The Math Guy: Many Little Happy Moments Or Dreaming Big?

I often get asked which lottery is the best one. Like so many things in life, the answer is: It depends. It’s not black or white, not best or worst, not good or bad.

Lotteries are a game of luck, and each person has a different perspective of luck and a different expectation of gratification. What is common to all lottery players is the excitement of potentially winning something big. It all boils down to what ‘big’ means to different players.

Let’s analyse three gratification approaches and their consequences on playing lotteries.

1. I want to be obscenely rich!

The first type of player is the most common one: The player who dreams of becoming super rich. There is only one thing that such a player can do: go for the biggest jackpots. This means that they will most likely prefer playing Euromillions, Eurojackpot, US Powerball, US MegaMillions or SuperEnalotto.

The odds of winning the jackpot for each of these lotteries are different. The question is whether it is better to play for a Eurojackpot of, say, €65 million with odds of 1:95 million, or a US Powerball jackpot of $250 million with odds of 1:292 million. 

My view is very simple: You need a lot of luck to win either of those jackpots, and thus at any point in time, go for the biggest one. This is the behavior demonstrated by most lottery players.

2. I want to change my life!

The second type of player also dreams of winning a big amount, but he defines ‘big’ more in terms of an amount which would allow him to live a completely different life. For most people an amount above €1 million would be life changing.

Now let’s examine whether such a player should choose lotteries other than the above-mentioned big ones. The Australian Monday and Wednesday lotteries have very good odds of 1:8 million to win the jackpot, but they do not really qualify as ‘life-changing’, as the jackpot is usually AUS $1 million, which is approximately €660,000.

The Austrian Lotto also has odds of 1:8 million for the jackpot, with the jackpot starting at €1 million and increasing to about €3 million. Other lotteries with similar odds for the jackpot are the Irish Lotto (odds of 1:10 million) and the Canadian lottery (odds 1:14 million). The jackpots for these lotteries can reach around €10 million.

These players have a 10 to 30 times better chance of winning the jackpot than the big lottery players, but there is no such thing as a free lunch; If these guys win, they will win a few million, not tens or hundreds of millions.

3. I want it often!

The third player prefers to win more often than to win big. His rationale is that winning something makes him happy, even if it does not necessarily change his life. These players should choose lotteries with high chances to win any prize.

The French lottery is perfect as it offers a 1 in 6 chance of winning any prize, closely followed by the Canadian lottery with 1 in 8.3. The UK Lotto has odds of 1 in 9.3, and Lotto America has a 1 in 9.6 chance to win any prize. To put this into context, out of the big lotteries, the best is EuroMillions with only a 1 in 13 to win any prize. The other lotteries in that heavyweight category have odds of over 1 in 20.

It doesn’t sound like a big deal to increase the chance of winning from 1 in 13 to 1 in 6. But buy 12 lines in the French lottery and there’s a 90% chance you will win something, do the same for EuroMillions and it drops to a 65% chance that you’ll win something. For the other lotteries in the heavyweight category, it drops even further, to around 50% - that’s quite a big difference from 90%.

So, what is the best lottery? It depends on what you want!

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