What's happened?
Its cost far outstrips the $15bn final bill for the London Olympics and even the $40bn that China spent to create an era-defining national showcase for Beijing 2008.
This despite the fact that the Winter Olympics are a far smaller event than the summer games: there are fewer athletes (2,500 versus 11,000), fewer events (86 versus 300) and fewer venues (15 versus 40).
What's more, the cost of the Sochi Games has ballooned further from its original estimated $12bn cost than any previous Olympics.
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Why is it proving so expensive?
The town, popular with holiday-making Russians since the Stalinist era, has a sub-tropical climate almost unique in Russia. Even in winter, temperatures rarely drop below 10C and given that snow is scarce, it had no winter sports infrastructure. So by picking Sochi for its proximity to the mountains, and because it has long been a personal favourite of Vladimir Putin Russia immediately guaranteed itself a mammoth engineering challenge.
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To make things worse, the town itself sits on a narrow strip of sloping land on the coast; the nearest wide, flat site for building arenas and stadiums is a flood-prone swampy plain that is riddled with underground streams.
So what happened?
Meanwhile, the Kremlin ordered that no expense should be spared in creating the infrastructure necessary for an Olympics that would showcase Russia as a resurgent power under its latter-day tsar Vladimir Putin.
This meant building not just the stadiums, venues and three Olympic villages, but a radical programme of upgrades to the region's Soviet-era infrastructure, including roads, bridges, railways, electricity supply, and even a brand new cargo port for Sochi. Critics say all this work explains the real reason behind the big surge in the costs.
Which is what, exactly?
IOC member Gian-Franco Kasper estimates that one-third of the $51bn price tag has been siphoned off in kickbacks to officials and embezzlement. Opposition leader (and Russia's ex-deputy PM) Boris Nemtsov puts the figure even higher, and has lambasted the Sochi Games as "an unprecedented thieves' caper".
In a detailed report, Nemtsov analyses comparative data on cost overruns in other Olympics. He concludes that excessive costs in Russia due to corruption account for $25bn-$30bn of the overall cost more than half.
Western journalists who have visited Sochi have found ample evidence to back this up, with numerous businessmen telling of giant payoffs to the officials awarding Olympic contracts.
What does the Kremlin say?
But firms run by his friends have won big deals. Firms owned by Arkady Rotenberg, the president's former judo partner, won contracts worth $7.4bn (more than the cost of the Vancouver Olympics).
The most valuable contract of all the $8.3bn job of building a new rail and road link between Sochi and the mountains went to the state monopoly run by one of Putin's ex-KGB comrades, Vladimir Yakunin.
To put this into perspective, Russia's edition of Esquire magazine calculated that for the money it cost to build, this 30-mile road could have been paved in a six-centimetre layer of truffles, or a one-centimetre layer of caviar.
What Sochi tells us about Putin's Russia
Boris Nemtsov concludes his report by noting that the budget for the football World Cup finals in 2018 is already $43bn. "If we want to [avoid seeing] that budget quadruple at the expense of robbing Russia and all of us then the investigation of the crimes at the Olympics must be brought to completion."
