Consists of 120 ordered pairs (s,d), where
s = 0, 1, ..., 39 and d = 0, 1, 2. Here, s represents
the space on the board (0 means Go, 39 means Boardwalk) and d is
the number of doubles rolled so far in this turn. By the rules of the
game, a player who rolls three doubles in one turn must go directly to
Since a player never remains on the "Go to Jail" space, and since we need
separate states for Jail and Just Visiting, it is convenient to assign
Just Visiting to
s = 10 and
Jail to s = 30. We will need to be careful in setting up the roll
matrix to account for this convention.
- In the LJ model, we have no use for three separate Jail states, so we
use only (30,0) and discard (30,1) and (30,2), leaving only 118
states. However, in the RIJ model, we use
state (30,1) to represent the situation when a player has failed at
doubles exactly once
and state (30,2) to represent the situation when a player has failed at
doubles exactly twice.
Note: Abbott and Richey use only
40 states (42 for RIJ), but at the expense of less accurate results.