This week, my attention was caught by a poster that you might have also seen if you live in French-speaking Switzerland. The poster praises the virtues of the European lottery game Eurodreams, which promises a monthly pension of 22,222 francs per month for 30 years to its winner. Launched in October 2023, the game has already encountered great success, with more than seven and a half million players for the drawing of last November 6th, for example.
The marketing arguments deployed here by the Loterie Romande are initially enticing: a high amount pension, a number made easy to remember by the repetition of the same figure, and above all the prospect of an income over a very long period. And this breakdown is certainly more memorable and tempting than if an equivalent amount of 8 million francs (22,222 francs per month * 12 months * 30 years) had been offered at once, an amount relatively modest compared to the 115.5 million won by a Swiss at the Euromillions in 2013.
Moreover, this mechanism also allows the organizers to make substantial savings compared to a one-time payment. Readers who have already heard of the concept of discount rate see where I’m going. For the others, this is the subject of this post.
The underlying idea is to assert that it’s better to win a franc today than a franc in a year, for two main reasons. First, inflation (a particularly salient issue in recent months) will have eroded your purchasing power, which will be lower in a year for an equivalent sum. Secondly, by taking possession of the franc right now, you have the opportunity to invest it and, if your investment is savvy enough, you will enjoy an amount in a year that will be superior, even subtracting inflation.
For the organizers of Eurodreams, these effects play out fully. If we assume that prices increase by about 2% per year each year, in line with the central banks’ target, 22,222 francs received in a year will have the same purchasing power as 21,786 francs today. By the same logic, in 30 years, the 22,222 francs will have a purchasing power equivalent to 12,268 francs today, a decrease of nearly half. The reasoning can be replicated for the entire period of receiving the winnings. All calculations done, and always based on a constant inflation of 2% per year for 30 years, it’s not 8 million francs of purchasing power that the winner receives, but the equivalent of a little more than 6 million.
The next logical question would be to wonder what happens to the 2 million difference between the two aforementioned amounts. This sum is simply redistributed to the entire economy, through the rise in prices over time. It is therefore difficult to argue, from this first angle, that the deferred payments directly benefit the lottery organizers.
On the other hand, they are potentially winners if we look at cash flows. Indeed, the game is fundamentally biased in favor of the organizer. The ticket statistically offers a one in 19 million chance for its purchaser to win the 8 million francs jackpot. Excluding intermediate prizes, the “expected” gain is therefore 8,000,000 / 19,000,000 = 0.42 francs, far from the ticket cost which, in Switzerland, is… 3 francs. Even in an “unlucky” case, where a winner would emerge from the first drawings, the organizers are not obliged to immediately disburse the entirety of the 8 million francs, and can “hope” to finance this first winning prize with the proceeds from subsequent drawings. No need, therefore, for the organizers to dig into their pockets.
Finally, the lottery organizers could have relied on another lever, namely the interruption of payments in case of the winner’s death during the 30 years, a case far from anecdotal when we know that the average age of a lottery player is 48 years old in France, and probably not very different from this number in Switzerland. In this case, the game rules explicitly state that “the remaining part of the monthly pension is transferred in accordance with the applicable law of succession.” The real winner here is less the lottery than the tax authorities.
The example of Eurodreams is an example of a broader perception bias, according to which we struggle to properly value receipts or expenditures that are distant in time – a bias that relies in part on the explosive nature of compound interests, but I’ll keep this topic for a future post. In the meantime, I hope you’ll remember this article the next time you come across such a poster on the street!