Generate state matrices by recursion
A weekly team record classifies each player's availability. The same transition rule is applied repeatedly
Use the state order available and limited. Every state matrix is a column in this order. In the transition matrix, columns are current states and rows are next states
One application of the transition matrix represents one week. The initial state is S_0, before any applications, so the index counts applications
\[T = \begin{bmatrix} 0.8 & 0.3 \\ 0.2 & 0.7 \end{bmatrix}\]
The initial state column gives counts of players
\[S_0 = \begin{bmatrix} 100 \\ 100 \end{bmatrix}\]
\[S_{n+1} = T S_n\]