The Ass is not a digital computer. It's an analog computer. It's subject to continuity. That's important.

If you look at the Ass's center of mass five seconds after the experiment starts, and vary the relative sizes of the bales of hay continuously, the Ass's position must also change continuously. If you found some ratio of hey where the Ass ends up at the left bale of hay, but if you add any amount, no matter how tiny, it ends up at the right bale of hay, the Ass is violating the laws of physics.

It gets a bit more complicated because you can't add less than one particle to the bale of hay, but there are other things you can do, such as slowly move one piece of straw between the bales, or move the bales closer and further from the Ass.