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%

% Markov.m Script - computes the Markov Chains associated

% with probability of playing successive

% Brownian games used to illustate

% Parrondo's Paradox

%

% Author: Evan Shechtman

% Apr. 3, 2002

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clear

% Set initial conditions

epsilon = .001;

n = 2250;

modulus = 3;

dollars = 100;

win = dollars+1;

% Set transition matrices for Markov chain

for x=1:win

for y=1:win

Ta(x,y)=0;

Tb(x,y)=0;

end

end

Ta(1,1) = (1);

for x=2:win-1

Ta(x-1,x) = (.5+epsilon);

Ta(x+1,x) = (.5-epsilon);

end

Ta(win,win) = (1);

Tb(1,1) = (1);

for x=2:win-1

if (mod((x-1),modulus) == 0)

Tb(x-1,x) = (.9-epsilon);

Tb(x+1,x) = (.1+epsilon);

else

Tb(x-1,x) = (.25+epsilon);

Tb(x+1,x) = (.75-epsilon);

end

end

Tb(win,win)=(1);

% Set state vectors

for x=1:win

InitState(x)=0;

end

InitState(floor(win/2))=1;

% Computing n successive moves starting

% at each state

GameA = Ta^n*InitState';

GameB = Tb^n*InitState';

current = InitState';

for i=1:(floor(n/4))

current = Ta^2*current;

current = Tb^2*current;

end

% End of markov()