A Cheating Yahoo

Last month's chess story discovered by the mainstream press was A Political Yahoo (June 2019). This month we have a story on every cheater's nightmare -- getting caught.

Summer doldrums? Hardly. Chess was the top Yahoo story after 'Coast Guard nabs drug-smuggling sub' and attention-getters like 'Fox News contributor sent vulgar texts to co-host'.

2019-07-12: Chess grandmaster accused of cheating after using phone on toilet during tournament (yahoo.com; The Telegraph).

The world of elite chess has been engulfed in a cheating scandal after a picture emerged of a top grandmaster sat on a toilet allegedly using a mobile phone to cheat. Police are investigating after Igors Rausis, who has represented Latvia, Bangladesh and the Czech Republic, was caught "red-handed", the game's governing body Fide said today. Mr Rausis, aged 58, stunned the chess world by reaching the game's top echelon at an age most players decline in strength. The former Latvian champion was hailed as an inspiration to older players as he climbed from a Fide rating of around 2500 - the level of an average grandmaster - to the verge of 2700 in six years.

That report was by Leon Watson (also of Chessable?), but the same story appeared on other news sources. The next report looks to be a rewrite of The Telegraph version.

2019-07-14: A star chess player admitted to cheating with his phone on the toilet at a tournament (yahoo.com; insider.com, related to businessinsider.com?).

The chess grandmaster admitted that though they are typically banned, a phone found in a toilet at a tournament in France belonged to him.

The Telegraph version of the story attracted nearly 500 comments.

TCEC S16 Leagues; CCC9/CCC10

Let's see. Where were we in last week's coverage of the world class engine tournaments? To summarize that post, TCEC S16 Qualification; CCC9 Bonuses:-

TCEC: The first stage of S16, the Qualification League, is well underway. • CCC: The 'Gauntlet Bonus III' is just getting started. • Both events might be finished in time for next week's post.

That last sentence was half right. The TCEC event finished, but the CCC event is still running.

TCEC: The chart shows the top half of the Qualification League. According to the current TCEC rules, the top six engines qualify for the next stage, now called 'League 2'. It should start soon.

CCC: Some of the details for CCC10 are available from planning documents. Called 'Neverending Story' (how true!), it will have the following rounds: Qualification (13 engines), Quarterfinal (12), Semifinal (6), and Final (2).

[For further information from the various stakeholders in the engine-to-engine events, see the tab 'TCEC/CCC Links' at the top of this page. • NB: Leela = LC0 = LCzero]

The World Was Watching

Some day, in the distant future, sociologists (*) will find this video and ask themselves, 'What was this activity that gripped an entire world so many times?' The video starts,

Chess used to be a worldwide phenomenon, with millions of fans spanning the globe. People knew the names of grandmasters. They were rock stars.

'Rock stars', I tell you! From Youtube's 'World Chess' channel...

World Chess Championship in London (1:53) • 'Published on Jun 19, 2019'

...The best chess player in the world was called 'the world chess grandmaster'.

But in 1997, Garry Kasparov, the world chess grandmaster at the time, was beaten by a computer, IBM's Deep Blue. After this unforeseen defeat of human intelligence, chess faded away [a woman is shown crying].

Garry insisted that IBM cheated. He still holds a grudge, but let's get back to the main story.

After twenty years of absence, the design of London's World Chess Championship of 2018 had to make chess attractive again. The tournament was portrayed as a meaningful exchange of skills between two intelligent, real-life individuals in the era of new technology. We presented chess as the art of playing, as an intimate act, something which re-established the contact between people, re-humanized chess, and made it accessible and understandable again.

Oh, so that's what that logo was all about.

We didn't expect the bomb to go off as it did. [shows text: 'Kama Sutra logo critisized'; yup, that's what it says] There were thousands of tweets [text: 'The WCC is making chess sexy again'], dozens of news stories [text: 'No, it is not a joke'], and a viral video from the world number one chess platform.

That was Eric and Jay's video. Thanks, guys!

Beyond the championship's branding, the campaign idea was supported by the industry as well as the chess community itself. In 2018, the World Chess Championship landed on the front pages. [text: '21.000 publications worldwide; 12 million visitors on worldchess.com, 1.9 billion media reach'] The campaign received 1.9 billion impressions, brought coolness to a young audience, and fostered a sense of intimacy for everyone involved. [closing text: 'The World Is Watching'].

What industry are we talking about here -- advertising? Have we already forgotten that the match 'landed on the front pages' because every game was a draw? Bottom line: we live in a multiverse of parallel worlds where every person creates a private reality.

(*) See also The Sociology of Chess (November 2016).

AlphaZero's Zeros

Earlier this year, in Kindle Best Seller (February 2019), I mentioned a Google Books preview version of Sadler & Regan's book 'Game Changer':-

I noticed a section in the book on engine evaluations of '0.00'. I think it was at the end of chapter 2, titled 'ZeroZeroZero'. [...] Now the preview has disappeared and the page is marked 'No preview'. I've been looking into the topic of engine evaluations '0.00' for some time, but I'm not prepared to write a full post on it. I had hoped to use the half-dozen (or so) 'Game Changer' pages to launch a discussion, but that will have to wait for another day.

Last week, while working on the post Interpreting AlphaZero, I discovered another preview copy of the book, which gives me the chance to continue that 'Best Seller' discussion. Chapter 2 of the book, titled 'ZeroZeroZero', starts,

The end of 2017 saw the release of 10 games from a match between the strongest superhuman-strength chess engine -- Stockfish -- and DeepMind’s AlphaZero. The match result was a comprehensive victory for AlphaZero.

A few pages later, the discussion of 0.00 kicks in with a section titled '0.00'. I assume it was written by GM Sadler:-

A couple of months ago, I was reviewing an excellent middlegame book of extremely complicated positions analysed by a world-class grandmaster. The author mentioned a few times when the crisis in a particular position was at its highest that his engines were assessing the position as 0.00. Judging from his comments, he wasn’t completely sure what to make of such an assessment which didn’t always tally with his intuitive or practical feeling about the position.

Any chess player who has analysed complicated positions seriously with an engine running in the background will recognise this scenario. You summon your inner genius, think up a brilliant doublepawn sacrifice to set the board on fire… and your engine responds with an evaluation of 0.00 and a best line ending in you forcing a bizarre repetition of moves. And it’s not just one engine: they all want you to force a repetition (though the ways to do so often vary). It’s perhaps the most irritating and obstructive thing that these otherwise fantastic engines do during analysis.

The discussion goes to the heart of engine analysis and I'll continue it in another post. As an aside, who is the 'world-class grandmaster' mentioned in the first paragraph of the previous excerpt?

Cool as Cucumbers

If climate scientists are right -- and there is no good reason to doubt them -- the heat waves we're experiencing in Europe are going to become more frequent. Last year I used a heat wave as an excuse for two consecutive posts : A Chess Board Is a Stage (July 2018; '♫ We're having a heat wave, a tropical heat wave ♫'), and Chess Greetings. This year I hope to use it only once.

How do you combine chess with the idea of hot? A web search returns many pages on the idea of 'hot girls' who play chess. Since that sort of sexism isn't appropriate to a blog 'For All Ages', what other ideas are there? The following photo does it for me.

Chess in the African Desert

The original eBay auction pegged the photo to 'WWII', but eBay sellers are not always knowledgeable historians. The fellow smoking the pipe has some sort of insignia on his helmet that probably dates the photo, but I have no idea what it means. More importantly, how do these guys stay so cool? Is it just a state of mind?

A Quotable Quote

Pictured here is a search snippet that appeared on a recent search. The search had nothing to do with the content of the snippet and when I tried the same search a few days later, there was no snippet at all.

I don't know why I clicked to expand the question, 'Is chess really that hard?' After all, it's just someone's opinion. Some people will say, 'yes'; others will say, 'no'. Nobody's right and nobody's wrong. The question expanded to this paragraph:-

Chess may not be the easiest game to learn, but it is far from the most difficult. You have to learn the moves of the six pieces, where the piece with the least value, the Pawn, has the most complicated moves. ... One aspect of this myth is true -- it is hard, very hard, to learn to play chess well.

My first reaction was to think, 'That's interesting'. I wasn't sure I agreed with the sentiment, but it sounded like the writer knew something about chess. Then I noticed the reference for the quote (I added speckles to the image to make it hard to read and add a little suspense):-

Top 10 Myths About Chess - Mark Weeks
https://www.mark-weeks.com/aboutcom/aa06f17.htm

The quote was from one of my pages! I wrote those words so many years ago -- June 2006 according to the URL -- that I'd completely forgotten about them. So Google thinks I'm an expert on something. Thanks for the vote of confidence! • For more about Google's 'search snippets' and 'knowledge graphs', see Celebrity Chess Players (March 2019).

TCEC S16 Qualification; CCC9 Bonuses

Although last week's post on the two major, ongoing engine-vs-engine tournaments, TCEC S16 Starts; CCC9 Finishes, summarized three weeks of play, the action at the time of the post was relatively low-key:-

TCEC: S16 is just getting started. • CCC: The 'Gauntlet Bonus II', a 200 game match between Leela and Stockfish, is currently underway and is too close to call.

What happened during the intervening week?

TCEC: The first stage of S16, the Qualification League, is well underway. Two neural network (NN) engine newcomers, ScorpioNN and Stoofvlees, are currently leading, while a third NN, ChessFighterNN, is fighting to stay out of last place. A Leela clone running on CPUs instead of GPUS, is in third place. TCEC chat commands point to resources describing the three NNs:-

• Scorpio (chessprogramming.org)
• Stoofvlees (ditto; the name is Dutch for 'beef stew' - why was it chosen?)
• Chess Fighter Neural Net (talkchess.com)

CCC: The 'Gauntlet Bonus II' finished with Leela beating Stockfish by a narrow, but convincing +29-25=146. The 'Gauntlet Bonus III' with five engines bashing each other over 15 double rounds (300 games total) is just getting started. Why all the bonus events? A chat command,'!whyb', explains,

We also sometimes run bonuses while we are working on new features and bug fixes that we want to have done before the next "official" tournament.

Both the TCEC Qualification League and the CCC Gauntlet Bonus III have another week to run. They might be finished in time for next week's post.

[For further information from the various stakeholders in the engine-to-engine events, see the tab 'TCEC/CCC Links' at the top of this page. • NB: Leela = LC0 = LCzero]

Contemporary Dutch Masters

By some kind of quantum, 'spooky action from a distance' phenomenon, this month's Featured Flickr echoes last month's The Original Dutch Masters. The photos are all from the album FishPartners Open 2019 (flickr.com), which took place in Bunschoten-Spakenburg (Netherlands), according to the photos' tags.

First photo: GM Vlastimil Hort © Flickr user Frans Peeters under Creative Commons.

GM Vlastimil Hort: Introducing the pictured notables from left to right, GM Hort isn't Dutch, he's Czech. What attracted him to the FishPartners Open? For another distant photo, one from 50 years ago, see last month's June 1969 'On the Cover'.

GM Jan Timman: GM Timman is one of the greatest Dutch masters of all time and there are many posts on this blog that mention him. I couldn't decide which one to reference.

Willem Gruenbauer: This photo appears to be the same fellow seen anonymously on this blog in 'Nice Jacket!' (January 2015), and A Chess Wardrobe (August 2017). His FIDE card, Gruenbauer, Willem FIDE Chess Profile, confirms he's Dutch. Even if he's not a chess master, he's a master of chess wardrobes.

Interpreting AlphaZero

From the July 2019 Chess Life, GM Andy Soltis's 'Chess To Enjoy' column, titled 'Meet General Principles : Some things never change':-

Chess To Enjoy: You must agree computers changed everything. AlphaZero was not programmed with your principles, the way engines used to. It just played gazillions of games with itself until it discovered the revolutionary truths of chess.

General Principles: Revolutionary? Here's what the book Game Changer has to say: There are 14 detectable features of AlphaZero's playing style. Number one is "AlphaZero likes to target the opponent's king." Number two is "AlphaZero likes to keep its own king out of danger."

Chess To Enjoy: Seems like I learned that the first week I played chess.

General Principles: Other discoveries are that AlphaZero likes to trade material when it has a winning advantage, it tries to control the center, and it seeks great outposts for its knights.

Chess to Enjoy: I see...

General Principles: And AlphaZero likes to sacrifice material to open attacking lines and to exchange off its opponent's most active pieces.

Chess To Enjoy: ...Well, OK...

General Principles: Then on page 129 it says, "AlphaZero may give the opponent the chance to go wrong."

Chess To Enjoy: Sounds like AlphaZero is being credited for inventing what every experienced player already knows.

It's been a while since I introduced the book by Matthew Sadler & Natasha Regan in AlphaZero Stars in 'Game Changer' (January 2019). Although I haven't read it cover-to-cover, I have read significant portions, and the topic that Soltis is gently mocking is one of the main themes of the book. In AI/NN research, the topic is called 'interpretability' : what can we learn from black box models?

Unfortunately, interpretability is not easy to understand or to execute. Wikipedia's page Explainable artificial intelligence starts,

Explainable AI (XAI), Interpretable AI, or Transparent AI refer to techniques in artificial intelligence (AI) which can be trusted and easily understood by humans. It contrasts with the concept of the "black box" in machine learning where even their designers cannot explain why the AI arrived at a specific decision.

I found a four-part PDF presentation 'ICIP 2018 Tutorial' on Interpretable Deep Learning: Towards Understanding & Explaining Deep Neural Networks (interpretable-ml.org). It answers the question 'Why Interpretability?' with five reasons:-

1) Verify that classifier works as expected
2) Understand weaknesses & improve classifier
3) Learn new things from the learning machine
4) Interpretability in the sciences
5) Compliance to legislation

The 'classifier' of a neural network (NN) is the portion of the software that makes the final decision about what the NN is seeing. Is it a cat (yes/no)? -or- What animal is in the photo (cat/dog/other)? A game playing NN has a more complicated classifier, which is the decision on what move to play next. The third item in the list ('Learn new things') above is illustrated in the ICIP tutorial by the following slide:-

The referenced game is AlphaGo, not AlphaZero, but the sentiment is familiar: 'I've never seen a human play this move.' What can we learn from AlphaZero? Probably not much beyond what is in the Sadler/Regan book, because AlphaZero has never been seen outside of DeepMind's laboratory. We might have better luck with Leela or with one of the other chess NNs that are rapidly emerging.

2019 CJA Award Entries

Just like clockwork, two months after the 2019 CJA Awards Announcement (May 2019), the Chess Journalists of America have announced the 2019 Entries, i.e. nominations for the various award categories (where I used the PDF version to prepare this post). For the past few years I've concentrated on my two favorite categories, 'Best Chess Blog' and 'Best Chess Art', so I'll continue the tradition this year.

'Best Chess Blog' is not the most competitive of the CJA award categories. In several recent years there have been no entries. Last year had one entry which was a single post. This year we have a full blog, First Move Chess (which I hadn't seen before), and a single post, The Day Leela Changed Computer Chess (chess.com). As far as I can tell, the first post in the full blog is dated after the deadline for CJA entries. In past years I've been crticized for pointing out facts like that, so I'll stop here.

'Best Chess Art' has been split into two categories:-

• 'Best Chess Art (graphic design, cartoon, other)'
• 'Best Single Chess Magazine Cover'

Since last year's entries were predominantly magazine covers, this year I'll summarize the six entries in the first category, shown below. First observation: chess art is alive and well.

Top row:

• Willum Morsch, "The Sinquefeld Super Trio"; ACM issue 8, p.34
• Direct Attacking Moves; Sean Busher; CL October 2018, Front Cover
• Infographic: On the 8th Rank; Natasha Roberts, Melinda Matthews; CL May 2019, p. 14-15

Bottom row:

• Infographic: Chess Firsts; Natasha Roberts, Melinda Matthews; CL January 2019, p. 13
• The Challenges of Chess Parenting; Carlotta Notaro; CL December 2018, p. 37-38
• Chess Adventures with FM Alisa Melekhina; Val Bochkov, Melinda Matthews, Natasha Roberts; CL Kids February 2019, p. 22

The last image in the top row and the middle image in the bottom row show the first half of double-page artwork. The middle image in the top row is reminiscent of an image I flagged a few years ago in Cutting the Mustard (August 2013), as superior to the award winner that year. The two infographic entries are attributed to the same team, who are also listed against the last image.

Which entry would I vote for if I were a judge? It's hard to say. I'm not a fan of the first entry in the bottom row, which looks like a text ad for chess books, but the other five are all attractive in their own ways.

With so many categories this year, some of them highly competitive, the judges are going to have to work hard to determine the winners. We'll find out next month who those winners are, but in the meantime, chess journalism is the big winner.

July 1969 'On the Cover'

Boris Spassky is perhaps best remembered by the non-chess-playing public as the Russian who lost to Bobby Fischer. This is as unfair to his record as the popular perception of Howard Staunton as the English player who ducked Paul Morphy. Spassky was a strong super-grandmaster whose greatest triumph was winning the title of World Champion in 1969.

Left: 'Boris Spassky - World Champion'
Right: 'Boris Spassky - 1966 Challenger, 1969 Champion'

Chess Life

To different people, the World Championship match looked like different things. Korchnoi, for instance, said that the match was developing in waves, and he was right —- first it was Petrosian and then Spassky and then again Petrosian who was on top, and then, when the first third was over, there was a quiet sea marking the second third of the match. At the time of this writing, they stood all even at 8-8.

That was the lead paragraph of the first article on the match:-

• 'Observation Point' column by Miro Radojcic, 'Now or Never!'; 3 pages (w/ games 7-16)

CL carried two more feature-length articles on the match:-

• 'O'Kelly on the Match' by Grandmaster A. O'Kelly, Chief Match Umpire; 2.5 pages (w/ games 1-6)
• 'With the Champions : A Moscow Memoir' by Dimitrije Bjelica; 2 pages

Chess Review

Boris Spassky of Leningrad has won the title of Champion of the Chess World. He did so or at least clinched the title as we go to press with this issue, scoring 12 1/2 to 10 1/2 against former World Champion Tigran Petrosyan of Armenia. The twenty-fourth game may not be played.

That was the start of the first story in the flagship 'The World of Chess' section, titled 'New World Champion'. The magazine had another article later in the issue:-

• 'World Championship : Middle Games', Annotated by Hans Kmoch; 4 pages (w/ games 9-16)

Earlier in the year Spassky appeared on the CL side of February 1969 'On the Cover', 'the 1968 "Oscar" for best player of the year was given to Spassky', with a link to his previous 'On the Cover' appearance. July 1969 was also not his first appearance on both covers. The October 1968 'On the Cover' listed three such double features, players who appeared on the cover of both magazines for the same month:-

Spassky, September 1966
Evans, September 1968
Larsen, October 1968

Spassky's CR photo has been seen before in the June 1968 'On the Cover'. That first time it was in black & white instead of the incongruous blue used in 1969.

NB: It's worth noting that CL's Radojcic article carried a half-page trailer titled 'Nona Keeps Her Crown', about Nona Gaprindashvili's defeat of Alla Kushnir for the Women's World Championship. Even so, half of that article was about Vera Menchik.

TCEC S16 Starts; CCC9 Finishes

After a three week break from posting about the top two engine-to-engine competitions (see TCEC Not-so-Rapid Bonus; CCC9 Stage Two for the previous post), how hard will it be to catch up? To summarize that previous post:-

TCEC: The 'Rapid Bonus' is still running with Stockfish and Leela currently tied for first. • CCC: The 'Gauntlet Qualification' finished with Leela ahead of Stockfish by a significant margin. The next stage is the 'Gauntlet Quarterfinals'.

How did those events finish and what happened next?

TCEC: The 14-engine, six-round 'Rapid Bonus' (78 games per engine) finished with the following top scores:-

1) 55.5 Stockfish
2) 53.5 LCZero
3) 53.5 AllieStein
4) 48.0 Houdini

Over the next few weeks, the TCEC released two reports on its plans for the next season. The first was TCEC Season 16 – information and participants:-

TCEC Season 16 will feature a new format. It will keep the acclaimed Premier Division and Superfinal as in previous seasons, but will give more chances to starting engines to climb up the rankings. For this reason three leagues of 16 engines will be created. The event will start with a Qualification League where all newcomers will be featured, including new AB engines and Neural Networks. The top 6 of the Qualification League will promote to League 2 (also 6 will relegate), and the top 4 of League 2 will promote to League 1 (also 4 will relegate). Finally, the best placed 2 engines from League 1 will qualify for the Premier Division (also 2 will relegate).

The change of structure for TCEC is necessary due to the present rapid development of computer chess. With the new format more engines will have a chance to climb up the ranks and have a shot to enter in the elite.

The second report was TCEC S16 starts:-

Season 16 of the Top Chess Engine Championship starts this Sunday July 14th at 15:00 CEST. A total of 18 engines will battle for six promotion spots in the newly formed Qualification Division. Among them are three Neural Networks – ScorpioNN, ChessFighterNN, and Stoofvlees. [...]

Many engines are now hopping on the Neural Network bandwagon, making full use of GPUs. Yet, the champion Lc0 has released a strong version playing on CPU only! It is not a unique engine by the TCEC criteria, but it certainly is exciting to see it perform against real competitors of 3000 ELO+ strength. Thus, Lc0 CPU enters TCEC as a promo engine in the field. It will play all games in the division, but at the end of the division all results of the engine will nullified.

Between the end of the 'Rapid Bonus' and the start of the 'S16 Qualification Division', the TCEC ran a number of exhibition events.

CCC: After Leela won the 'CCC9 Gauntlet Qualification', the following events were held:-

CCC9 Gauntlet Quarterfinals (10 engines, 14 rounds)
1) 83.0 Lc0
2) 82.0 Stockfish
3) 76.0 Leelenstein
4) 74.5 Allie

CCC9 Gauntlet Semifinals (6 engines, 40 rounds)
1) 113.5 Stockfish
2) 112.5 Leelenstein
3) 110.5 Lc0

CCC9 Gauntlet Final (200 game match)
1) 103.5 Stockfish
2)   96.5 Leelenstein

Despite the close results, it's surprising to see that Leela did not qualify for the final match. I haven't found any Chess.com reports on the series of events, but I'll be patient before looking elsewhere for the reason(s). After the 'CCC9 Final', an exhibition match was organized:-

CCC9 Gauntlet Bonus (100 game match)
1) 53.5 Lc0
2) 46.5 Stockfish

The 'Gauntlet Bonus II', a 200 game match between the same two adversaries, is currently underway and is too close to call. After it finishes in a few days, we might see CCC10, for which plans are available.

Both the TCEC and the CCC have seen significant evolutions in their organization and documentation since I started weekly posts in January. Without their archives and other online aids, I would have been unable to produce this post. Kudos to both.

[For further information from the various stakeholders in the engine-to-engine events, see the tab 'TCEC/CCC Links' at the top of this page. • NB: Leela = LC0 = LCzero]

Dr.House: S3E23 "The Jerk"

Remember when Youtube was filled with short clips featuring chess scenes from movies and TV shows? Those were the days! When everyone realized that the service was in blatant disregard of international copyright law, the short clips all but disappeared. From time to time they reappear in 'official' channels. This one is from the Dr.House channel.

16 Year Old Destroys House at Chess!? | House M.D. (7:09) • 'Published on Jun 10, 2019'

The description starts on a positive note for chess:-

House plays a young chess champ in order to stress him out and reveal some of his underlying symptoms but instead seems to lose in the process. Will House be able to reclaim his dignity?

Then we learn that the scene is from 'Season 3 Episode 23 "The Jerk"':-

House meets his match in the form of Nate (Nick Lane), an obnoxious 16-year-old chess prodigy with intense head pain and behavioral issues, who manages to annoy and offend every member of the team during his course of treatment.

File this under 'Not everyone likes chess'.

Tolkien Says 'Dwarves'

The title of this month's selection for Top eBay Chess Items by Price (March 2010) was 'Old ~1930 Franz Bergmann Vienna TWO DWARFS PLAYING CHESS Cold Painted Bronze'. I would have used 'TWO DWARVES PLAYING CHESS' (although with CAPS off), but according to Wiktionary's entry for Dwarf, it's not so simple:-

At first, dwarfs was the common plural in English. After J.R.R. Tolkien used dwarves in his works, that form became the standard for the plural of the mythological beings. For a non-mythological dwarf (people with dwarfism), dwarfs has remained the preferred plural form.

Whatever plural form is preferred, the piece attracted only one bidder. It sold for US $699.99 'Buy It Now'.

The description added,

I had the chance to buy a small collection of 100% antique Vienna Bronzes. They are all pre-WW2, approximately 80-100 years old. In my opinion these are all Franz Bergmann designs, some are marked with "Austria" or the typical "Jug-Mark". Others are not marked. But also the unmarked pieces are old and original Vienna Bronze pieces. But please see pics and judge yourself. This scene is unmarked.

As these are antique objects, they may show dust, wear, paint chips, patina and other imperfections. The max. height is 77 mm (3 inches). 120 mm maximum width (a bit less than 5 inches).

For another eBay chess bronze, see The Artist and the Artwork (April 2015); 'titled "Antique Austrian cold painted bronze orientalist playing chess signed Chotka", sold for US $995 after a single bid'. For another chess playing dwarf, see Chess Mardi Gras (February 2018).