American in Spain

In Spain, there’s a lottery company called ONCE, which I wrote about once here, that only employs disabled people, thereby softening the greed-based gambling of lottery by adding an aspect of altruistic charity for the less fortunate. In 2008, I’ve decided to play 5 € in the ONCE lottery for 52 weeks straight and see how much I end up with at the end.

Prizes

An ONCE ticket looks like this:

It consists of a primary 5-digit number (65640 in the above example) and a 3-digit series (077 in the above example). The primary number is the same for an entire sheet of tickets, so when you buy more than one ticket, they all have the same number, but different series values. The prizes are as follows:

Strategies

There are two basic brainless ways to play the lottery: bet the same amount every time, or bet all your money every time. Let’s see how they stack up…

Play One

The Play One strategy is to buy 5€ worth of tickets every week and keep all winnings. I have run a computer simulation to calculate the probability of all possible final year-end balances using this approach. The most likely results are:

Let’s look at the full scatter plot:

I don’t know about you, but this is not at all what I was expecting. Even a freshman Statistics major can see the common “bell curve” shape replicated in there several times, all centered around various values. What’s up with that? See how the dots are all cluttered way down below 0.5%? They go way out to the right way off the chart approaching zero as the pot gets more lucrative.

So after playing the lottery for 52 weeks with a total of 260 €, the most probable final balance is 31 €. It sure looks highly probable that the final balance will be between 20 and 40. So let’s break it down by groups!

Okay, so it’s pretty clear that we shouldn’t expect much more than 60 € or much less than 10 € at the end of this using the Play One strategy, since 88.4% of all possible results lie in that range. But what’s really important here is what is the probability that we will end with a profit or loss? Can I quit my day job or not? If you’ve been paying attention, you should already know the answer.

It’s interesting that the probability that I more than double my money is more or less the same as the probability of any profit at all, so the majority of those values fall above the “doubled profit” line.

To summarize, if I go with the Play One strategy, I’m looking at a 98.86% chance of losing money with this venture, but I’d have to be really unlucky to lose it all. Since I will probably end up with between 20-50 euros, I’m looking at a likely loss of between 210 and 240 euros.

Play All

Now lets look at what would happen if I choose to re-bet all my winnings every week. Due to the sheer explosive nature of the permutations, I was forced, in my computer simulation, to limit the definition of this strategy to be “play up to 40 € of my winnings every week”. Like before, let’s look at the most probable outcomes:

The first thing to notice is how much higher the top probabilities are than with the Play One strategy. With Play One they barely got above 4%, but here the top two most likely outcomes make up a 50% chance! Let’s look at the scatter plot.

The values below a final balance of 10 € account for 96.986% of the possible outcomes. This looks like a terrible strategy. For completeness, let’s look at the win/loss probabilities, too.

So with both strategies, I’m practically guaranteed to lose money, but at least with the Play One strategy, I’m also practically guaranteed of not ending with empty pockets, whereas that outcome is much more likely with Play All.

Final choice: Play One

I’m going to play 5 € every week and save whatever winnings I get, never re-gambling them.

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