Matthew writes new piece(s) without a commission each year.

Each of his works has a % chance of being performed the year it is written. Each time it gets performed, it has the same chance of being performed the following year.

He receives a new commission every performances (although he never composes more than pieces per year).

He receives an average of $ in royalties for each performance, and an average of $ for each commission.

 

Mathilda does everything exactly the same, except that for her, the chances of a performance are %, not %, and she receives a new commission after every performances, not .

 

After years, Matthew has about performances per year, and Mathilda has about (% as many). They have composed and works, respectively, of which % and % were commissioned. At this point in his career, Matthew earns $ from composing in a typical year, while Mathilda earns $.