Let’s start with a different scenario:

Assume there is only one fox, and one chicken. In that case, the fox will obviously eat the chicken, and then it will simply live out the rest of its life as a chicken. There are worse outcomes.

Now,

if there are two foxes, still with only one chicken, neither fox will want to eat the chicken – if they do, they will turn into a chicken, and then it will just be them and the other fox, and they’ll get eaten.

Therefore,

with three foxes, and of course, one chicken, the foxes will be incentivized to eat the chicken, as once one of them does, there will be two foxes and one chicken, and as we just saw, the chicken will be safe.

However,

in the case of four foxes (and just the one chicken, obviously), none of the foxes will want to eat the chicken, because then there will be three foxes left with the fox-turned-chicken, and as we just saw, that will quickly mean only two foxes and one fox-turned-chicken.

I’m beginning to see a pattern here:

If there are an even number of foxes, the foxes will not eat the chicken because that will put them in the scenario in which there are an odd number of foxes, in which the foxes will eat the chicken, because that will make an even number of foxes, in which case the foxes will not eat the chicken because, well, you get the point.

Therefore, in our original scenario with 160 foxes,

our prodigious poultry protagonist will prosper in perpetuity. Phew!