Michelle Terry’s inaugural two productions as artistic director at Shakespeare’s Globe are a mixture of the good, the bad and the plain cuckoo. They’re delivered with the deadpan mischief of school-children who have been asked to re-do their homework in stricter accordance with the teacher’s instructions on the black-board – superficially compliant and yet abounding with provoking surprises.

Terry’s predecessor Emma Rice – a martyr to the cause of innovation at this Bankside bastion of the replica olde-worlde – departed after two tempestuous years, bringing an end to the lighting rigs and sound systems that had made the place resemble an off-shoot of Glastonbury festival. Those who don’t regard Shakespeare as the precursor to Jean Michel Jarre may be happier bunnies but there’s a snag: Hamlet and As You Like It are veritable orgies of egalitarianism.

“All the world’s a stage,” as that famous soliloquy by melancholy Jaques has it – but the roles in the 50/50 gender-split ensemble launching the 2018 season haven’t been allocated with deference to ‘patriarchal’ precedent. Hamlet is played (very finely, actually) by a woman (Terry), Ophelia by a bloke (Shubham Saraf); she/he, raging and reeling about the stage, tells the restrained and demure him/her to “get thee to a nunnery”, shouting in his face. How’s that for putting the boot on the other foot? When the Prince says “So, gentlemen, with all my love I do commend me to you” the ‘gentlemen’, Horatio and Marcellus, are Catrin Aaron and Tanika Yearwood wearing male garb but there’s no male actor in view.

Over in As You Like It, answering the core identity confusions with a heap more, there’s an even more pronounced sense of switcheroo. The diminutive, boyish Bettrys Jones plays Orlando, while the gangly Jack Laskey is the heroine Rosalind; whenever the pair came into close proximity, I pictured Ronnie Corbett beside John Cleese in “the Class sketch”; slight shades too in Laskey of Les Dawson?

As You Like It? It’s as they damn well please. Gender-blind? Tick. But also colour-blind and disability-blind – in perhaps the most striking touch, Nadia Nadarajah – who’s deaf – plays Rosalind’s cousin Celia. You won’t have heard famous lines like “You have simply misused our sex in your love-prate” delivered this way, to wit un-spoken, before. She uses sign-language – inviting confusion in us, but also generosity. And Hamlet – most misfitty of Shakespeare heroes – leads the way in embracing this break from the norm when Nadarajah crops up as Guildenstern, Terry accompanying that “Denmark is a prison” speech with more evocative gesticulations than you’ll see during a street altercation in Italy.

Bettrys Jones as Orlando and Jack Laskey as Rosalind in As You Like It Credit: Tristram Kenton

Both plays – written round the same time – depict stifling, repressive courts – Hamlet finds his release, tragically, in death; the escapees from the clutches of Duke Frederick meet with comic bewilderment in the forest of Arden. The thrust of this pairing, then, is to loosen the confining shackles of convention the better, in theory, to honour the imaginative liberality of Shakespeare’s model. It hands the reins back to the actors (there are co-directors, Federay Holmes and Elle While, but they’ve shaped what has emerged, collectively, in rehearsals). The play’s the thing, the company itself, so often playing against ‘type’, is the conceit.

Some will fume that it’s a case of never mind the quality, feel the quota – poetry sacrificed on the altar of orthodoxy. Yet the overall mood is more tongue-in-cheek than that, more joyful, finding the flux in Shakespeare, not imposing a new fixity. Yes, the Eurovision levels of gender-bending are pushed to breaking-point. Call me old-fashioned but I’d have rather seen Laskey as Orlando, Jones as Celia, Terry (underused in the comedy) as Rosalind and maybe Nadarajah as part of a double-act with Touchstone (a klaxon-honking Colin Hurley). Yet the risk-taking, albeit hit and miss, still throws up more illuminations than a fancy lighting kit.

Richard Katz, Nadia Nadarajah and James Gamon in As You Like It Credit: Tristram Kenton

You get the sense of things having occurred spontaneously in rehearsals – even in performance – and being incorporated. Lots of little details reach wide – “He was a man, take him for all in all,” says Terry’s touchingly still, grief-stricken Hamlet, gesturing round the Wooden “O”, bringing the loss of his royal father into the circumference of ordinary experience. By contrast, Pearce Quigley’s wonderfully off-hand Jaques in As You Like It gets a big laugh looking morosely out into the auditorium on being asked what the nonsensical ‘ducdame’ means in the verse he has composed: “Tis a Greek invocation to call fools into a circle”. The joke’s on us, yet the gesture isn’t combative, ‘tis but a nudge and a wink. A promising start.

Until Aug 26. Tickets: 020 7401 9919; shakespearesglobe.com