## What Really Matters in the Lottery

**Posted:** November 14th, 2009 **Tags:** Math, Probability

3 Comments »

I saw a funny thing this morning on the TV news: They invited the man in charge of the National Lottery to answer some questions about new plans and stuff about current "concerns" from sellers and buyers of the lottery tickets. They eventually came to the oh-so-old topic of the "married tickets". For those of you not related with the term, here in Panama many lottery ticket sellers force you to buy lottery tickets ending in a number over 31 if you buy a lottery ticket that ends in a number less or equal to 31, so you have to buy two "married" tickets, which is actually illegal (yet as many other illegal things in Panama, it's quite common). The reason is simple, yet not logic at all.

Since people have to decide what ticket to buy, the most popular way of doing so is through dreams: If you dream about somebody, then you buy a lottery ticket ending in his or her birth date, and since only numbers from 01 to 31 can be birth dates, lottery tickets ending in these numbers are sold a lot more than the rest of them. Some other popular methods to decide what lottery ticket to buy are those that associate abstract concepts from dreams with numbers from 00 to 99 (for example, dreaming about a rat could be 62, or dreaming about funerals could be 30) but there is no official documentation on what are the associations so this method is not as popular as the first one explained.

What seemed really funny to me was the fact that these people take air time on the TV to discuss something that has no logical sense at all. We have a random process of picking balls out of a bunch and people have developed heuristics that are solely based on dreams, which have no proven relationship to the process mentioned. Furthermore, each buyer uses these heuristics to try to determine what numbers will come out of a given execution of the ball picking process (that is, next lottery draft) yet each buyer has an independent input to the heuristic process which will of course yield independent (not necessarily distinct) results, so under what scheme can someone validate this heuristic? What statistical data first related dreams with the weight of the probability of a ball to be picked out of a bunch?

So to summarize, a popular misbelief have created a legal problem which "concerns" the whole community of lottery ticket buyers, sellers and authorities. Notice how different this is from other legal problems like drug dealing and robbery, which are striking hard in our society, are based in real problems like economy and security and should be taking air time on TV. To solve this problem I propose two methods:

- Lottery authorities could take some time to explain that there's no association between dreams and lottery drafts, yet if someone was illuminated enough to understand that dreaming is not a valid heuristic for the lottery draft guessing problem, he would most likely be wise enough to understand that there's actually no valid heuristic to the problem at all and would stop buying lottery tickets because if it is a totally random game, he might as well save that money and would have a significant amount of money in a deterministic fashion... but authorities surely don't want that to happen.
- Lottery authorities may use the second heuristic mentioned on this post: Upon publishing an official revisited mapping from abstract concepts to numbers from 00 to 99, they can convince people of using this new heuristic which would effectively widen the range of numbers buyers will be looking for. A proper way to do so would involve a statistical analysis on what are the most popular abstract concepts people dream about and create a uniform distribution of the top 100 concepts in the integral range [00, 99]. Yet, the obvious easy way of doing so is sitting and drafting 100 random concepts and their associated numbers... if people haven't questioned the dream to birth date heuristic in so many years, why would they question this mapping at all?

I would of course just ban lottery and any other activities alike from the governmental engine and focus on serious matters like education if I was the president, yet that is not likely going to happen. Another proposal of my own is utopical, yet 100% percent effective and is based on Nash's game theory: Lottery tickets here in Panama are composed of 4 numbers, yielding only 10,000 possible numbers for the three prices drafted. Panama's population, on the other hand, is of 3 million people, and there are surely more than 10,000 of them buying lottery tickets, so why don't 10,000 people join together and assign a number to each one of them,Â buy tickets according to their respective numbers, and then split the sum of the three prices among all the participants? That would indeed render the lottery system unsustainable after a while (maybe two weeks?) yet is a sure strategy for this particular game (notice how some problems are still solvable by brute force these days :D).

Finally, I'd like to add that all of these (useless) considerations are valid only if the ball picking process is truly random. If it is not then there is indeed a strategy to guess the numbers (maybe dating the one in charge of selecting them?) and that, my friends, is what would really matter in the lottery.