I have a probability question I am looking for some help with.

In the scenario I perform a task on an object. I will either succeed or fail. Success rate is 1/3.

I score a point if I succeed AND the last 3 points I scored were not on the same object.

Given 4 objects to cycle through performing this task on, what is the optimal number of times to perform the task on one object before moving on to the next?

Simply cycling after one attempt seems inefficient, see below example situation (with modified success rate for demonstration) with objects A B C and D.

A succeed (point scored)
B succeed (point scored)
C succeed (point scored)
D succeed (point scored)

A Fail (no point)
B succeed (no point, last 3 points scored include on B)
C succeed (no point, last 3 points scored include on C)
D succeed (no point, last 3 points scored include on D)


Can anyone point me in the right direction with this?