I'm not so hopeless after all, mum!

So, I'm sitting here trying to work out if I'm any better at the Entanglement game than a trained monkey, when my phones rings. It's my friend, calling on the way to the airport for a romantic weekend in Bangkok with a new lover. "What are you up to?", she asks (except she's Californian, so she actually says, "Hey! Wotcha doin'?"). "Trying to see if I'm better than a trained monkey at playing a computer game", I don't reply, partly because I'd then have to explain about the monkey.

And I'm pleased to announce that I am indeed better than a trained monkey. Yay, me! My mother will be pleased. Although no doubt she'll find fault somewhere. Still, at least she didn't raise a complete idiot. I've resigned myself to the fact that I'm just not very good at this game though. The best scores every day are all 400+, and I've only passed 300 once. I have no idea how that happened as the score just appeared without my knowing what was going on. Maybe the monkey did it while I was making a cup of tea?

So how did I do (and a chance to insert some images for the first time)? I played 30 games using each approach. The top graph shows the mean score after each game, the bottom one shows the standard deviation. The monkey is red, and I'm blue.

The main points are that my strategy produced better and more consistent results. I also improved with time, whereas the algorithmic approach didn't. Maybe that was because I started to hone my strategy, but this isn't really about me. Just look at the opportunities there are for the classroom!

I'm not expecting 11-year old students to be computing variances, but they can draw bar charts and pie charts, calculate means and ranges, and interpret their data. Surely that has to be a whole lot more fun, and hopefully therefore a whole lot more memorable as they have something enjoyable to hang the ideas on. How about some display work? One class against another? So we've tricked them into doing some work while they play the game, and then again when they analyse the results!

Well, I think I'm done with Entanglement, at least for the time being. It now feels like one of those moments at the end of a Simpson's episode, when Homer and Marge are looking back on the events of the previous twenty or so minutes, and wondering what it all means. Maybe there is no meaning? Maybe it's just a bunch of stuff that happened?

A fine line between work and play

To anyone else, he was just having a long soak in the bath. To Archimedes, it was work.

And so it is that my time today has not been pointlessly spent playing Entanglement, but has been a thoroughly time-efficient exercise in developing teaching ideas and resources.

The absence of sufficient Geometry teaching during my own schooling has left my capacity for spacial understanding hopelessly under-developed, so I am still rubbish at the game (current best score: 348; percentage of scores about 200: <10%). But I've turned this rubbishness to my advantage. By appreciating that my own strategies weren't working, I developed a new one, and it's produced interesting results.

My new strategy is: accept whichever piece is offered, in its original orientation, assuming it won't end the game. If it will, then keep rotating clockwise until it doesn't, and accept that. If they all end the game, the I use the swap button and repeat with the spare piece. If nothing offers me a way of continuing the game, I take the highest scoring move to finish.

How has my new strategy worked? It produced two new scores above 200, including my third and fourth best so far! Which might suggest I'm even more rubbish than I thought, were it not for the fact that it has also produced some of my worst scores, including my only single-figure score.

So how is this work? With two classes about to start studying hypothesis testing I'm sure there's some scope here. I can't imagine them complaining too much if I set them a homework to play this game 20 times and record their scores (of course, it needn't be this game, but I'd want it to have some Mathematics in it). The lesson will then be about seeing if Player A is better than Player B. At the 95% confidence level.

Right, I'm off to see if an algorithmic approach really is better than trying to think about each move. I may publish the results, if they aren't too shameful.

Tangled up in red

The much anticipated day back at work didn't happen. A slight relapse is going to mean a trip to the doctor and some drugs. Hopefully that'll sort me out.

It's an ill wind, and all that, and the extra day off has given me time to look at something that I only found out about relatively recently and think is probably worthy of an enrichment lesson. But more on that later, as it didn't take long before I was once again caught up in Entanglement.

Despite a good few hours of my day wasted invested playing the game, I don't seem to be making much progress. My top score so far is a paltry 348, which does at least put me 78th on the leader board. For today. So far. I'm trying to set a target of scoring at least 200 points, a target I have met. Once. Which is starting to make me question whether the act of setting targets alone is enough to improve performance. Who knew?

The main problem I'm having is which strategy to use. Okay, the main problem is that I'm rubbish, but the main problem that I can do something about is which strategy to use. I've tried several: inside to out, outside to in, prioritising making long chains and trying to attach to them, and prioritising joining up loose ends.* But all of those seem inferior to my current "try something different and see if you can stumble upon a better strategy". Well, I say inferior... the current strategy hasn't actually produced any results yet. But I'm optimistic.

All of this makes me wonder whether we should be taught more Euclidean geometry in school. I remember lots of algebra and statistics, but not many geometric proofs. Which reminds me of an interesting probability proof that uses similar triangles. Oh, if only Blogger would let me include PDF files I could show you! Maybe that's a good thing... you could try it for yourself. Here's the problem:

You are playing a game which involves spinning two coins. If they are both the same, you win; if they are different, your friend wins. If the coins are fair, then so is the game. But what if the coins aren't? For the sake of simplicity, let's say that they have the same bias, and in favour of the same side (hmmm... maybe I should have started by saying there was one coin, which we spin twice). Does the game now favour me or my friend?

There's a fairly simple algebraic proof which the absence of a superscript button on the formatting toolbar prevents me from demonstrating (Wow! Now I know just how Pierre de Fermat felt!) but can you come up with a geometric one? Go on... give it a try!

* This might make more sense if you've played the game.

So much for an early night...

I was just about to go to bed, honest I was! And then I discovered this. Go on, try it... and I bet you won't be able to stop either!*

* Assuming you have the sound muted.