Expected Number of Rolls Until Player Lands in Jail

• Let m be a column vector of length 120 - 3 = 117 and 1 a column vector of 117 ones, and solve m = 1 + Q · m, where Q is the 117 × 117 matrix obtained by removing from P the rows and columns corresponding to the Jail spaces. Solving for m, we have m = (I₁₁₇ - Q)^-1 1.
  (This computation takes less than one second with Mathematica.)
  
  
• Starting in State (s,d) (independent of choice of LJ or RIJ)
  
  
• Starting at Space s
  
  
• Overall Expectation

  	LJ:	24.2872
  	RIJ:	22.9184

  
  
• Plot

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