Lottery Year

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:

ONCE Cupon

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:

Match Pay Out
The right-most digit of the primary number 2.50 €
The two right-most digits of the primary number 6 €
The three right-most digits of the primary number 60 €
The four right-most digits of the primary number 600 €
All five digits of the primary number 35,000 €
All five digits of the primary number and the series 6,000,000 €

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:

Final Balance Probability
31.00 € 4.2919 %
33.50 € 4.0821 %
28.50 € 4.0585 %
25.00 € 4.0585 %
27.50 € 3.9017 %
22.50 € 3.7974 %
36.00 € 3.5208 %
26.00 € 3.4177 %

Let’s look at the full scatter plot:

Final Balance Probability Distribution for 'Play One' Strategy

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!

Grouped Final Balance Probability Distribution for 'Play One' Strategy

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.

Final Result Probability
Lose Everything 0.000478 %
Lose Money 98.862015 %
Break Even 0.000016 %
Gain Money 1.137460 %
More Than Double Money 1.137124 %

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:

Final Balance Probability
1.00 € 26.7041 %
0.00 € 23.9738 %
2.00 € 15.5747 %
3.50 € 6.7439 %
0.50 € 6.1533 %
2.50 € 5.9699 %
4.50 € 3.9931 %
1.50 € 1.9930 %

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.

Final Balance Probability Distribution for 'Play All' Strategy

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.

Final Result Probability
Play One Play All
Lose Everything 0.000478 % 23.97387 %
Lose Money 98.862015 % 98.845143 %
Break Even 0.000016 % 0.000989 %
Gain Money 1.137460 % 1.148936 %
More Than Double Money 1.137124 % 0.398635 %

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.

History

Lottery Year 2008

Date Balance Gambled Won Delta Total Delta
Jan 1, 2008 260 €
Jan 4, 2008 260 € 5 € 5 € 0 € 0 €
Jan 11, 2008 255 € 5 € 0 € -5 € -5 €
Jan 18, 2008 250 € 5 € 0 € -5 € -10 €
Jan 25, 2008 245 € 5 € 0 € -5 € -15 €
Feb 1, 2008 240 € 5 € 0 € -5 € -20 €
Feb 8, 2008 235 € 5 € 0 € -5 € -25 €
Feb 15, 2008 230 € 5 € 0 € -5 € -30 €
Feb 22, 2008 225 € 5 € 0 € -5 € -35 €
Feb 29, 2008 220 € 5 € 0 € -5 € -40 €
Mar 7, 2008 215 € 5 € 0 € -5 € -45 €
Mar 14, 2008 210 € 5 € 0 € -5 € -50 €
Mar 21, 2008 205 € 5 € 0 € -5 € -55 €
Mar 28, 2008 200 € 5 € 0 € -5 € -60 €
Apr 4, 2008 195 € 5 € 0 € -5 € -65 €
Apr 11, 2008 190 € 5 € 0 € -5 € -70 €
Apr 18, 2008 185 € 5 € 0 € -5 € -75 €
Apr 25, 2008 180 € 5 € 0 € -5 € -80 €
May 2, 2008 175 € 5 € 0 € -5 € -85 €
May 9, 2008 170 € 5 € 0 € -5 € -90 €
May 16, 2008 165 € 5 € 0 € -5 € -95 €
May 23, 2008 165 € 5 € 5 € 0 € -95 €
May 30, 2008 160 € 5 € 0 € -5 € -100 €
Jun 6, 2008 155 € 5 € 0 € -5 € -105 €
Jun 13, 2008 150 € 5 € 0 € -5 € -110 €
Jun 20, 2008 145 € 5 € 0 € -5 € -115 €
Jun 27, 2008 145 € 5 € 5 € 0 € -115 €
Jul 4, 2008 140 € 5 € 0 € -5 € -120 €
Jul 11, 2008 135 € 5 € 0 € -5 € -125 €
Jul 18, 2008 130 € 5 € 0 € -5 € -130 €
Jul 25, 2008 125 € 5 € 0 € -5 € -135 €
Aug 1, 2008 120 € 5 € 0 € -5 € -140 €
Aug 8, 2008 115 € 5 € 0 € -5 € -145 €
Aug 15, 2008 110 € 5 € 0 € -5 € -150 €
Aug 22, 2008 110 € 5 € 5 € 0 € -150 €
Aug 29, 2008 105 € 5 € 0 € -5 € -155 €
Sep 5, 2008 100 € 5 € 0 € -5 € -160 €
Sep 12, 2008 95 € 5 € 0 € -5 € -165 €
Sep 19, 2008 90 € 5 € 0 € -5 € -170 €
Sep 26, 2008 85 € 5 € 0 € -5 € -175 €
Oct 3, 2008 80 € 5 € 0 € -5 € -180 €
Oct 10, 2008 75 € 5 € 0 € -5 € -185 €
Oct 17, 2008 70 € 5 € 0 € -5 € -190 €
Oct 24, 2008 65 € 5 € 0 € -5 € -195 €
Oct 31, 2008 60 € 5 € 0 € -5 € -200 €
Nov 7, 2008 55 € 5 € 0 € -5 € -205 €
Nov 14, 2008 50 € 5 € 0 € -5 € -210 €
Nov 21, 2008 45 € 5 € 0 € -5 € -215 €
Nov 28, 2008 40 € 5 € 0 € -5 € -220 €
Dec 5, 2008 35 € 5 € 0 € -5 € -225 €
Dec 12, 2008 30 € 5 € 0 € -5 € -230 €
Dec 19, 2008 25 € 5 € 0 € -5 € -235 €
Dec 26, 2008 20 € 5 € 0 € -5 € -240 €
 
  • Jake

    Couldn’t help but notice on your first ticket you at least recaptured your initial investment. Well done!

  • http://www.hillbillyplease.com/blog/ jane

    This is, without doubt, the nerdiest thing I have EVER seen.

    The. Nerdiest.

    Good work. :D

  • Anon

    They say it’s run by disabled people… but they’re actually super-abled. They’ve figured out how to rig the system so that you always win the first time, and then never again. Good Luck.

  • http://erik-rasmussen.com/blog Betsy

    Your graph sure is consistent. Have you given up on the project or have you just not entered the last couple of weeks?

  • http://www.erik-rasmussen.com/ Erik R.

    I’ve just fallen behind on updating this page. Once they do the drawing today, I’ll add the last three weeks.

  • Paul

    Is there still excitement when you check to see if you won?

  • http://www.erik-rasmussen.com/ Erik R.

    Mild excitement, sure. But it’s more of a “Ho hum, let’s go verify that I’ve lost again this week…” than, “Let’s see if I won!”

    I’ve been falling behind a bit on updating this page. I’ll try to do better.

  • http://www.isoglossia.com sgazzetti

    I’ve always thought of the lottery as either A) license to fantasize for a week or B) tax for stupid people. Somehow your project steadfastly refuses to fall into either category. Now I have to add a third one: C) Math death.

  • http://www.spainexpat.com Editor

    Erik, are you rich yet?

    This is also a great page for the people who don’t know how Once lotteries work (like moi) yet want to get in on the action. Also good for realizing our odds are worse than we thought. :)

  • http://www.erik-rasmussen.com/ Erik R.

    Not rich, yet, no. The odds are pretty rough, yes. We’ve still got a half year to go. C’mon big money!!

  • http://www.flickr.com/photos/aparejador/2599152197/ Ray Tibbitts

    Nice to see some stats that confirm my intuition on this matter.
    Thank You.

  • http://www.flickr.com/photos/aparejador/2599152197/ Ray Tibbitts

    Okay, I have to admit intuition was NOT confirmed by the whole ‘unlikely to go completely broke playing only five at time.’

  • http://www.latortugaviajera.com/ Erin

    I don’t understand any of this and have decided you are the smartest person I know. Congrats!