Professor Dirk Laurie, mathematician

Vic Christie has observed that there have been quite a large number of repeated pairs in the winning numbers: after the first seventeen draws, no fewer than sixteen pairs had appeared more than once, with two of them even appearing three times.

This is at first glance surprising, since there are C(49,2)=1176 possible pairs and only C(6,2)=15 of them appear in any one draw. One might therefore think that it would take 1176/15=78.4 weeks before a pair is repeated.

What the above argument finds, however, is not the average time between repetitions, but the maximum possible time. It is impossible to have more than 78 consecutive draws without repeating a pair, since too many pairs have then been used up.

It is fairly easy to calculate what the chances are that a pair is repeated from one draw to the next. Using the table that appeared in my column "How many ways are there to play Lotto?", one finds that the chance that a ticket has at least two numbers right is 2111774/13983816, or about 0.151.

Now suppose that you never heard the proverb "lightning does not strike twice in the same place" and went out and bought a ticket with last week's winning numbers on it. Your chance of having at least two numbers right is 0.151, and that equals the probability that at least one pair from last week's draw has been repeated.

We can crudely approximate the chance that no pair from the previous k draws has been repeated by

k |

1-(1-0.151) |

The actual chance is a bit lower because this approximation does not take into account that pairs get used up. For k=4 we get 0.52, a little over half, and thereafter it drops to under a half.

Therefore in any particular draw it is more likely than not that some pair from the previous five draws will appear again.

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