Nintendo has often flouted the mediocre-game rule of thumbs — bad plural pun intended — for new consoles, which has added to the frustration of Wii U owners. The company built its reputation in 1985 with the Nintendo Entertainment System, which came bundled with Super Mario Bros., one of the greatest video games ever designed.

An early game for the Nintendo 64 in 1996 was Super Mario 64, which players regard with similar reverence. It brought Mario, the jumpy Italian plumber into three dimensions for the first time and inspired the creators of the open-world Grand Theft Auto games, among others. And, of course, the original Wii came packaged with Wii Sports, one of the very best games for that system. It remains the purest execution, for any system, of the power of motion controls to add realism to play.

Now, with Super Mario 3D World, Nintendo has at last delivered the kind of game for the Wii U that its players probably expected from the outset. Like the best Mario games, Super Mario 3D World is a surreal celebration of play and exploration. It’s a dazzling display of shifting perspectives, with an inventive use of light and shadow.

Mario has been with us long enough that the fundamental strangeness of these games may be wearing off. It’s not particularly clear why Mario — or Luigi, Toad or Princess Peach — is collecting green stars, breaking blocks and jumping on flagpoles. Nor is it clear why, in the game’s most prominent new trick, the characters can use a bell to turn themselves into cats. Or why they eat cherries that create doubles of themselves, or why they glide on trapezes, ride giant ice skates and clamber atop stone cubes tumbling through a lake of fire. Or why the villainous Bowser, in his newest incarnation, is the leader of some kind of disco circus.

In these games, none of the why matters. Except perhaps, for players who have been with the series for almost 30 years and know the back story: Princess Peach has been ritually kidnapped by Bowser only to be rescued by Mario more times than Batman has battled the Joker. In a Mario Bros. game, to take control of a no-longer-helpless Princess Peach and enable her to defeat her longtime nemesis is an act of cathartic vengeance on the order of the far more realistic violence carried out by characters like Beatrix Kiddo in “Kill Bill” or Lisbeth Salander in “The Girl With the Dragon Tattoo.”

One great game won’t save a console. There are other good Wii U titles, but the console’s lineup is still pretty thin, especially in comparison to Nintendo’s own hand-held 3DS, which has shipped almost 35 million units worldwide in its two and a half years on the market, including more than 11 million in the United States.