In 2018 I bought 8 VikingLotto lottery tickets.

One every week, for 8 weeks straight. I didn’t win anything of course. Unlike the person from the screenshot below, who won 33M. Good for them.

But it got me thinking - does it make sense to buy a lottery ticket? The intuitive answer is “of course no”, but why not?

After all, it is a perfect example of an asymmetric trade with limited fixed downside and the upside is potentially live-changing.

## Probability of winning the jackpot (spoiler: it’s very, very low)

Let’s take Vikinglotto, which was the first pan-European lottery, as an example.

The rules of VikingLotto are as follows - the player needs to select six main numbers from 1 to 48 and one bonus number from 1 to 8. The bonus number is drawn out of a separate pool. The jackpot goes to the player who matches all seven numbers.

So your probability of winning the VikingLotto jackpot can be calculated as (48*47*46*45*44*43) / (6*5*4*3*2*1) * 8 = 8,835,488,640 / 720 * 8 = 98,172,096

In other words, there’s a 1 in 98,172,096 chance that you’re going to win.

Imagine someone dropped a 1 euro coin (23,25mm) on their way from Madrid to Berlin (2,318 km). You take the same road trip, stop randomly in 1 place, get out of your car and pick up that coin. You are about as likely to find the coin this way as you are to win the VikingLotto jackpot. It’s 1 in 98,172,096 vs 1 in 99,570,447.

## Potential issues

Ok, so we know that probabilities to win the jackpot are low, but that leaves 4 potential issues or special cases when buying a lottery ticket might be an economically rational investment.

1. there are other ways (guess 4 or 3 numbers) to win a smaller prize.

2. you could buy more tickets to increase odds.

3. you could buy tickets only when jackpot is > N.

4. the downside is so small, perhaps it just makes sense to do it.

Solutions:

1. The added expected value of these smaller prizes is tiny.

2. Maybe if you buy tickets with all possible combinations, like Stefan Mandel did 14 times.

3. Don’t forget about taxes, net present value (jackpots are usually paid out in 25-30 yearly instalments or you get 60-70% of the sum upfront). Most importantly, bigger jackpot means more tickets sold, which means expected value is still negative.

4. Consider opportunity costs. It’s a zero-sum game, and it doesn’t work in your favour in a multiverse setting (for every world in which you win the VikingLotto jackpot, your 98,172,096 parallel selves will lose. )

## Conclusion

I will quote Richard Meadows here.

[…] the questions we need to ask in evaluating an investment opportunity:

1. How efficient is the market?

2. Do we have an exploitable edge?

3. Is there a large or unbounded upside (+EV)?

4. Is it an all-in bet, or can we take a portfolio position?

Buying a lottery ticket fails every test: the market is highly efficient, no-one has an edge, and the EV is negative, which means that taking a portfolio position isn't going to help.