One hundred years ago today, the San Pedro, Los Angeles and Salt Lake Railroad Company held an auction for 1,200 lots of barren desert, where they promised a new town would soon spring up. In a glimpse of what was to come, the speculators and settlers got carried away in their land lust, and the auctioneers shifted $70,000 worth of dust for a total of $265,000.

Las Vegas was born in a flurry of dollars — and the house had already won.

Yet this is an anniversary that could have been commemorated with nothing more than a street parade and a cake-baking contest in another anonymous Midwest town — had the local lawmakers not decided, in 1931, to ride out the depression on the back of an always reliable source of wages — sin.

In one commandment-busting swoop they legalised gambling, prostitution, no-wait weddings, no-blame divorces and, just for the hell of it, professional boxing. They probably thought they’d generate a few extra jobs, maybe collect enough funds for a new town hall — in fact, they’d just created Sin City. Also known as America’s Playground. Also known as the holiday destination that ate the world.

You know how Americans tell you everything is bigger and better where they come from? Well, Vegas is where Americans go to be impressed. The world’s biggest tourism industry (with 130,000 hotel rooms; no other city on earth reaches six figures) pumps the cash spigot for the fastest-growing city on the continent, a sonic boom town that claims to fulfil every desire imaginable, and many you never thought you had.

Want to visit the Eiffel Tower, the Sphinx, the Statue of Liberty and St Mark’s Square, all within three blocks of each other? No problem. Want to eat dinner surrounded by £30m worth of original Picassos? Why, of course. Want to get married on the bridge of the Starship Enterprise, with Captain Kirk presiding? Full speed ahead, Mr Sulu. Want to see the sinking of the Titanic re-enacted by 60 topless showgirls? Twice a night, with weekend matinées. Want a pride of lions living in the middle of your hotel? Check. Want to win £20m just by putting one dollar bill in a slot machine? Someone did it last year. Want to have a good holiday? Well ...

There’s the rub. Many Brits — particularly those blessed with more than their share of style — could happily serve out 100 years of their own without squandering one day of annual leave on Vegas. Venality and vulgarity, gambling and girls, girls, girls — a good idea for a cable television channel, but not, perhaps, a holiday.

Yet Vegas desperately wants you to think otherwise — it wants you to forget the past 100 years and focus on the lavish new hotels, the world-class restaurants, the art collections, the exclusive shops, the spas. It wants you to believe that you can do Vegas with class.

And can you? Without a doubt — thanks mainly to a new generation of hotel resorts offering style, luxury and, on occasion, even restraint. But let’s be honest, all class and no kitsch isn’t the way to get the best from Vegas — to really love this city, sometimes you just have to set your irony force field to full strength and get stuck into the shamelessly glitzy, unutterably cheesy, high-fat, lowbrow side to America’s Playground.

All together now: “Bright light city gonna set my soul, gonna set my soul on fire...”

THE BIG QUESTION: TO GAMBLE OR NOT?