How can you win the lottery: the basics

Worked through by hand, "How can you win the lottery?" begins with the pool. The odds of winning the lottery follow from counting. A draw picks a set of numbers from a larger pool, and every possible set is equally likely, so the chance of one ticket matching the whole set is one divided by the number of sets. What those odds look like depends on the size of the pool and on how many numbers are drawn, and the counting is the same for every game of the kind.

What is lottery odds for one person holding one ticket? The same number as for everyone else. Your chances of winning the lottery do not grow with loyalty, with a lucky shop or with years of play, because each draw starts fresh. The honest answer to what my odds are is printed in the game rules: one chance for every combination bought, against the full count of combinations the draw permits.

A lottery odds calculator does the counting for any pool: enter how many numbers are drawn and from how many, and it returns the odds for each tier. For multiple tickets the calculator simply adds the chances, since each ticket covers a different combination. Ten tickets in a draw of fourteen million combinations give ten chances in fourteen million; the odds improve in step with the money spent, never faster.

Common doubts

What is one in fourteen million as a percentage?

About seven millionths of one percent, a figure so small that most people take it for zero.

Do extra tickets improve lottery odds?

Chances grow in proportion: ten different tickets in a draw of fourteen million give ten chances in fourteen million, never faster than the money spent.

How are odds for smaller prize tiers worked out?

Each tier needs a partial match, and its odds come from counting the ways to hit some drawn numbers while missing the rest.

What does a lottery odds calculator do?

Enter how many numbers are drawn and from how large a pool, and the calculator returns the odds for every prize tier of that game.

What is the hypergeometric distribution in lotteries?

The pattern of drawing numbers from a pool without putting any back; it gives the exact probability of matching three, four or five numbers, and the tier table writes it out.