Playing Disneyland's numbers game

Acomedian once joked that developers like Li Ka-shing should be applauded for teaching everyone in Hong Kong Einstein's theory of relativity by making space relative - because the size of your flat can vary greatly, depending on whether you are talking about loosely defined 'gross' or 'saleable' floor areas. And every developer has its own obscure method of calculation.

Disneyland, I have observed, has had a similar pedagogic effect on my own children, aged five and seven. They caught their first glimpse of advanced game theory and statistical inference after several hotel stays at, and visits to, the troubled theme park this summer.

Not that they are particularly bright when it comes to maths - just normal for their age. And that's why I really have to hand it to the Disney experience.

Their mathematical insight stemmed from my family's valiant effort as Hong Kong citizens and de facto taxpaying investors to boost the park's falling attendances - and, actually, to make as many visits as possible before our annual passes expired. As the South China Morning Post has reported, Disneyland is expected to achieve a mere 4 million visitors in its second year of business, well below its first year's 5.2 million. This translates into a daily average of less than 11,000, or about a third of its capacity of 34,000.

But even this level of attendance is still too crowded, judging from our experience. Though true Disney fans, our children quickly realised it was no fun visiting on busy days with long queues at every ride and live show. So we tried to guess which days the park would be less busy and worth a visit, based on our experience the week before. We did this for two months during the school holiday, but please don't laugh.

Without knowing it, my youngsters had stumbled on a well-known game-theoretic scenario I read about in university called the El Farol bar problem. The original involves a number of people who all want to go to the same bar, but not on the same night. But, here, let's stick to Disney.

The game is played repeatedly for 'N' number of players, who do not know each other, and have to choose one of two courses of action each time.