Matrices
Note:
In the LJ model we have 118 states [no (Jail,1) or (Jail,2)], so all
matrices are 118 × 118.
In the RIJ model we have 120 states, so all matrices are 120 × 120.
Also, we index the rows by the current state and the columns by the
next state, but Abbott and Richey reverse this convention. In other
words, they consider the transposes of the (40 or 42 state versions of
the) matrices given here.

block matrix with nine blocks, four of which are
blocks of zeroes

Jail Matrix J
Abbott and Richey use a matrix to
simulate the Go to Jail space and to
approximate the rule about three doubles sending a player to
Jail, but our
choice of state space avoids this approximation.
For
consistency, we
will take J to be the identity matrix.

differs from the identity matrix
in exactly
nine
rows
(since there are three Community Chest spaces and three
values for
d)

differs from the identity matrix
in exactly
nine
rows
(since there are three Chance spaces and three values for
d)

Note that the order of multiplication is important. In particular,
see spaces 33 (CommunityChest3) and 36 (Chance3).
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