Inspired as I was by such great science and sceptical blogs as Bad Astronomy and Moonflake I was slightly at a loss about what exactly the blog should contain. (The more discerning reader might have noticed that I have not yet mentioned why I intend to start a blog. Surprisingly the reasons are so mundane and trivial that I have opted to leave that step out in recounting the creation of this blog.)
While I consider my self a scientist, I am not an astronomer nor astrophysicist or biologist or any other of the sciences that seem to be the target of so much unsceptical thinking. My field is that of computers and Information Systems and how people and society interact with them. No flat earth theory, or moon hoaxes to debunk in this field!
Further thinking about my field and the kinda of superstitions inherent in it made me realise something: dealing with information, and using the systems that manage it, without a proper understanding of how the systems work, will naturally lead to some unsceptical thinking at least.
And hence the idea for my first post came about: The Lottery.
“The lottery: a tax on people who flunked math.” ~ Monique Lloyd
That quote for me sums up the main problem with playing the Lottery (or the Lotto as it is known in South Africa). The problem is not some much the staggeringly bad odds (something like 1 in 13 million for the South African Lotto to win the Jackpot, see this wiki page for more information: Lottery) but a problem, really, with counting.
You see when I reached 2nd year University mathematics course I was expecting topics of great difficulty and import with long collections of Greek symbols on pages and pages of forumlae. Instead I was confronted with a section on Counting. After a brief mental check (yes, 5,6,7 and then… er 8! yes still got it) I actually started reading what it was all about.
In probability mathematics the basic formula is: The probability of some event is equal to the number of occurrences of that event divided by the number of all possible events.
For example the probability of getting a heads in a single coin toss is: the number of occurrences of a heads (namely 1) divided by the number of all possible events (namely 2, either heads or tails).
This is of course 1/2 = 0.5.
And this is where Counting comes in. One needs to be able to accurately determine how many occurrences are there of the specific event you are looking for and how many possible events are there.
Furthermore one needs to know when to count what. Failing to do this correctly can, obviously, lead to an incorrect assessment of the probability of some event happening. Which is not something one wants when betting money on the likelihood of something happening.
An example of this kind of mistake, when it comes to the Lottery, is people thinking that the more times they play (in a new draw every time) the better chance they have of winning. This is, unfortunately not true. Here’s why:
Assuming you buy only 1 ticket for the first draw, you have a 1 in ~13 million chance of winning the Jackpot (lets ignore getting 4 or 5 or how many ever numbers correct though the same principle applies). If you then play the next week’s Lotto and buy 1 ticket, you once again have a 1 in ~13 million chance to win. Each successive draw has no impact on the next, and thus your odds do not improve as you play.
Remember also that each time you enter a draw you have to pay. Thus even if you say that you win every 5 times you play, you are still paying 5 times as much as a single draw. Not good odds.
Another common misconception is that because somebody wins in nearly every single draw that the chances must be good for me to win. Unfortunately this is not true. With a country the size of South Africa (~40 million people) for someone to win any given Lotto draw is not that unlikely. If every 4th person buys one ticket, the odds are (10million tickets bought/13million possible numbers) = 0.77 or 77% that someone will win the Jackpot. (Assuming unique numbers are picked of course).
The bad news is that this is the chance of someone out there winning, not your chance of winning.
This is similar to the belief that because someone you know (or usually someone, who someone you know, knows) keeps winning that the odds are good for you as well. This is just not true. Once again somebody else’s good odds have no effect on your odds. (In fact while they have no effect on the odds of you getting a specific number, if they win a lot they will most likely decrease your possible winnings because you’ll have to share any winnings between other people who get the numbers right).
And this is just the Lottery from a mathematical point of view. The problems in terms of winners squandering their money, greedy relatives and friends or becoming a target for scams and fraud make the idea of playing the Lottery even worse!
So at the end of the day the Lottery really isn’t a wise investment of your money. Instead rather donate it to worthwhile cause (say, for example a sceptical blogger!) or buy yourself something nice. We pay enough tax as it is, no need to get taxed because of ignorance as well.
PS. This is an amateur blog so feel free to correct any of my mathematics or statements in the comments. Oh and comment. Please