It will be directed by Ian Rickson and produced by Sonia Friedman.
According to a report in the UK's Daily Mail, the roles that Williams and Scott Thomas play will be decided nightly by the toss of a coin before curtain up.
Director Rickson is quoted, saying it would be "creatively exciting to mine the play, by having both women playing the parts and swapping on different nights," adding that there's "a very strong connection between Anna and Kate and they do somehow share the same soul. Sometimes we might even toss a coin to decide who goes on playing what part. Rufus [Sewell] also loves the idea, because it gives him lots of opportunity."
The play is set in a farmhouse where a married couple Deeley and Kate await a visit from Kate’s old friend and roommate Anna, whom they haven’t seen for 20 years.
Dates are yet to be announced, but producer Friedman has confirmed the production to Playbill.com.
