In the full glare of the ferocious midday sun, a chubby teenage boy scoops up his plastic castle, and moves it one square forward on the giant marble chessboard carved into Elista's central square.
Murmurs run through the watching crowd. The only person who doesn't adopt a horrified expression is Lenin, who remains stoic surveying the square from a pedestal.
"You idiot!" cry out three men in unison. Sure enough, a few seconds later his metre-high castle is pole-axed by an opposing pawn, and the game is all but lost.
The boy wanders away dejected, and another takes his place to challenge the victor, a youngster sporting a Barcelona football shirt.
Chess is everywhere in Kalmykia, an arid chunk of steppe, that lies on Russia's Caspian Sea coast.
The fetish is largely down to Kirsan Ilyumzhinov, an eccentric millionaire with a taste for sharp suits and fast cars, who has ruled the isolated republic for almost 15 years.
And since 1998, when Ilyumzhinov added the presidency of the World Chess Federation (Fide) to his portfolio, the ex-schoolboy champion has turned his region into a chess mecca.
Despite crippling poverty and unemployment in the republic, which is one of the poorest of Russia's regions, US$50 million was found to build a "City Chess" complex outside Elista, and compulsory chess lessons for every child over 6 were introduced in schools.
And last year at another Elista arena his ultimate chess fantasy became reality.
Fide champion Veselin Topalov and classical champion Vladimir Kramnik went head to head in a match that ended the divide in international chess and created a single world champion for the first time since 1993, the year Ilyumzhinov came to power.
Elista is a dilapidated but pleasant city, filled with cottages and five-storey Khrushchev-era apartment blocks, the windows covered in silver foil to keep out the ferocious sun.
But out of the capital, life is hard. Farming is still the major source of income, despite the difficulties of rearing livestock in almost-desert conditions. Incomes are as low as US$50 per month and unemployment is rampant.
Ilyumzhinov doesn't share these financial problems.
At Elista's weed-strewn airport, the only two planes are the presidential jet and a rusty 32-seater Yak 40 jet that meanders to Moscow three times a week. And once on the ground, he has a fleet of Rolls-Royces to call on.
He made his money in murky circumstances during the early 1990s, and seems to have become richer during his time as leader of Kalmykia.
Opposition figures say this additional wealth is the result of corruption, where companies taking advantage of Kalmykia's tax haven status in the 1990s made payments into Ilyumzhinov's personal account. He denies the allegations.
The Kalmyk leader has great faith in the predictions of an elderly Bulgarian fortune teller named Vanga, who apparently foretold his presidencies of both Fide and Kalmykia.
He counts among his friends Chuck Norris, the Dalai Lama, and the late Saddam Hussein, whom he met during an attempt to bring the World Chess Championships to Baghdad.
Ilyumzhinov's office set three interview dates but cancelled them all at the last minute.
As a substitute, they provided a copy of his 1998 autobiography, entitled The President's Crown of Thorns, a strange mix of pseudo-philosophy and stream-of-consciousness reminiscences.
One chapter is entitled: "Without me, the people are incomplete." Another is charmingly headed: "It only takes two weeks to have a man killed."
Among the stranger claims of Ilyumzhinov is that he was abducted by aliens in September 1997.
"I was taken from my apartment in Moscow to this spaceship," he said in a recent television interview. "We went to some star. After that I said 'Please bring me back' because the next day I had to go to Kalmykia and then to Ukraine, and they said 'No problem, Kirsan, you have time'."
He rejects the idea that these claims make him appear to be a few pieces short of a full chess set. "I'm not a crazy man. From the United States every year more than 4000 people are contacted in such a way. It's an official statistic."
Ethnic Kalmyks make up just over half of Kalmykia's 300,000 population. A Mongol people who originated in what is now western China, they settled in the area nearly 400 years ago, and are traditionally Buddhist.
The Kalmyks didn't have a very good run during the Soviet period.
All the Buddhist temples were destroyed in the 1930s, and the entire Kalmyk population was deported to remote Siberian outposts in 1943 for alleged collaboration with Nazi forces.
In a dark page of the Russian war effort, that rarely forms part of public discourse on the World War II here, around 10,000 troops were mobilised in Kalmykia. And on a cold morning in December 1943, Kalmyk families were bundled out of their homes on to cattle wagons. Most of the men were fighting at the front, so the victims were mainly women, children and the elderly.
In the three-week journey to Siberia, and in the first difficult months of exile, more than 40 per cent of the Kalmyks perished, estimates local historian Vladimir Ubushayev.
"There was a special wagon at the back of each train that was used to hold the bodies of those who died on the way.".
In 1957, the Kalmyks returned as part of Nikita Khrushchev's thaw, but the years in dispersed exile had taken a toll on their traditions and language. Now, few people under 50 speak fluent Kalmyk, a language close to Mongolian.
Buddhism, however, has undergone a gradual renaissance since the fall of the Soviets, with the Dalai Lama making three visits to Kalmykia, and new temples springing up every year.
The most impressive is the Golden Temple in central Elista, a cream and white structure of immense proportions - the largest Buddhist temple in Europe.
It was officially opened in December 2005, but the interior is still being painted by a team of travelling Tibetan artists, a pleasingly medieval process that could take up to five years.
"Before 1917 there was a strong tradition of Buddhism here, but then the communists destroyed it," says Tupten Shaty, a Tibetan monk at the temple. "Now we're here to revive the tradition."
On the top floor, a luxurious multi-roomed suite awaits a return visit from the Dalai Lama to bless the completed temple.
Nobody else is allowed to stay in the palatial residence, but so far even Ilyumzhinov's charms have been unable to bring the Dalai Lama back to town - Moscow is wary of issuing him a visa given improving relations with China.
Pictures of Ilyumzhinov with the Dalai Lama abound in Elista, as if the Kalmyk leader wants to reinforce his credibility among his Buddhist people.
In fact, Ilyumzhinov's portrait is everywhere. Here he is with the late Pope John Paul II; there he is with Vladimir Putin. He even makes it into a display about antelopes in the local museum.
Many Kalmyks seem to be happy with their leader.
"Kirsan does the work of three men, and is an excellent role model for young children," says Anatoly Shamakov, a tutor at a chess school. "I think he was sent to us from God."
Sanal Shavaliyev, the editor of a local newspaper and chairman of the Kalmykia Union of Journalists, agrees.
"He's an exceptionally intelligent man and has turned Kalmykia into a place that people all over the world know about," he says. "We're very proud to have him as our President."
The approval is not unanimous.
"He's a pathological liar with serious psychological problems," says Semyon Ateyev, director of the Kalmykia Bureau of Human Rights. "After 14 years of his rule, we're still one of the poorest regions of Russia.
"We have a Minister of Economic Development, who's also in charge of organising chess tournaments. We don't have any economic development, because he spends his whole time organising chess tournaments."
Many also suggest that there's a darker side to the quirky Kalmyk ruler. Nine years ago, Larisa Yudina, editor of Sovietskaya Gazeta, a local Opposition newspaper, was murdered.
"She told me she had found some documents that clearly implicated Ilyumzhinov in a huge corruption scheme," says Valery Badmayev, the paper's current editor. "A few days later she was dead."
Two former members of Ilyumzhinov's administration were found guilty of the murder, but the leader himself escaped the fallout.
When President Putin abolished elections for regional leaders in the aftermath of the Beslan school siege, analysts pointed to one potential positive outcome being that unaccountable local rulers could no longer manipulate local elections and remain in power.
"In 2004, in just one month we collected 74,000 signatures against Ilyumzhinov's rule," says Badmayev.
It was expected that Ilyumzhinov would be one of the first victims of Putin's new law.
But in 2005, the President came to Elista and reappointed Ilyumzhinov, giving him a mandate until 2010.
"The Opposition here is going through a bad period, like in the rest of Russia," says Badmayev. "We've given up hope of getting rid of Kirsan while Putin is in power."
They can only pray that the aliens come for Ilyumzhinov again, and this time don't bring him back.