Recognize and predict a periodic pattern
If it is really close to random (background noise, bits from random number generators or hash codes), I don't expect there is much you can do, except create a large collector. (Or are you only allowed one collector?)

You may want to throw in a few random checks. Those won't prove anything but may give you some insight into the pattern.

If you want to create a successful model, you'd have to come up with some assumptions about parameters that could affect the success of your model, and create and test that model.

For instance, one of my assumptions would be that there are rows with higher probability.
One other assumption would be that there is some hysteresis effect (either positive or negative), so the probability may depend on the actual outcome of the previous event(s).