If we number the states as 1: Win; 2: Loss; 3: Draw, we get the transition matrix from the given table:

This is the onestep transition matrix. To obtain the longterm behavior using technology, we need to compute the matrix P^{}. The rows of P^{} are given by the solution of the following system of equations:
where P is the above transition matrix. This gives the following system of linear equations:
x + y + z  =  1 
0.6x + 0.3y + 0.3z  =  0 
0.4x  0.6y + 0.3z  =  0 
0.2x + 0.3y  0.6z  =  0 
Solving the above system gives x = 1/3, y = 10/27, and z = 8/27. P^{} is now the 33 matrix whose rows are [ 1/3 10/27 8/27 ]. These three solutions are also the fraction of times England can expect to win, lose, and draw in the long term.
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