The Chief Economist’s blog: Playing the lottery is not investing

Winning the jackpot in the first round

Most Finns know the Finnish lottery game called Lotto. You win the jackpot when you guess the correct 7 numbers out of 40. There are 18,643,560 possible combinations of numbers. This means that the probability of winning the jackpot is approximately 0.000005 per cent. In our hypothetical exercise, we play every combination of numbers once. One combination will cost 1 euro, and we will put 18,643,560 euros in play. This way, we can be 100 per cent sure that we win the jackpot in the first round.

Every euro played returns 41 cents on average

In Lotto, the likelihood of winning the jackpot is negligible. The probabilities of winning smaller prizes, such as five right numbers or four right numbers, are much higher and, at the same time, the winnings are clearly smaller. On average, 41.1 cents will be returned for each euro played, i.e. the payout ratio of Lotto is 41.1 per cent.

After the first round, 7.7 million (41.1% x 18.6 million) will be returned of the initial investment of 18.6 million. That is, the profit in the first week is quite bad. If one continues in the same way according to the chosen "investment strategy", i.e. so that each euro won is reinvested in the lottery each week, the losses accumulate rapidly. The playing of Lotto that began in January will result in the millions having petered out at around Midsummer. The return is -99.99999 per cent.

Even the worst period in the equity market wins playing the lottery

Let us, in comparison, take a look at the worst possible investment in the equity market. I chose the worst corresponding period of time of the S&P 500 index. This was in early 1932, when the return on the S&P 500 index was -50.6 per cent at its worst. It would make a lousy equity investment, but it would still be much better investment-wise than playing Lotto. The decline in the equity market continued further after this period, but despite that, we have never seen return figures as bad on the equity market as in the lottery.

A distorted public image

The lottery has a false public image. Only the winners are heard and seen. However, the losers, who the majority of the players absolutely consist of, are never so much as mentioned. Or have you ever seen a newsstand poster with a headline like this: "A couple from Pori lost five euros playing the lottery - the mortification is huge"? So the odds are against the lottery player. This means that on average, one will always lose when playing the lottery. Playing Lotto is not investing. Playing Lotto is entertainment.

Lasse Corin lasse.corin(at)aktia.fi
Twitter: @lassecorin