On the evening of 1 December 2020 the South African PowerBall machine released five balls, and they came out in order: 5, 6, 7, 8, 9. The powerball, drawn from its own drum, was 10.
The reaction was immediate and almost unanimous. A sequence like that does not happen; therefore something had happened. The National Lottery Commission examined the draw and reported finding no irregularity, which convinced roughly nobody, because the objection was never really about evidence. It was about the feeling that 5-6-7-8-9 is not the kind of thing a fair machine produces.
That feeling is wrong, and it is wrong in a way worth being precise about.
A South African PowerBall line is five numbers from fifty and one from twenty. There are 2,118,760 ways to choose the five, and twenty powerballs to go with them: 42,375,200 outcomes, each as likely as the next. The sequence had exactly the same chance as the draw the week before and the draw the week after. It is not a rarer event; it is an event we have a name for, and names are what make some outcomes feel like signals.
The Split
South Africa’s PowerBall, 5 from 50 with a powerball from 20. The jackpot that night was R113,769,364.20. Move the winners.
Chance of any one line winning: 1 in 42,375,200 — unchanged, whatever the slider says. Each winner takes R5,688,468, against R113,769,364 alone.
Twenty is not the slider’s invention: it is what the prize table for 1 December 2020 records. Across the 1,711 draws of this game we hold a prize table for, the median is nought and 89% have no jackpot winner at all. The previous record was four.
If every line were played equally often, this many winners would be expected on 0.13 of a night’s draws. For 20 to be the ordinary outcome the line would have to be held 154× more often than an average one. No measurement of how popular individual numbers are comes close, because what made that night was the shape of the line rather than the numbers in it.
So the balls did nothing remarkable. Here is what was remarkable.
Twenty tickets matched all six. In the 1,711 draws of this game for which we hold a prize table, the median number of jackpot winners is nought; the mean is 0.13; eighty-nine per cent of draws have no jackpot winner at all. Before that night the record was four. Another seventy-nine tickets matched the five main numbers without the powerball, against a median of two — nearly four times the previous high of twenty-one.
Nothing about the machine explains those numbers, and nothing needs to. They are a fact about the players. Thousands of people, independently, had decided that 5-6-7-8-9 was a line worth writing down — some as a joke, some because it is easy to remember, some precisely because they had been told it would never come up. When it did, they discovered what they had really bought: not a smaller chance, but a smaller prize.
Each of the twenty took R5,688,468.20. One winner would have taken R113,769,364.20 alone.
This is the only sense in which some lines are worse than others, and it has nothing to do with the balls. Every line has the same probability. Lines that look like something — sequences, birthdays, the diagonal of the play slip, the numbers on a fortune cookie — are held by more people, so they pay less when they land. You cannot improve your chance of winning. You can, in a small and entirely reliable way, improve your chance of not sharing.
The commission was right. The public was right to look. And the draw remains the clearest demonstration this database contains that a lottery's biggest surprises are usually facts about us.