# Problem 84: Monopoly odds
In the game, Monopoly, the standard board is set up in the following
way: 

    GO A1 CC1 A2 T1 R1 B1 CH1 B2 B3 JAIL 
    H2                                C1 
    T2                                U1 
    H1                                C2 
    CH3                               C3 
    R4                                R2 
    G3                                D1 
    CC3                              CC2
    G2                                D2 
    G1                                D3 
    G2J F3 U2 F2 F1 R3 E3 E2 CH2 E1 FP 

A player starts on the GO square and adds the scores on two
6-sided dice to determine the number of squares they advance in a
clockwise direction. Without any further rules we would expect to visit
each square with equal probability: 2.5%. However, landing on G2J (Go To
Jail), CC (community chest), and CH (chance) changes this distribution.
In addition to G2J, and one card from each of CC and CH, that orders the
player to go directly to jail, if a player rolls three consecutive
doubles, they do not advance the result of their 3rd roll. Instead they
proceed directly to jail. At the beginning of the game, the CC and CH
cards are shuffled. When a player lands on CC or CH they take a card
from the top of the respective pile and, after following the
instructions, it is returned to the bottom of the pile. There are
sixteen cards in each pile, but for the purpose of this problem we are
only concerned with cards that order a movement; any instruction not
concerned with movement will be ignored and the player will remain on
the CC/CH square. Community Chest (2/16 cards): Advance to GO Go to JAIL
Chance (10/16 cards): Advance to GO Go to JAIL Go to C1 Go to E3 Go to
H2 Go to R1 Go to next R (railway company) Go to next R Go to next U
(utility company) Go back 3 squares. The heart of this problem concerns
the likelihood of visiting a particular square. That is, the probability
of finishing at that square after a roll. For this reason it should be
clear that, with the exception of G2J for which the probability of
finishing on it is zero, the CH squares will have the lowest
probabilities, as 5/8 request a movement to another square, and it is
the final square that the player finishes at on each roll that we are
interested in. We shall make no distinction between "Just Visiting" and
being sent to JAIL, and we shall also ignore the rule about requiring a
double to "get out of jail", assuming that they pay to get out on their
next turn. By starting at GO and numbering the squares sequentially from
00 to 39 we can concatenate these two-digit numbers to produce strings
that correspond with sets of squares. Statistically it can be shown that
the three most popular squares, in order, are JAIL (6.24%) = Square 10,
E3 (3.18%) = Square 24, and GO (3.09%) = Square 00. So these three most
popular squares can be listed with the six-digit modal string: 102400.
If, instead of using two 6-sided dice, two 4-sided dice are used, find
the six-digit modal string.