Hey guys! I'm currently working on a personal project and have had a problem gnawing at me for some time. Hopefully someone out there might be able to shed some light on this situation or point me in the right direction. I spoke with my Calculus 3 professor and he mentioned that it has to do with Binomial Distribution but a second opinion is always helpful. I'd like to analyze the rate of decrease of units given by the following information:

Say I have 30 units of whatever and assume that an iteration is one second. Every iteration (or second), you have a 40% chance to gain a unit and 60% to lose a unit. Additionally, at every n iteration interval, you lose one unit not including the first iteration. I've included a text demonstration below if my description is confusing.

Given that you have a higher chance of losing a unit and that you lose a unit after n iterations, I would assume that you would generally, over time, have a net loss of units. How would I go about finding the rate at which I am losing units given n iterations? Any pointers or tips would be greatly appreciated! Thanks!




Start simulation: (Rolls 0-99, 0-39 gain, 40-99 loss)
n = 4 second intervals
Starting units: 30

Roll 56. Loss. 29 units remain.
Roll 76. Loss. 28 units remain.
Roll 14. Gain. 29 units remain.
Roll 67. Loss. 28 units remain.

Lose 1 unit. 27 units remain.
Roll 92. Loss. 26 units remain.
Roll 32. Gain. 27 units remain.
Roll 20. Gain. 28 units remain.
Roll 44. Loss 27 units remain.

Lose 1 unit. 26 units remain.
Roll 56. Loss. 25 units remain.
Roll 77. Loss. 24 units remain.
Roll 41. Loss. 23 units remain.
Roll 32. Gain. 24 units remain.

...

etc.