At first glance, this year's Edinburgh Hogmanay festival is as civic-mindedly populist as it comes.

Or at least that's the case as presented in its brochure with a big number "13" emblazoned on the cover in neon-styled lettering with the words "BE LUCKY" beneath. The annual torchlight procession is in there, as is the candle-lit concert at St Giles' and the Concert in the Gardens, this year headlined by the stadium pomp of Simple Minds. The Loony Dook is a must, and even the sled dog races have made a return.

Look beyond all this, however, and there is a very subtle subversion in the programme that takes the avant-garde out of the art-house and unleashes it on the streets and in some of Edinburgh's most august institutions. Most of this is to be found in Your Lucky Day, a New Year's Day construction which invites revellers to throw dice which, depending on how they land, will take them to one of 12 destinations in Edinburgh city centre. Once there, they will be regaled by some form of performance before being invited to roll the dice once more to define their next destination, and so on.

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These will include music from the likes of Unthanks singer Becky Unthank, some thought-provoking words from pop psychologist Professor Richard Wiseman, a performance of ancient mummers play, Galoshins, and spoken word and performance poetry from the team behind Glasgow's Words Per Minute night. Once participants have been around as much of the circuit as they choose, the day climaxes with Big Bang, an epic street theatre spectacle by French auteurs, Plasticiens Volants.

Before any of this happens, those in search of guidance will have the chance to seek their fortune via Lady Luck – The Cult Of Fortuna, a participatory installation created by live art duo, Walker and Bromwich. This will involve a seven-and-a-half metre high gold-coloured inflatable "statue" of the ancient Roman goddess, Fortuna, who was the personification of how the hand of chance worked.

"We like to bring people into an idea using something that's both fun and visually seductive," Zoe Walker explains. "That way people become part of the experience and the idea and can maybe feel something so they go away uplifted."

"We hope to be creating a space where people can reflect and have time to think," Neil Bromwich adds. "People come and make a pledge to a god, then promise to repay them once their wish has been granted. People are thinking like that anyway at this time of year, except here they're making a deal with a god."

Walker and Bromwich have consistently redefined ancient rituals with playfully political intent. At this year's Glasgow International Festival Of Visual Art, Art Lending Library allowed members of the public to borrow donated artworks, while the pair unleashed their Love Parade – a pink inflatable cannon firing balloons as it is led through the city streets by a parade of dancers and drummers – on this year's Hull Festival. At time of writing, Walker and Bromwich were immersed in Gateshead's Baltic Centre undertaking The Encampment Of Eternal Hope, a similarly utopian sculptural installation working towards the Mayan calendar's so-called end of the world.

"It's about trying to build a new society in a post-apocalyptic work," says Walker. Lady Luck – The Cult of Fortuna will open for business for two days prior to Your Lucky Day.

Also on show as one of the 12 events around town as part of Your Lucky Day will be Galoshins, a seventeenth-century Scottish folk play presented by Glasgow-based musician Shane Connolly's Sokobauno Puppet and Object Theatre. The piece is performed by Connolly, who is also a percussionist with Tattie Toes, and internationally acclaimed singer Alasdair Roberts, whose excavation of the folk song tradition makes his canon sound dangerously contemporary in a manner that recalls Nick Cave's savage reinvention of blues music. The pair originally presented Galoshins as part of Archive Trails, which saw contemporary artists tap into the cultural goldmine to be found in the of Edinburgh University's School of Scottish Studies, an institution co-founded by poet Hamish Henderson.

In terms of scale, however, Your Lucky Day's undoubted highlight is Big Bang. As the name suggests, this latest extravaganza by Plasticiens Volants travels backwards in time to the explosion that created the universe as we know it. The fact that the company does this via a gigantic set of ever-morphing inflatables lends an appealingly user-friendly texture to a set of highly complex ideas to create a theatre in the sky.

"In the beginning we wanted to try to find a new form of show," explains Plasticiens Volants director Marc Mirales in an appropriately Year Zero fashion. "Before, we have created shows using fairy tales and myth, but with Big Bang we wanted to make a show out of something that was more scientific. We met with an astro-physician, who described himself as a detective who was looking for clues to solve the mystery of the universe. That is why we begin at the end, and go back to the beginning, to try and recreate that mystery."

Such artistic entryism isn't new to Edinburgh's Hogmanay. Plasticiens Volants have brought several shows here over the years, while other major street theatre conceptualists have attempted to adapt what is more often seen at European summer festivals to Scotland's more intemperate winter climate. Many of these companies were born of a post-rave club culture that inherited the 1960s counter-culture's sense of playful mischief. This could be said too of some of the contributors to Edinburgh's Hogmanay 2011. Last year, the National Museum of Scotland played host to a giant game of chess initiated by live artist Spotov as part of a game-themed day of events around the city which also involved the likes of art-pop band, Found.

This continuing sense of subversion was most evident two years earlier, when giant puppet installation Big Man Walking paraded the Royal Mile to a techno soundtrack, while in St Giles' Cathedral, Fragile Pitches was an sound installation by electronic experimental stalwarts Michael Begg and Colin Potter that distorted natural sounds recorded locally for a thrillingly atmospheric experience.

The beginning of the universe, then, is as good a way to start the year as any.

Your Lucky Day, January 1, 2013, begin at the National Museum of Scotland, Edinburgh, noon-5pm. Big Bang starts at 5pm, 13 Buccleuch Place, Edinburgh