Schrodinger’s lottery ticket

19th March, 2005

Dear Economist,
My lottery ticket, the physicist Erwin Schrodinger tells me, is the winning ticket up until the moment of observation. Thus from Saturday evening through to Sunday morning, when I check my numbers, I am a millionaire. How do I best capitalise on this newfound wealth?
— Joseph Kelly, Carlisle

Dear Mr Kelly,
Regrettably, anyone wishing to securitise the indeterminate winnings and pay you accordingly is likely to insist on observing the ticket, thus ruining an interesting prospect.
In general, lottery tickets have a very low expected value because the chance of winning a million pounds is much less than one in a million. You may take those odds anyway because you love risk. To be consistent, you should cancel your house insurance and enjoy the thrilling possibility that it may one day burn to the ground.
Still, it is possible to buy lottery tickets with a positive expected value, according to finance professor William Ziemba. In many lotteries, jackpots are shared when people have the same numbers, so your expected winnings increase if you pick unpopular numbers (historically these include 32, 39 and 40 – which are never chosen by people who choose birthdays as numbers).
Unfortunately even if you play all over the world you should not expect to win for several thousand years. A faster way to win, while guaranteeing excitement, is to choose six numbers but not buy a ticket. The expected value of this gamble is usually positive, while the nail-biting thrill of watching the draw and praying that the numbers don’t come up has to be experienced to be believed.

Luck helps too. Professor Ziemba reports that one winner chose the number 48 because he “dreamed of the number seven for seven nights in a row, and since seven times seven is 48…”

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