Playing Disneyland's numbers game

PUBLISHED : Thursday, 30 August, 2007, 12:00am
UPDATED : Thursday, 30 August, 2007, 12:00am

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.

To make it simple, let's say 100 fans with no contact with each other want to visit Disneyland regularly. Because the park is so small, a visit is enjoyable only when fewer than 60 of them show up on any one day.

They don't know anyone working at Disney, so they have no advance information about the number of people coming each day; and, as they don't know each other, they can't share past experiences. All they have are their own experiences from previous weeks.

A player will go if he or she thinks a visit will be enjoyable (that is, there are fewer than 60 visitors); otherwise, he or she will stay at home. If everyone analyses the problem the same way and takes the same alternative, everybody loses. Hence only a minority can win. Each player will form various hypotheses to predict the following week's visitor numbers from the previous weeks' figures. (Incidentally, this maths game also captures something of the essence of technical analysis, the voodoo art of trying to predict future stock or currency prices from past movements.)

Alas, I never learned what the best guesses were, because I was stupid at maths. However, I did tell my economics professor that the real moral of the game is that the bar owner, in this case Disney, is never going to make money. She was not impressed.

But, as far as I can see, size does matter. When it's enjoyable for you and me to visit, Disney starts losing money - so it has to work to attract so many people that most of them wouldn't want to visit. Back in the real world, the only way out is for Disney to expand and build more facilities - and not to force us to play the game. But will it bite the bullet?

Alex Lo is a senior writer at the Post