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The Arithmetic of Winning at Lotto

September 11, 1988

This is to correct the calculations presented by Don Payne.

Payne's calculations are correct only under the following terms of reference: the same number can be chosen more than once; the chosen six numbers must be in a particular order.

The actual requirements (praise the lotto gods) are: a number can be chosen only once and the six numbers chosen can be in any order. Therefore, the number of ways (or combinations) in which 6 numbers could be drawn from 49 is:

494847464544 = 13,983,816

654321 Any chances of my paying off the mortgage on my house and taking my wife out to dinner are therefore, on any 1 ticket, about 1 in 14 million -- not the 14 billion Payne has proffered.

Incidentally any Junior Cambridge/Middle School student of Montfort Boys' High School, Yercaud, Madras, India, where I first learned the equation 42 years ago, could have identified it. I am advertising the school because, having been in your great country 9 years now, and being homesick enough to want to make contact with Old Montfortians, I am hoping that you'll be a good sport and print this letter.


Mission Viejo

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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