Oddverse.com

Well, as of Saturday, I am a student again. And this time, I'm not studying anything scientific, no. I am an arts student.

I have yet to work out what this means. I suspect that it means becoming the butt of jokes about not looking out of the window in the morning so I have something to do in the afternoon, and maybe it means that at the end I will be qualified to ask people if they would like fries with that. But in the short term, it's filling me with a fair amount of fear. I am an arts student at the Open University, and that's too close to "Open Prison" for me to be entirely comfortable.

I'm already intimidated by my fellow students. I met some of them on Saturday, and while they all seem very nice, they all seem a bit more committed already. There's me, with my small notepad and pen, and they've got A4 books full of stuff. Me with my blank look, them with their handfuls of handouts. Them with their airs of confidence, me with my mumbling and stammering. They're my tutorial group. One is a large woman who lives round the corner from me. One is a slightly less large woman who is a teacher, so only works half days and gets really long holidays. One is a guy about my age, who just has the look, with the indigo denim jeans, the roll neck sweater, the leather jacket. He's moisturised and toned and invited me to a party within hours of meeting him. A little too serious, though, and a definite threat.

Yes, threat. Within five hours of sitting down in a room with my tutorial group, I'm already thinking in terms of oneupmanship, of competition. I know that's wrong. I know I should be thinking about them as support, as potential allies in my journey along the path of whatever path I am going along. And maybe I will.

But in the mean time, I've got to go. I have an essay crisis.

This is where I admit that I'm sufficiently sad to have heard of Big Brother.

For those of you who don't know what Big Brother is, it's essentially a show devoted entirely to probability problems, cunningly disguised as a nine week game show where people are shut in a house with each other. Doesn't sound terrific and exciting? That's because it generally isn't.

Anyway, the other week they had the thirty number conveyer belt problem.

This is how it's stated.

You've only got one prize to pick and you know there are, say, 30 prizes on the conveyor belt. They are coming through one at a time and what makes you press the button to stop the conveyor belt and say, "I want that prize?" 'I think the mathematical way of doing it is to look at the first ten items - the first third. Then, the first thing you see out of the next two-thirds that is better than anything you have seen before, get that. Because if the first ten items are spread evenly on the good or bad scale, then you will get a couple of things in the 90 per cent area. 'It's unlikely you are going to get the 100 per cent best item in your first third of the sample. So you choose the best thing in the next two-thirds which is better than you have seen before. You're going to get something pretty good.

Let's translate this in to something more sensible, generalise it, and then solve it.

You are presented with a series of m numbers, in no particular order. Each number is presented once and once only. As each number is presented to you, you may select it or pass. Once you select a number the game is over, and your score is the number that you've been given. If all m numbers are presented, your score is the mth number.

In this game, it is postulated that in order to maximise your score you should watch a series of n trials. You should then select the next number that exceeds the greatest number in these n trials.

First off, it's interesting to note that this strategy does - in general - work. For example, if there are thirty numbers and you watch for ten, you've got about a 1 in 3 chance of getting the highest score, and a 50:50 chance of being in the top 20%.

Secondly, it's interesting to note that I sat down and proved this.

Interesting, but dull.