The thread "I am in math heaven" seems to be irretrievable so I will give the answer to the math homework I assigned there in this thread.

The question was, if there are only 7 players, and they play each other only, and they play forever, what will their average scores be? Will it be infinite?

Answer: Infinity, yes.

I don't have the math skills to work it out directly, but I set up a simpler problem on a spreadsheet. Suppose you flip a fair coin over and over. For each head, you gain one point, for each tail, you lose one point, but if your total score falls below zero, it is restored to zero.

I ran this for 12,000 iterations on a spreadsheet and found that you have a positive score about 98 percent of the time. So every 50th toss, on average, you will go into negative territory and be given one point. So, your score will roughly be 200 points for every 10,000 interations. In other words, unbounded.

In kdice, will the average player have a positive score 98 percent of the time? It remains to be seen.