It's one of the world's best-known car names – five million built, masses available on the used market, desirable and statement-making. But buying can be a gamble: with potentially big wins... and even bigger losses.The Mini, re-bred by BMW in 2001 as a 21st-century take on the 1959 original, has been available in a bewildering array of models and variations. But the three-door hatchback is, to many, the purest version of the "new Mini".It's this version – despite being twice the weight, 2ft longer and 1ft wider than the original – that conjures images of nippy, smile-on-the-face driving, and one badge in particular embodies the Mini's charms, having done so since 1963: Cooper S.Fast, fun and cheeky, the Mini Cooper S outpaces larger, supposedly faster, cars across country or in motor racing. All are brilliant fun, but while most affordable used Cooper S hatchbacks look broadly the same, buying one can be Mini roulette.I'm on my third Cooper S, having owned a delightful 2005 car, a disastrous 2009 example and my current 2012 model, so I know which models to covet and which to be wary of. Here's how play the numbers game.Writer Iain Macauley with his modified 2012 Mini Cooper S - Paul Cooper1. Narrow the fieldHere I'll focus on 2002-2013 Cooper S. The most accessible and affordable Mini for maximum fun are 2002-2006 and 2010-2013 cars. Post-2013 models are good, but enthusiasts say they are more like driving a BMW than a Mini. As for the 2007-2010 Cooper S? They can appear to be bargains, but beware the N14 engine… that may not be such a lucky number.2. Consider the ChiliBefore discussing the various engines (good and bad), cars with the optional extra Chili Pack are the most sought-after. The pack includes stiffer suspension, larger wheels and tyres, sports seats, air-conditioning, Xenon headlights and, on earlier cars, a limited-slip differential that helps prevent the wheels spinning under hard acceleration while aiding handling and roadholding.3. Hone in on the R53 with a 'facelift'The original BMW Mini Cooper S (2002-2006) was known as the R53 and had an engine designated W11. It was a Chrysler design, re-engineered as a Tritec in a joint venture led by BMW. The original version (2002-2004) developed 163 brake horsepower (bhp), with the next "facelift" model (2004-2006) having 174bhp because of a modified and more reliable supercharger."The 'facelift' R53 Cooper S is the most desirable, a modern classic," says David Young, BMW Car Club Mini "Captain". He has covered hundreds of thousands of miles in an array of earlier BMW Minis after ordering his first R53 on launch day. "Modern Minis have lost all their personality by comparison," he says.Experts agree that the so-called 'facelift' R53 Mini Cooper S is the most desirable of the modern BMW versions - BMWDes Roper, of independent specialist Signature Mini in Lancashire, agrees – albeit with a caveat: "The R53 is just so much fun. But they are horrendous on fuel, lucky to exceed 22 miles per gallon," he admits. "But they are bulletproof, provided they have been maintained properly. Early to mid-life R53s are definitely modern classics."Part of the appeal is the unique engine noise as a result of the R53's power-boosting supercharger, that emits an intoxicating whine when worked hard.4. Treat the 'bargain' R56 with cautionThe R53 was replaced with, as it turns out, an occasionally frighteningly unreliable R56 model of the Cooper S. With the larger R56 Mini came a new engine: the N14. Designed by Peugeot, this unit quickly gained a reputation for imploding.Phil Thexton, a Mini service specialist at PT Engineering, that works closely with Signature Mini, says the prime issue was that the R56 lacked a low engine oil level warning light. That – combined with the N14 burning oil at an alarming rate and manufacturer-recommended 15,000-mile service intervals – meant engines were easily damaged because owners sometimes unwittingly drove around with virtually no oil.Mini Cooper S models between 2007-10 have become known for their engine troubles - Drive Images/Alamy Stock PhotoThe most obvious sign of impending doom is the "death rattle", according to Thexton. This indicates that the timing chain could be about to snap, meaning that myriad engine parts spinning at thousands of revolutions per minute suddenly all collide.Preventative measures such as a £500-ish timing chain replacement and fresh oil can help avoid such disasters – and a replacement engine costing thousands.I found this out the expensive way. I had bought a great-looking R56 Cooper S with an N14 engine. I checked the oil before I drove it home – clean and fresh – but the engine blew within 50 miles. A history of neglect had been masked by a pre-sale oil top-up. Rather than pay a repair bill greater than the value of the car, I sold it at a loss.5. If you've got an N14 engine, service it often"Never mind 15,000 miles or two years between services, do it every 6,000 and check the oil level every week," advises Thexton. "I run a Cooper S with an N14 engine. It has now done 114,000 miles, but it has been serviced frequently and shows no sign of problems."The damage can be done early in a car's life, so make sure there's a thick wad of service history and evidence of frequent oil changes."Roper, Thexton and Young all agree that an R56 with an N14 engine can appear to be a bargain. The gamble is in whether it is hiding imminent expensive failure, or whether it has been pampered.The Mini Cooper S: fast, fun and cheeky, but still a gamble when bought second-hand - Checkmate Media6. Read the small print – and ignore the manufacturer's adviceMost adverts will state whether an early Mini is an R53 or an R56. Some might also mention whether it has a potentially troublesome N14 or the later N18 engine.The N18 is far more tolerant of longer service intervals, says Thexton, burning oil at a slower rate. "But ignore the manufacturer's recommended service intervals and change the oil every 6,000 miles," he advises.My own 2012 Cooper S, shown above, is a Coupe model designated R58 and I bought it at a bargain price as a dealer trade-in. It had an extensive dealer service history, but it also had a misfire… which I cured with £64 worth of spark plugs. Not everyone is so fortunate.7. The expert verdictAll of our Mini experts agree that the R56 with an N14 engine is a gamble. However, the more recent N18 is worth considering as long as it has enjoyed frequent oil changes.Yet they are unanimous in their belief that the Mini sweet spot is an original and well-serviced Cooper S R53 "facelift". It will not only be a pleasure to drive and fun to own, it could also turn a handsome profit when you sell it.Try full access to The Telegraph free today. Unlock their award-winning website and essential news app, plus useful tools and expert guides for your money, health and holidays.