i was talking about how to potentially implement a capped system on paper, not about an actual implementation. if two strips would give you free rides for the rest of the day you probably would not throw them away.
i know the but ticket system from los angeles 25 years ago. you could use each strip only once because you had to hand them in. i think you got a second strip on the next bus so you could potentially make an unlimited chain. if people would throw them away then only because they got one they didn't use. you were also not allowed to use the strip for a return trip on the same route.