I'll freely admit that the chief reason I was keen to see the RSC's current production of Richard II was the promise of David Tennant in the title role. My previous experiences of the play had left me with an impression that it was one of the duller Shakespeares.

Having seen this production, I'm a total convert. In director Gregory Doran's hands, the piece has pace, wit, emotional depth, and characters you can root for (even if you are sometimes left shaking your head at some of their choices). There's plot and political intrigue galore, but never of the sort that leaves you wondering who those last six lords were and which side they're on: it's always clear what's going on. All in all, it's a compelling and frequently moving story, well told.

Tennant's portrayal of the eponymous king proves – if further proof were needed – that he has a range that extends far beyond Doctor Who and comic roles. His Richard is a slight, almost girlish figure, but though he may be effete, capricious, and inclined to become sulky if he doesn't get his own way, he's neither weak nor shallow. There's a steelier layer below the surface, and real human vulnerability and affection under that, and Tennant shows us all this and more over the course of the evening. It would be perilously easy for the character to be unlikeable, but he isn't: exasperating, perhaps, and sometimes even annoying, but Tennant does a masterful job of keeping him constantly sympathetic.

But excellent though Tennant may be, he's not the only fine actor in the cast. Oliver Rix tugs at the heart-strings as the youthful Duke of Aumerle, while Emma Hamilton is both strong and sensitive as the Queen. Oliver Ford Davies gives a characteristically solid performance as the Duke of York, and he – along with many of his fellow cast members – is adept at mining more humour from the text than you would have thought possible. The shifts in mood between sombre episodes and the lighter sections are handled with ease. There are also some wonderful cameos: I was disappointed not to get to see more of Antony Byrne as Mowbray and Marty Cruickshank as the Duchess of York, to name but a couple.

There are occasional lapses: the odd moment of overacting and some rather unconvincing stage crying from some cast members (though also some moments of real pathos: it's hard not to be moved by Jane Lapotaire's Duchess of Gloucester's tear-stained face in the opening sequence). This production also chooses to make a small but significant change to the events which end the play (a choice also made in the BBC's recent Hollow Crown version), which may upset some purists. I wasn't personally convinced: while arguably it does make the plot hang together better dramatically, for me it doesn't quite ring psychologically true for the characters as they'd been developed up to that point.

It's not easy to get a ticket for this production: most performances are already sold out. But those who are lucky enough to be able to see it won't be disappointed: it's a complex, rolling, many-splendoured drama that will keep you hooked until the final moments.

Richard II runs in Stratford-upon-Avon from 17 October to 16 November 2013 (previews from 10 October) before transferring to the Barbican Theatre in London on 9 December for a seven-week run. The production will be broadcast to cinemas worldwide on 13 November 2013 as the first production in the 'Live from Stratford-Upon-Avon ' initiative.