The very best theory I've ever heard concerning the mysterious way that Mario games get made runs like this: deep inside Nintendo's development structure, you can find people taking care of Mario stuff all the time, aside from specific games. They're just toiling away in the Mario mines, churning out endless ideas for anything and everything - bosses, collectables, enemies, traversal gimmicks, ghost house hallways, the works. Mario is definitely being made, and practically any idea can lie within its remit. Mario is games, and all games - all toys, all play - can eventually be folded in to the mix.

That certainly explains a game title like Super Mario 3D World - just one more Mario title where each new level can be trusted to throw in a one-off idea that's forgotten seconds later. 3D World has a story, but as ever, it drifts to the ether the minute you take your first jump. It's world themes - desert, ice, grasslands - but they're largely ignored as you hop between pools of bizarre brilliance that defy easy categorisation. Autumn, water parks, the circus: each level takes you somewhere different, while every minute of play spools outwards in a friendly 60fps jumble of nutty concepts - perhaps nuttier here than ever before. And yet! And yet that famous Mario coherency still rules - because whatever you encounter in a Mario game reminds you of something else you encountered in another Mario game. Because Mario is games.

Exhibit A: We want to talk about the goomba shoe. You know, the goomba shoe from Super Mario Bros. 3, a single-shot power-up that appears only in level 5-3, where you discover a goomba stomping around in a large green boot - a trunk you are able to steal.

Hardly anybody remembers the goomba shoe, but, behind the scenes, Mario's custodians were playing the long game. Nintendo was just biding its time, twiddling its thumbs, awaiting the right moment to remind everyone about this weirdo footwear. And the right moment - outside the odd cameo in the RPG spin-offs - is level 3-1 of Mario 3D World: a snowy playground in that you move through pine forests and over deep drifts before venturing onto a frozen lake in which a goomba awaits, turning dreamy circles in an ice skate. An ice skate you can steal.

The ice skate's a one-hit deal, but it's great while you have it.

There are always a handful of explanations why this is noteworthy. Firstly, it turns out that the goomba in a ice skate - serious, self-contained, frowning with lofty pride like all too alert to the vital role he plays in Bowser's master plan - is clearly the single funniest thing you might find this year. Secondly, the goomba ice skate is an elegant reminder that even when a Mario game looks a little underwhelming in some recoverable format, even if some have suggested this indicates somewhat phoned-in, well, even then it's still better to reserve judgment.

Like Super Mario 3D Land, then, 3D World is definitely an endless freewheeling treat of a game title, and it starts using what feels as though one of the greatest Mario power-ups of time. Cat Mario is really a near-perfect mixture of all Nintendo's skills: its animations reveal focus on detail condensed by an incredibly childlike level of abstraction, its lock-on swipe attack solves the problem of close-up combat in complex 3D spaces, and that skittering, claws-out scrabble lets you scale the steep walls that will otherwise have hemmed you into these compact level maps. Like Yoshi or the cape in the original Mario World, Cat Mario makes you feel powerful. You can certainly do astonishing things whenever you wield that fluffy uniform, but you're vulnerable too, and you'll wince with fury whenever you lose your toys fumbling over a silly risk.

Cat Mario's the stand-out, nevertheless the double cherry, another 3D World debut, will be the craziest power-up ever. Double cherry chucks in another Mario each time you eat one, each recent addition moving in sync as you race across a map. You can chain double cherries until you're wielding only a little Mario dance troupe, and you are able to split them up and fan them out by bumping them, tactically, in to the environment. Everything you might hope for Nintendo to do with this concept is well and truly covered. Control four of these and you will find they produce a strangely socialist image: a quartet of punchy little comrades bobbing along in braces.

The art direction's still brilliant, and multiplayer's enlivened with a little gentle rivalry as you fight for the crown that would go to the victor of every level.

The cat and the cherries mingle nicely alongside old friends such as the tanooki and the fire flower, the boomerang and a scattering of new weirdo asides which are too good to spoil in advance. They're all slotted right into a game that gives a kind of antic, hyperactive cheekiness - from a level that hides its first collectable behind the starting place to others that drop you into the middle of the action with only 100 seconds on the clock.

With shortish stages - for the absolute most part - and plenty of'em, 3D World is really a creative blur. This can be a game that's thought of as much ways for you to scale that end-of-level flagpole as it has levels that end. Halfway through the whole adventure, you'll suddenly realise that, in the midst with this chaos, somebody's quietly altered the way Mario accelerates, offering some sort of two-speed gear change with a burst of nitro in the middle.

It's typical of Mario's designers, really. Pick a level at random, and you obtain astonishing blink-and-you'll-miss-it invention. One stage I've just chosen more or less blind offers a power-up that turned my head in to a cannon, a view of some goombas relaxing in rubber rings, and a frog that expels huge gobs of coins when stepped on. Moving outwards, the chunky snooker-felt-and-hard-plastic overworld maps that bring these levels together are filled up with lovely details that exceed mere hidden trinkets to search out. Listen hard in World 2 and you'll hear cats singing along with the whistling sands. In World 3, the feet ring out a musical tinkling effect as you shift from running on snow to racing down frozen train tracks.

It's beautiful along with busy, too. While Nintendo stumbled on HD textures late, it's benefited a lot more than most - probably because it's rendering interests that go beyond rust and gunmetal. Mario's world is definitely scattershot in its materials, but 3D World really revels in sending you from an assault course built of quilting to a different made from cake batter. It's gorgeous stuff.

Even Cat Mario's walking animation is ideal - body bouncing gently, head turning to left and right - a cat out and about with nowhere it needs to be.

Other nods to the precise strengths of the Wii U - whatever they could come out to be - are relatively few. There are a couple of levels where you've to prod the GamePad screen to smash crates and raise or lower platforms (or move them about by blowing), and there's off-screen play and Miiverse integration. You are able to share ghost Mii runthroughs, Trackmania-style, and you may also draw on the screen to highlight things for other players (or to annoy them).

By and large, though, you'll have equally as much fun with remotes and nunchucks or pro controllers - more pleasurable, actually, as multiplayer is yet again nestled right near one's heart of the entire experience, letting you pick between the line-up from Super Mario Bros. 2 (Peach really has that hover move, although this has been reined in a little) and turn each level right into a ceaseless, primary-colour barroom brawl where life expectancies are measured in seconds as opposed to minutes. The implementation's as straightforward as you may hope for: it's essentially the multiplayer systems of New Super Mario Bros. Wii brought into three dimensions. The game camera struggles a bit when it's really hectic and you're all headed in numerous directions, however it doesn't matter as much as it would because of array of levels that provide large, open spaces at the start or end. Multiplayer Mario's about hilarious disasters more than precision team-work, anyway. It's concerning the plummet as much as the jump.

If there's an overarching theme to a game title as nutty as 3D World, though, I suspect, like Mario 3D Land, it's regarding variation. Mario's glorious 3DS outing would interrupt the conventional flow of programming every now and then to tilt the camera down and saddle the plumber with the mechanics of Zelda, say, and there is a similar impulse at the office here. This still isn't a great reinvention in the design of Galaxy. Instead, there's a more ad-libbed drive to see how stretchy Mario may be, and to explore how a variety of situations he can be squashed into without changing the basic rhythm of play. There exists a level that employs stealth mechanics, for example, and another where you're cast, from time to time, as a Mario shadow-puppet. There are rhythm action sequences, lock-and-key tasks, and Captain Toad levels where you can't jump at all.

Stealth! No jumping! Mario, inevitably, copes with everything thrown at him, while each stage still manages to stuff in the requisite collectables - in this instance, three green stars to help open progress gates, and cute little icon-printing stamps you can use in Miiverse posts. Meanwhile, the soundtrack is arguably the series'greatest yet - and that's including Super Mario Galaxy 2. It's as lavish and quick-changing while the agenda: Ealing Comedy 1 minute, risqué 70s gameshow the next. The mournful, yawning strings of a ghost house feel just like a true series highlight - this is pastiche at its most skilful, its most panoramic.

Compact by the standards of the Galaxy adventures but nonetheless laden with bountiful secrets, under the warm familiarity of 3D World lies one of many strangest Mario games in years - or at least one of the very random in its influences and its moment-to-moment indulgences. And that is clearly a very, very good thing. The Wii U sees Nintendo's mascot racing into venerable middle age by going wonderfully loopy - by dialling up the vitality, even though the end result is frequently absolutely insane. After every one of these years, who could blame him?

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