%%
   
function [NewBoardPosition,GameOver] =PlayNim(CurrentBoardPosition,JStartEnd,Qas)
%
%  This function is called by NimScript.m
%  
%  It   uses a soft max policy to decide on the next board position
%
% Input: 
%     CurrentBoardPosition: this is an integer index which yields the state
%           of the game. The actual configuration of the board can be found
%           in NimScript.m such as NimColumn{CurrentBoardPosition}.
%
%     JStartEnd: This is comprised of rows of two elements indicating all the possible
%         transitions in the game. A typical row might be  [1 4] indicating that
%             one can move from board position 1 to board 4. It represents
%             the topology of the game.
%
%     Qas: This is comprised of rows of two elements. The first element of
%            each is the value of the corresponding row of JStartEnd.
%           The second element represents the number of times that the
%           choice  given by the row JStartEnd has been taken.
%
% Output:
%     
%    NewBoardPosition is the choice of the board given by PlayNim
%    
%    GameOver is a flag indicating that the game is over (last step
%           reached)
%%      
%     The algorithm is a softmax policy.
%

tau=3;
%indsPlayed= find(JStartEnd(:,1)==1);
%TotalPlayed= sum(Qas(indsPlayed,2 ));
sEnd=max(JStartEnd(:,2)); % the index of the empty state => GameOver
GameOver=0;


indQas = find(CurrentBoardPosition==JStartEnd(:,1)); % find indices possible moves
TotalPlayedQas= sum(Qas(indQas,2 ));        % Total Number of moves played
tau= 3* min(1,500/TotalPlayedQas);          % temperature depends on
tau=max(tau,.3);


relevantQs = Qas(indQas,1);         %  These are the values of the possible moves


expQs= exp( relevantQs/tau);      % This the Boltzmann weighting for the moves
sexpQs= length(expQs);

choiceVec= expQs/sum(expQs);      % This is the relative probabilities of the choices

%%         Given the relative probs, pick a random number and choose a move
%            out of the possible moves.  Do this by finding the cumulative  
%           distribution (sumChoiceVec), then find in what interval a random number falls.

sumChoiceVec(1)= choiceVec(1);

for jj=2:sexpQs
    sumChoiceVec(jj)= sumChoiceVec(jj-1)+choiceVec(jj);
end


rrand=rand();

inds = find(rrand<sumChoiceVec);
inds=inds(1);   % This is the index of the choice that we want

NewBoardPosition=JStartEnd(indQas(inds),2);

if NewBoardPosition==sEnd
    GameOver=1;
end
%%