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.
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.
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. )
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.