So I was doing one of the euler questions, and it asks:

In the game, Monopoly, the standard board is set up in the following way:

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 to directly 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):
  
  
  
  1. Advance to GO
  
  
  2. Go to JAIL
  
  
  
  
  


• Chance (10/16 cards):
  
  
  
  1. Advance to GO
  
  
  2. Go to JAIL
  
  
  3. Go to C1
  
  
  4. Go to E3
  
  
  5. Go to H2
  
  
  6. Go to R1
  
  
  7. Go to next R (railway company)
  
  
  
  8. Go to next R
  
  
  9. Go to next U (utility company)
  
  
  10. 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.

So I decided to build a monopoly simulator. I did it at first at work, but it didn't give me good results. Damn VB's randomizer did not like mt too much I'm guessing. So before I went to bed, I redid the entire simulator in Java. Its pretty sick, I now know the probability of landing on any square, so listen up to know which property you should buy!

If you were to number the squares from 0 to 39, here's the number of times you'd land on each square, assuming you rolled the two dice 10 million times.

1. Jail - 622228
2. Illinois Ave - 318336
3. New York Ave - 309739
4. GO - 308705
5. B&O Railroad - 307718
6. Reading Railroad - 297163
7. Tennessee Ave - 293212
8. Pennsylvania Railroad - 291143
9. Free Parking - 287501
10. Kentucky Ave - 283870
11. Water Works - 279720
12. St. James Place - 279563
13. Indiana Ave - 273179
14. Atlantic Ave - 269697
15. St Charles Place - 269678
16. Pacific Ave - 268251
17. Ventnor Ave - 267982
18. Boardwalk - 262216
19. North Carolina Ave - 261937
20. Electric Company - 259929
21. Marvin Gardens - 258568
22. Community Chest 2 - 258082
23. Pennsylvania Ave - 250309
24. Virginia Avenue - 246854
25. Short line - 242476
26. Community Chest 3 - 238379
27. States Ave - 237184
28. Vermont Ave - 232893
29. Income Tax 1 - 231599
30. Connecticut Ave - 230336
31. Oriental Ave - 226835
32. Park Place - 219057
33. Luxury Tax - 218509
34. Baltic Ave - 216265
35. Mediterranean Ave - 213695
36. Community Chest 1 - 189488
37. Chance 2 - 103436
38. Chance 1 - 87370
39. Chance 3 - 86898
40. Go To Jail - 0