ruin

%%%%%%%%%%%%%%% Gambler's ruin computations %%%%%%%%%%%%%%%%

0001 %%%%%%%%%%%%%%%% Gambler's ruin computations %%%%%%%%%%%%%%%%
0002 n=5;              % n+1 possible states, numbered 1 to n+1, corresp to 0 to n
0003 P=zeros(n+1,n+1); % blank matrix to work with
0004 for i=2:n,
0005   P(i,i-1)=0.5;   % transitions from transient states
0006   P(i,i+1)=0.5;
0007 end
0008 P(1,1)=1;         % transitions for absorbing states
0009 P(n+1,n+1)=1;
0010 t=2:n;            % index vector of transient states, to pull out Q
0011 Q=P(t,t);         % SLICK!  Pulls out columns and rows 2 to n of P
0012 RT=inv(eye(n-1)-Q);   % matrix telling expected number of visits
0013 r=[1,n+1];        % index vector of recurrent states, to pull out L
0014 L=P(t,r);         % SLICK!  Pulls out rows 2 to n and columns 1 and n+1 of P