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The Arithmetic of Winning at Lotto

September 11, 1988

Don Payne of Anaheim displays his lack of understanding about how lotto works and how to find combinations of numbers.

The odds that he quotes (one in 13.8 billion) would be correct if lotto winners had to pick their numbers in the same order they were chosen by the machine and if a number could be chosen more than once. However, that is not the way lotto works.

According to his odds, there would be something like one jackpot winner every 10 years; not quite the one every two weeks or so we're getting now.

The real number of combinations is given by 49!(6!43!), which makes the lotto odds one in 13,983,816.

That makes a $1 bet on a $35-million prize a pretty darn good wager.



The Times received 15 letters in response to Don Payne's calculations. All but one agreed that the winning Lotto odds are one in 13,983,816.

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