It’s no coincidence that in the next line of that number, Elvis announces: “I’ve got a whole lot of money that’s ready to burn.” Despite the diversification into all-round entertainment, this city will always thrive by separating fools from their billfolds.

The cavernous, blinking, clanking casinos are still the town halls of Vegas, where you’ll be regaled by signs commemorating the insane jackpots collected by lucky Iowa housewives — “It happened here!” — and be befuddled by the purposefully labyrinthine floorplans, the cunning lack of signs and clocks, and the obsessive obliteration of any pesky time-revealing natural light. There may be no truth to the urban myth that the casinos pump pure oxygen through the air con to keep clients awake, but the air is certainly cool and sweet, adding to the impression that sitting at a table and opening your wallet is strictly for the suckers.

However, it’s a finer calculation than you might think — because gamblers get free, generous and decent-quality food and drink, and even the odd free night. How it works, in theory, is that you get the house “edge” back in kind — the edge being your statistical, unavoid-able rate of loss. For example, most slot machines will keep about $5 for every $100 gambled, but during the 30 minutes or so that would take to do, you’ll get a $5 drink.

Spend an hour playing $10-a-go roulette and statistically, you’ll be down $15-$20, and due lunch at the $17-a-head buffet. To claim these “comps”, you need to join your casino’s gamblers’ club, which is free and easy, and your gambling time will be monitored and rewarded. Simple! But — and this is the “but” that built Las Vegas — casinos have another source of income. The “hold” is the real amount of money that gamblers leave behind as a result of bad tactics, desperation, drunkenness and inexperience. And that averages $120m (£64m) a week.

On balance, unless you have the self-discipline of a lama, or plenty of experience of playing cards for cash, steer clear. There are much more enjoyable ways to throw your money away in Las Vegas.

NOW, CHOOSE YOUR HOTEL

In Vegas, you can stay wherever you want — Venice, Paris, New York, imperial Rome, colonial Singapore, mythical Arabia, ancient

Egypt, even 1950s Las Vegas. After 15 years of ever more extravagant hotel launches, the city’s famous Strip now offers the most awe-striking accommodation in the world. These are my choices — thankfully, as all hotel shops and restaurants are open to nonresidents, you can gawp and giggle at the whole lot during your stay.

For tasteful travellers, there are two options. The undoubted princess of the Strip is the Tuscan-themed Bellagio (00 1-888 987 6667, www.bellagio.com; doubles from £84), which combines restrained decor with wholly unfettered opulence — the fountains alone cost £21m. Or, to really feel like a high roller, pick the brand-new Wynn Las Vegas (702 770 7100, www.wynnlasvegas.com; doubles from £126). America’s most expensive hotel has no strict theme, but it does have top-notch rooms, lovely pools and glamour to spare.

Then there’s the “extravagant to the point of insanity” bracket — which may well be more fun. The Venetian (888 283 6423, www.venetian.com; doubles from £89), with its indoor St Mark’s Square and Grand Canal Shoppes — “shoppes”? Venice? — is simply absurd, but it also has two Guggenheim museums on the grounds, and some of the most fashionable bars in town.

Times recommends

• 10 of Rough Guides' best images
• How to do Florence for free
• The UK and Ireland's 25 best Christmas events