Let's say I have the following 2 systems:

System 1: Pressing a lever drops a transparent box which contains a random amount of reward, and the amount of effort required to open that box is proportional to the amount of reward in the box.

System 2: There is a lever and a button. After pressing the lever some number of times and then pushing the button, a reward is dropped from a random distribution (let's say geometric) whose mean is based on the number of times that the lever was pressed before the button is pushed. That is, the more times the lever was pressed before the button is pushed, on average the greater amount of reward is dropped.

Are there any relevant findings in the behaviorist literature which would tell me which of the above 2 systems would produce more response rate (or if they're equivalent)?

All I have found so far is that variable-ratio reward schedules produce the greatest response rate. Both of the systems I described above are variable-ratio reward schedules but arguably the first system produces a greater delay between seeing a reward and actually receiving it, whereas in the second system the reward is received as soon as it is seen. I couldn't find any studies on the effect of the delay between seeing the reward and actually receiving it on response rate.

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