Cost-Reward Analysis

• Salary (Passing Go)
  
  
  • Compute 200 Σ π_i p_ij, where π is the limiting distribution computed previously and the sum is taken over all ordered pairs (i,j) such that a player passes Go when moving from state i to state j.
    
    
  • Determining the set of ordered pairs is quite tricky.
    
    
  • A first approximation is to include all transitions where the space number s weakly decreases.
    
    
  • Many complications need to be considered:
    • "Go Back 3 Spaces" Chance card
    • advancing to ReadingRR, Boardwalk
    • starting from Jail
    • ending up in Jail (sometimes after passing Go, sometimes not)
    • passing Go twice in a single roll
  
  
• Expected Income Per Roll from Bank

  	LJ	RIJ
  Salary (Passing Go)	29.6594?	28.0021?
  Taxes (Income and Luxury)	-6.29194	-5.93507
  Community Chest	1.71135	1.57546
  Chance	1.08882	1.04918
  Bail	-1.97499	-1.07435
  Total	24.1926?	23.6173?
  Assessment and General Repairs:
  Each House	-0.311414	-0.291667
  Each Hotel	-1.02563	-0.96411

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