I noticed they raised the Powerball lottery jackpot numbers on the billboard down the street. I take it, nobody won the most recent jackpot, and it rolled over to the next drawing. I’ve never bought a lottery ticket. If I did, I would choose the numbers 1,2,3,4,5,6 because they are easy to remember. When I tell people that, they often remark:
“You fool. Do you know what the odds of that are?”
Well, let’s see. If things work as intended, every numbered ball has an equal chance of being picked as any other ball. That mans ball #1 has an equal chance of being picked as ball #14. The same holds true for the other 5 balls, where any number has an equal chance of being chosen as any other number remaining in the tumbler. That means, any six numbers have an equal chance of any other six numbers, and 1,2,3,4,5,6 has an equal chance of 3,7,16,24,25,41.
The number on the ball is really just a name that identifies that particular ball, and has no mathematical significance. In fact, they could put letters on the ball instead of numbers. If the letters they chose were in alphabetical order, it would only seem miraculous because we have arbitrarily determined what alphabetical order is. If the alphabet was arranged differently (sorry Big Bird), then the order of the lettered balls would no longer seem miraculous. Or, if you identified the balls using squiggles or shapes that have no cultural order, then no matter what six balls were chosen, it would always seem random. Choosing six balls with consecutive numbers only seems miraculous because we have defined what “consecutive numbers” mean in our numeric system. To the universe, it means nothing.
A common bumper sticker says:
“Lottery n. A tax on people who are bad at math.”
Who is the fool now?
I should point out there is some advantage to certain numbers over others. The machine theoretically chooses the balls at random, but the humans playing the game do not. If you choose numbers that nobody else chose, you won’t have to split the jackpot. I’ve heard one strategy that says most people choose birthdays as lucky numbers, and you increase your chances of not having to share the jackpot if you choose numbers higher than 31. But of course, you have to win first.