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Numfield - the Pi Experiment

Don Reble

The idea is to have an empirical look at the clique phenomen, that is that strategies can profit from each other from cooperating.

He suggest the following "stupid class", which is called Pi for obvious reasons:

class Pi extends Strategy
{
    private int pi[] = {3,1,4,1,5,9,2,6,5,3};
    public int initial_turn() 
    { 
        return pi[0]; 
    }
    public int turn(int last_turns[], int scores[],
                int carryOver, int turn_no)
    {
        return pi[turn_no % pi.length];
    }
}

This little guy plays the same digits in the the same order over and over. In general its best expectation is to remain unrecognized and perform as good as a simple randomized strategy. A smart learning strategy could outlearn Pi very easily and take advantage of its very static behaviour.

But what happens if there are a lot of Pi's in an environment? Obviously a bunch of Pi's easily cooperate with each other, so if there are too many, they might actually force the other stratgies to react upon them:

There are learning strategies in the environment which are able to cope that clique of 10 Pi's. Alabama also, but Alabama doesn't perform well in the standard setting. Anyway the Pi test remains a very interesting benchmark for new strategies.

To make that benchmark even more valuable I've made a modified version of Pi, which is even harder to cope. I call that modification BlindPig, it is on the next page.