Guesstimating

I recently read a review of the book:
Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin by Lawrence Weinstein & John A. Adam

The authors encourage their readers (and their students) to have a feel for the size of numbers, and developing the skill of estimating reasonably accurately the scale or size of some measurable event or situation. The publisher's website for the book gives some examples, as well as a pdf of the first chapter. Something in the latter intrigued me. Suppose that there is a lottery with a hundred million tickets. If all those tickets were piled high, what would the height be?

In the UK, there is a National Lottery with about fourteen million different entry tickets. Like many university lecturers, I have used it for examples of simple (and not so simple) probability and statistics. So I started to wonder how high the pile of cards would be for the UK National Lottery. Following Weinstein and Adam, you start by thinking how thick a ticket would be, and conclude it is somewhere between 0.1 mm and 0.2 mm (a pack of 500 sheets of paper for the computer printer is 5cm thick, and lottery tickets are thicker). If we work with the smaller figure, we are talking of a stack 1,400,000 mm high, or 1,400 metres, or 1.4 kilometres. The figure is more than this, but less than twice, so we may as well call it 2km. Now we have a sense of the small probability of winning. 2km is higher than the highest mountain in the UK. Put that stack down, along a straight road; now it will take 20 minutes to walk from one end to the other, with just one card being the winner.

Guesstimating the size of things has more serious applications than this, but I am pleased to see that a publisher thinks it is worth putting a book like this in the marketplace. O.R. people use guesstimates quite often, to get a feel for the rightness of an answer, or a feel for the problem. In the early days of O.R., in the UK in the second world war, Winston Churchill heard of a ship crossing the Atlantic with a load of dried egg and asked one of his scientific advisers to estimate from the tonnage of the ship how many eggs were in the ship. The serious business of war was held up while the adviser worked it out, on the back of an envelope. Weinstein and Adam would be proud!