% Copyright 2005 William S. Krasker

% U(p0,pFG,pTD) is win probability at the start of a drive, if the win probability at
% the end of the drive is p0, pFG, or pTD according to whether the drive ends in
% no score, a field goal, or a touchdown respectively.

p1=0.985;
p2=0.4;

% Guess win prob at start of 4th OT for team with first possession.
Fguess=0.5;

for i=1:10

   % At middle of 3rd OT, find win prob for team that goes second as a function
   % of what the team that went first did.   
   S0=U(Fguess,1,1);
   S3=U(0,Fguess,1);
   S6=U(0,0,p2+(1-p2)*Fguess);
   S8=U(0,0,p2*Fguess);
   
   f0=1-S0;
   f3=1-S3;
   f6=1-S6;
   f8=1-S8;
   
   %Win prob at start of 3rd OT for team that goes first.
   F=U(f0,f3,p2*f8+(1-p2)*f6);
   
   Fguess=F;
   
end

% At middle of 2nd OT, find win prob for team that goes second as a function
% of what the team that went first did.   
S0=U(F,1,1);
S3=U(0,F,1);
S6=U(0,0,p1+(1-p1)*F);
S7=U(0,0,max(p1*F,p2));
S8=U(0,0,p2*F);
   
f0=1-S0;
f3=1-S3;
f6=1-S6;
f7=1-S7;
f8=1-S8;
   
%Win prob at start of 2nd OT for team that goes first.
F=U( f0, f3, max(p1*f7+(1-p1)*f6, p2*f8+(1-p2)*f6) );

% At middle of 1st OT, find win prob for team that goes second as a function
% of what the team that went first did.   
S0=U(F,1,1);
S3=U(0,F,1);
S6=U(0,0,p1+(1-p1)*F);
S7=U(0,0,max(p1*F,p2));
S8=U(0,0,p2*F);
   
f0=1-S0;
f3=1-S3;
f6=1-S6;
f7=1-S7;
f8=1-S8;
   
%Win prob at start of 1st OT for team that goes first.
F=U( f0, f3, max(p1*f7+(1-p1)*f6, p2*f8+(1-p2)*f6) );