The Irrationality of EuroMillions

Away from the Olympics, there has been a massive rush for lottery tickets ahead of tonight’s £105 Million Euromillions Draw.

Its not really new or interesting to point out how irrational playing the lottery is.  Playing the lottery is often called “a tax on stupid people”.  It is not only irrational in the sense that people pin their hopes on something extremely unlikely to happen, but also economically irrational.  The ‘expected return’ (a function of the probability and the amount invested) is much less than other types of gambling too.  The odds of winning the UK lottery jackpot are 13,913,816 to one, which suggests thatyou should win at least £13,913,816 on a £1 stake, should your six numbers come up.  Instead, the lottery jackpots are usually much lower (typically about £2 million).  That’s like getting only £15 winnings after putting a quid on a 100/1 horse at the Grand National!

However, playing the UK lottery does become economically rational if the rollover jackpot goes over £14 million, because then you’re actually taking a bet with a better return than the odds would suggest.  This happened frequently in the past, though less so in recent years as the popularity of the Lotto decreases.

There’s no such benefit with EuroMillions however. The odds are one in 95,344,200, and the price of a ticket is £2 in the UK.  That means it is only economically rational to play EuroMillions when the jackpot is £190 million or more.  This has not happened yet.  the biggest win so far was £161 million. In fact, rules for that lottery cap the jackpot at €185 million.

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