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.