Switching balls among 3 piles

Question

There are 3 piles of balls. Each hour, I take a ball from one pile and move it to another. The amount of points I earn from this move is the amount of balls in the pile I took the ball from minus the amount of balls in the recipient pile (not including the ball placed in the recipient pile). Notice that I may LOSE points in a move. What is the maximum amount of points I may gain after 1000 years?

Answer 1

Call the piles $A$, $B$, and $C$, and start with $2$ balls in each pile. $$\begin{array}{|ccc|c|c|c|} \hline A&B&C&\text{Move}&\text{Move score}&\text{Total score}\\ 2&2&2&&&0\\ 1&3&2&A\to B&2-2=0&0\\ 2&2&2&B\to A&3-1=2&2\\ 1&3&2&A\to B&2-2=0&0\\ 2&2&2&B\to A&3-1=2&4\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ \hline \end{array}$$ So the maximum score depends on how long you live. (You won't be around long enough to complete the $1000$-year game.