Role-swapping: just a gimmick or an extra dimension to the drama?

Kristin Scott Thomas and Lia Williams are alternating parts in Pinter's Old Times revival. It's a tradition that has led to both rows and awards

All change: Lia Williams as Kate and Kristin Scott Thomas as Anna in 'Old Times', and after switching roles (Simon Annand)

Once a week, Kristin Scott Thomas and Lia Williams toss a coin to decide who will play which role on stage in the West End that night. The two actresses are starring in Harold Pinter's play Old Times, a three-hander in which a married couple, Kate and Deeley (played by Rufus Sewell), are visited by Kate's old best friend, Anna.

Or are they? As always in Pinter, all is not quite as it seems. This is no cosy dinner-party reunion. The first sign that things are a little off is when Anna tells Deeley, "You have a wonderful casserole… I mean, wife." Later Kate tells Anna "I remember you dead." The play, which had its premiere in 1971 with Vivien Merchant, Dorothy Tutin and Colin Blakely, is one of Pinter's most mysterious, a dream-like 80-minute wonder. Is it a love triangle? Or the memory of a love triangle? Is Anna a figment of the role-playing couple's imagination? Or are Anna and Kate the same woman, two halves of the same whole?

It was with this last question in mind that Scott Thomas came up with the idea of swapping the roles of Anna and Kate. It was 2011 and she was starring in Ian Rickson's production of Betrayal, Pinter's 1978 three-hander about a woman who has an affair. "She said, 'Why don't we swap the men's parts around?'" says Rickson. "But it was too late by then so we decided to do Old Times properly and have her play both parts."

The two actresses will switch between the inscrutable Kate and the more talkative Anna every few nights. Rickson invited a psychologist into rehearsals to explore the idea that the two women represent one split personality. "You could read it that in order to become a wife Kate has lopped off the extrovert part of herself, or Anna. And so to explore their marriage the couple invite back this lopped-off self, explore her and grieve for her. I like that," he says.

Both parts are a gift for the 52-year-old actress and have been played by a series of venerable pairings down the ages, from Harriet Walter and Julie Christie in 1995, to the last West End production in 2004 which starred Helen McCrory and Gina McKee. Scott Thomas and Williams have learned both parts but the real challenge will be to shift between them. Sewell, meanwhile, will have to remember which actress is playing his wife each night. "I underestimated, frankly, how demanding and challenging it is for everybody to carry both productions," says Rickson. "For me it's like directing two at the same time. And in terms of the malleability the actors need… it is the Acting Olympics."

Old Times is not the first production to feature role-swapping. Danny Boyle mixed man and monster in Frankenstein, with Benedict Cumberbatch and Jonny Lee Miller changing between lead roles at the National Theatre two years ago. Before that Mark Rylance and Michael Rudko alternated as brothers – one a successful screenwriter, the other a talentless drifter – in Sam Shepard's True West at the Donmar in 1994. And long before that, in 1935, John Gielgud and Laurence Olivier switched places as Romeo and Mercutio six weeks into a run of Romeo and Juliet.

For the actors, the rewards for such a virtuoso display can be handsome – if it comes off. Cumberbatch and Miller were joint winners of an Olivier and an Evening Standard Theatre award last year. "In rehearsals you're listening to your lines, you're watching the decisions another very good actor is making, and you're thinking about your own choices," said Cumberbatch of the process. "It's a very harmonious way to work."

That's the best-case scenario, but the risks are high. And comparisons are inevitable. In his book Acting Shakespeare, Gielgud recalls how he disapproved of the false nose Olivier wore to play Romeo and thought he was inclined to be "too athletic" in his bedroom scene with Juliet. For his part, in On Acting, Olivier recalls how the two fell out over how best to speak Romeo's verse. "I think I was right, and I know that John will go on thinking that he was. Whatever the results, whichever side people come down on, we must have been fascinating to watch."

And there's the rub. Is role-swapping just a gimmick, an invigorating gamble for the cast, or does it add an extra dimension to the drama for those watching? In the case of Pinter, interchanging two actresses should nudge audiences to imagine one woman in the other's place, just as Deeley does on stage.

It is a commercially canny move, too. Frankenstein sold out in double-quick time because audiences were keen to see both versions. Even the critics went in twice, on consecutive evenings. For Old Times, a performance schedule is posted online, apart from the weekly "coin toss nights" that will be decided on the day. At the first preview, Scott Thomas played Kate and Williams Anna but the casting for press night – which one might expect to be closest to the director's vision – is the reverse. "I don't have a preferred version," says Rickson. "That would be like choosing which of your two children you love more."

'Old Times', Harold Pinter Theatre, London SW1 (0844 871 7622; www.oldtimestheplay.com) to 6 April