And for something that comes from an era where there were such things as Fred Savage movies, Mario 3 has aged well. It still looks brilliant, for one thing, lustrously basking under peachy skies and filled with little lo-fi gimmicks, such as the flashes of light that dance rhythmically across the game's bricks or the subtle sense of three-dimensional depth as Mario's head wobbles when he runs. The ragtime soundtrack - with a bold blast of reggae when you reach Sky Land - still holds up, and there are plenty of stylish flourishes, such as the dandy zig-zag strip that marks each level's transition to night as you approach the finish line.
When you take Mario games apart - particularly the early ones - it can be like unpicking the dry specifics of a dazzling magic trick. Where's all the fun gone? Mario at his most basic is just running and jumping. The secret, though, lies with the way these basics are handled. The Mario designers tend to treat the simple things as if they aren't that simple. Instead, they seem to spend ages getting them just right, tweaking inertia, weight, and stickiness, until just running and just jumping are fun in and of themselves.
Then, of course, they feed in the extra stuff, and it's the extra stuff that defines Mario 3.
Above all else, Super Mario's third adventure is filled with secrets - filled in the same way that the best Simpsons episodes are filled with jokes. This is the kind of density designers only arrive at by going back over things again and again, by sneaking in one last thing, and then one other last thing because they just can't help themselves.
The first Super Mario game is hardly shy about layering in concealed treats, but there were so many hidden, unlikely Easter eggs in Super Mario Bros. 3 that you could spend a fair amount of time simply looking for things that weren't actually there, wrong-footed by cruel playground hoaxes that had you defeating roving Hammer Bros. in specific locations, or being eaten by that huge fish in 3-3 when the timer hits a certain number. (Being eaten by that fish, incidentally, remains one of the few genuinely horrible moments in a Mario game. It's up there with the sequence in Dark World where the hands reach up and pull you off the map.)
Even when you were looking for things that did actually exist, the breadth of asides and gimmicks can still be staggering. Most levels will have hidden power-up blocks, coin-changers, or the odd magical musical note tucked away somewhere, many will have secret areas stuffed with coins and clouds to run around on, and a handful will feature secondary exits that let you collect the ultra-rare Warp Whistles.
Meanwhile, there's an unprecedented range of power-ups to mess about with, too. We remember the classics, like the Raccoon suit or the Frog outfit - pure evil if you fire it up for the wrong challenge - but Mario 3's also home to one-shot oddities like the Goomba Shoe, making its series cameo in 5-3, and allowing you to do the unthinkable, such as stomp on Bob-Ombs without sending them into countdown mode, or finish off spiked enemies from above. It's a crazy idea in a slightly crazy game, and to prove all that, you'll find it in a level that has the audacity to kick off by scrolling right to left.
Playing Mario 3 today, it's heartening to discover that the game's as difficult as I remember it, too - although difficulty in Mario games is often a subjective, rather personal matter. Close as it is to the start, the treadmill miseries of 1-4 or 3-2 still trouble me far more than a lot of the things that lands 6 or 7 will throw my way, just as the Cheese Bridge in Super Mario World strikes me as being far harder than most of that game's Star Road challenges. Whichever bits tend to do you in more than they should, spare a thought for anyone who has to face those tanks in Dark Land, though. Bristling with cannons, turrets, and flame-throwers, they just keep on coming, and the best you can generally hope for when you've beaten them is a fight with some jerk holding a boomerang.