, 200 knots for GM level (of course, all these figures are not verified at all, but it should give an idea of what I mean).

To be continued ...

Best regards,

Zwischenzugzwang

Oh, that's simple. Bibs only wanted to show me that there are all kinds of trees around - apple trees with apples, cherry trees with cherrys, spaghetti trees and also chess position trees with a chess position on each leaf, pieces as fruits (some trees have white, some have black pieces, you can pick them, but you shouldn't eat them), and if you cut the tree you'll find that the wood is checkered.

Happy New Year, dear Jupp!