Firstly: the controls, whether you're free-running or swinging a sword, are easy to learn and fairly simple to master. The first thing you'll need to remember is that A now allows you to jump, there's no pre-loading your jumps so you can just leap off at the end of a wall-run. Pressing B allows you to interact with the various rings that are situated on the walls and so on, letting the prince extend his wall-run or catch onto another ring.
There are several new acrobatic features in the game, including that of the roof-run. When the prince is against the ceiling of an area and there's a place this trick can be performed, a quick press of the A button will send him running upside down along the roof and if there's a ring, you can tap B to extend that even further. You can slide down walls thanks to the prince's sharp taloned metal gauntlet, so no longer do you need to worry about finding the right tapestry to shred.
Many of the acrobatics are based on wall-runs, extended moves, pole swinging, wall grinding and using Elika's magic to help you leap further.
By pressing the Y button Elika will reach out and hurl the prince a greater distance allowing you to get to distances you normally couldn't reach. The game will let you know this since all the colour bleeds out of the world as you jump towards the further point, time your Y press correctly or you'll end up falling. This brings me to the important point: THERE IS NO DEATH in this game. If you fall, Elika will save you and deposit you on the nearest safe platform. If you get swallowed by the corruption, Elika will save you and pull you out of harm's way. If you're knocked off a platform or about to be killed in combat, Elika will save you.
You might think that removes a lot of the challenge, and yes, it does in a way. It is also a gutsy move on Ubisoft's part to mess around with a core mechanic of so many other games and that's what makes Prince of Persia different and enjoyable. I haven't had to interact with a Game Over screen, I haven't had to really bother with a menu apart from the in-game map where you can set a destination and use Elika's magic compass ability (Y outside of combat and greater jumps) to point the way.
In battle the combat is cinematic; it's a gorgeous tweak of the Assassin's Creed combat system. There are small simple quick-time events where you have to press a button to avoid an untimely demise (where Elika saves you) or counter an opponent's furious barrage of attacks. Timing is essential and it can really be broken down like this, you can block, time your block correctly and you'll get a chance to strike your enemy whilst they reel from the impact.
You can attack with a sword (X) and Elika (Y) along with your gauntlet (B) and acrobatics (A) in various combinations. There are at least 20 hit combos that are possible (though I haven't managed it yet) in the game and the combat system is beautifully fluid when you get to grips with it. It does seem rather simplistic at first until you work out the nuances. The strength in the combat system comes from the fact that it's not legions of bad guys, these are all varied boss characters (even Ahriman's rank and file warriors are dangerous) with their own set patterns of attacks, defences and even special moves.
It's worth noting that you can also taunt the enemy by using the left trigger in battle. This will allow the prince to snap out some amusing one-liners based on his opponent at the time and can give you an advantage by making them angry.