Zeno's non-paradox

Last night, I lost half the amount I lost the night before. This got me to thinking. If that kept happening every night, would there be a cap on how much money I'd lose, and if so, what would it be? This reminded me of Zeno's paradox: 

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

— as recounted by Aristotle, Physics VI:9, 239b15

https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise

In the case of the poker problem, I quickly realized that the solution is simple and non-paradoxical. The answer? Yes, there is a cap, and it's twice the amount lost on the first night. The cap itself is never actually reached, since each night, the amount spent is half the remaining distance to the cap.

style flavor buy_in entry players hands entries paid place winnings

MTT-R NLHE    43500  6500       9    40      74   15    51        0
MTT-R NLHE    43500  6500       9    43      70   15    25        0

delta: $-300,000
MTT with rebuys NLHE balance: $40,151,500
2018 balance: $6,428,000
balance: $51,941,260