2 1. You Can’t Beat the Odds

Many lottery players imagine that they can outwit chance by

choosing numbers that have not appeared frequently in the past. Such

a strategy is wholly without merit, for chance has no memory. Even

if, say, the number 13 hasn’t been drawn in a long time, in today’s

drawing it has exactly the same probability of being chosen as any

of the other numbers. Other lottery players swear by their own clev-

erly devised systems for beating the odds, but all such attempts are

nothing but wasted eﬀort, for it has been many decades since it was

proven that there is no system that can fool chance.

Let us close with a bit of advice: In fact, there is some positive

action that a lottery player can take, and that is to choose a combina-

tion of numbers that is unlikely to be chosen by many other players.

Then if, by some small chance, one wins, one is less likely to have

to share the prize with a large number of other winners. That, how-

ever, is easier said than done. On one recent occasion, many lottery

winners saw their dreams of millions greatly reduced when it turned

out that the winning numbers, which formed a cross on the selection

card, had been chosen by a surprisingly large number of people.

In the end, however, mathematics has nothing to say about the

sweet feeling of expectation that inspires plans about all that one

might do with one’s fabulous winnings. I wish you good luck!

And Why Exactly 13,983,816?

How does a mathematician arrive at the pre-

cise number 13,983,816 of possible selections

of lottery entries? Choose two numbers, let’s

call them n and k, and let us assume that

n is larger than k. How many diﬀerent k-

element subsets are contained in a set of n

objects?

While this may seem an abstract math-

ematical question, it concerns us directly in

the question of the lottery. A lottery entry is, after all, nothing other

than a selection of six numbers from among the numbers 1 through

49. So in this case we are dealing with the numbers n = 49 and k = 6.