Why it is so damn difficult to catch a running hen?

I have often spent my childhood summers in an obscure village called Munupalle near Guntur in Andhra Pradesh. The game catch-the-hen was a great favourite of the kids there. Not mine, because I would usually take twice the time to catch a hen, twice the time of the youngest girl there! Having often wondered why is it so damn difficult to catch a hen, I atlast found a possible answer in Game Theory. The math and the jargon are obscure so let me simplify it.

If the hen swerved to one side only (either left or right) it would be easily caught. Ideally it should have a strategy such that any presumptive strategy on my part makes it difficult for me to catch it. The strategy followed is randomization. If you have chased a hen, the problem is that you have no idea which side it will turn. It is not as if the hen knows it, but that evolution plays its role in selecting such a strategy.

Interestingly, the same line of reasoning leads us to the answer of the bilateral symmetry of our bodies. Having an extra leg on one side or a super strong leg will make it possible for the predator to guess our moves better. We would have lost out.

How is all this relevant to policy? Well, randomization could be an essential strategy when you want to lower enforcement costs of a policy. Tax-compliance, for example.