Monday, 1 October 2012

Random draws and skewing the odds

What are the odds of one kid winning a car two years in a row after the Bridge to Brisbane race in a random draw? A friend of mine said that happened in 2010 and 2011, and I don't know for sure if it's true, but if it was, someone should have done some very serious investigation right away.

Let's say there are 40,000 people in the race and that 20,000 put their random prize draw tickets in for the car. Someone is going to win, and the chances of it being anyone in particular are 1:20,000. Pretty low. Still, someone is going to win, so we shouldn't be surprised when there is a winner. But if you won last year, your chances of winning again this year should still be 1:20,000. Your personal chances of winning two years in a row would be 1:400,000,000. Staggeringly, mind-bogglingly unlikely. So unlikely, in fact, that it should raise immediate red flags for someone running the competition. I'm not calling "cheat" here, I'm just saying that the occurrence of this spectacularly unlikely event means that something must have skewed the odds. And I have a theory on that.

See, this particular car draw is done with everyone placing their tickets in the boot of the car, and then someone comes along later to draw out a winning ticket from among them. Because this happens after the race, the tickets will tend to be layered, bottom to top, in order of race time. The person drawing tickets at random is most likely to get them from the very top, and the people who finished last are the ones most likely to have their tickets at the top of the pile. That means that people who finish last are the only real contenders for the prize in the first place. From that much smaller pool, it is more likely that the same ticket will be drawn two years in a row, because a person's finish time is likely to remain comparable from year to year, and a child is more likely to finish last than a fit adult.

That's the skewing of odds. It's why such draws are usually done from barrels that are tumbled around beforehand. If you just dump in the tickets as they come, then draw straight from that pile, the last entrants are most likely to win, so we tumble the pile to make it more random. Tumbling the car to make that draw more random is not an option. The solution? Use a barrel.

Mokalus of Borg

PS - In this case, it's in your best interest to put your entry in late.
PPS - Which either means finishing the race slowly or waiting to enter until the last moment.

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