The Chessmap

[Ovyron]

I always wanted to see a Chessmap, an image that would show chess as a whole, so that any game played eventually would land in a place on the map. It would allow one to see at a glance the relative sizes of the variations, compared to others, and for chess players wanting to learn chess theory, it'd give a rough idea of the amount of theory they'd need to learn in a line.

When I looked at what SequoiaView could do I thought "this is it!" so I made The Chessmap based on my analyzed nodes:


(Click for larger)

It may not be very useful if you don't know ECO, I might come later with one that shows moves played.

I was very surprised by the outcome, I had expected some large split between 1.e4 and 1.d4 and another like this for 1.e4 e5 and 1.e4 c5, but it turns out the Sicilian (B20-B99) is very small, almost as small as the English (A10-A39)! Though the Spanish (C60-C99) and the Italian (C50-C59) put together are still smaller than the Sicilian. Other surprises were the French (C00-C19) being larger than the Spanish, 1.d4 being really huge (so much that I had to split Queen's pawn A40-A41 and the Dutch A80-A89 to the other side) but I guess that's why ECO gives it its share of 3 ECO codes (most of A and the entire D and E, now I see why!) Finally, I never saw Reti (A04-A09) coming, I always assumed the Najdorf (B90-B99) alone would be bigger, but it doesn't hold a candle to it.

I wonder if this is really representative of chess and how far away is it, there's some really suspicious humongous ECOs (like D02 or... A46?? ) and then B01-B09 (the answers to e4 that aren't c5, e5, e6, or c6) looking greatly over-sized, while the Caro-Kann looks really tiny! If you can compare proportions with your database it'd be cool, though I'm not giving percentages because if a specific one is needed to fix the size of something it's probably not too far off, I'd like to hear about big differences, and I bet there's no way A46 is actually that big!

[Ovyron]

He's the Chessmap with the moves played and some opening names if the space allowed it. I had to use some lines to represent bridges between countries.


(Click for larger)

[Ovyron]

I've been bothered by the bottom-right square, A45 and A46 take an abnormal proportion of the map (and they're some ECOs that sound random to me), so I thought that maybe zooming into them would reveal if something went wrong...

I'm talking about these ones:



ENHANCE!



Huh, so all those variations end up here? Weird...

And named openings kind of suck, "in this zone you will find openings such as the Bronstein, Paleface, and the Wagner Gambit" *Zooms in* "You can't find them? Well, they're somewhere in one of those tiny squares of the zoomed in picture"

[Ovyron]

Now I want to zoom into the messiest place on the entire map, the ECO A00-A03 Zone at the bottom-left of the map. Because it's so small one can only see that all white opening moves are there, except for 1.d4, 1.e4, 1.c4, and 1.Nf3, but no idea where, or in what proportion... the place looks like this:



ENHANCE!



This is the worst of chess, because to remain on this zone both white and black are forbidden to play popular moves that would transpose them to other parts of the map (outside of this zone.) Apparently the most common transposition of the zone is from the Benko to B20 Sicilian (via 1.g3 g6 2.Bg2 Bg7 3.e4 c5 and their permutations), so that's not on this part of the map. Also, bigger boxes eat the moves of smaller boxes (again 1.g3 d5 2.f4 is on the Birds box, not Benko's.)

This map brings up more questions than it answers, like, why is 1.g4 so big if it's almost losing? Shouldn't it be some micro-box sitting with Na3/a4/f3? (which I don't even know their frontiers without zooming in), instead, it's bigger than 1.c3, somehow.

Fun fact: I've been using the Van Geet opening to beat stronger players at lichess, I was kind of excited when I covered it

[Ovyron]

I've been zooming into the chessmap for my game against mmt in where I try to beat 1.g4 here (with 1.g4 zoomed in) and here (after 1.g4 d5 2.Bg2 Bxg4).

But what does a chessmap really tell us? Is it just relative sizes of variations in one particular database, which would only tell us about that database, not about the opening itself?

A good chessmap would tell us the relative size of variations because it'd be based on a good database that represents chess. This one is based on some 4 million analyzed nodes, so it's about 2000 times smaller than the CDBCN one, what I would like to know is if the proportions remain accurate as the variations grow, or if my over-representation of the Reti and under-representation of the Caro-Kann is pure nonsense, but at least when I match these lines against the lines of CDBCN, CDBCN always ends up short (its move qualiy starts degrading at about move 12 and doesn't include the main line of the best lines) so the proportion of the strongest lines should be fine.

For comparison, this is how Scid shows proportions on a database:



*Zooms on B*



*Zooms on B9*



*Zooms on B90*



So B90 should be the largest box, right? with some largest box that contains B90r?

Well, the problem is that B90r has the moves 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6 6.Be3 e5 7.Nb3 Be6 8.f3 Be7 9.Qd2 O-O 10.O-O-O Nbd7, and every time these moves are played, they're counted again. They should only be counted once and the B90r box would only contain the moves after 10.O-O-O (which are in the B90q box) 11...Nbd7, instead of making the first 18 plies of the game increase the size of the box overall for every game that plays this line.

This is the flaw with state of the art ECO browsing. The flaw with my chessmap is that nobody can browse it, and it takes me a looong while to manually zoom in and figure out what is what (if it wasn't I'd already have provided a zoom of everything, but just a small part takes considerable time...)

[Ovyron]

Rybka Forum user Antares requested a zoom into the C20-29 box, so here it is:



ENHANCE!

[karger]

I suggest you guys check out Remi Coulom's homepage. He has a treemap visualizer chess engine listed. Some years ago there was a Windows compile of it called simple treemap WB engine available on the net. I might have it on a flash drive somewhere ... His website ... https://www.remi-coulom.fr/ I have been collecting chess engines for 50 years & have a lot of obscure stuff. John Karger

[Ovyron]

Thanks karger!

From their page:



What I don't see mentioned is transpositions, if there's a big box with 1.d4 Nf6 2.c4 d5 then all variations coming from 1.d4 d5 2.c4 Nf6 would appear on the bigger box, it's unclear if his treemap visualizer would just hold 2 different boxes for the transposition.

[Ovyron]

The chessmap mapped to the Mandelbrot Set: