% moves2048 computes the number of moves used on a 2048 game, based on the
% tile values and the general score.
%
% Usage:
% * m = moves2048(score, board) computes "m", the total number of moves
%   used plus two. This is the same as the total number of tiles that
%   appeared in the game: one on each movement, plus the two initial tiles.
% * [m, p] = moves2048(score, board) also estimates the probability of a
%   random tile being 2. The product m*p efectively results in the total
%   number of "2" tiles that appeared in the game, while m*(1-p) results in
%   for the number of "4" tiles appeared.
%
% Example:
% * m = moves2048(130788, [64   16    8   2;
%                          32 8192  512  64;
%                           8 1024 2048 128;
%                           2   64    4   2]);
%
% * [m, p] = moves2048(4, [4 4 2 2])
%
% See also:
%   http://gabrielecirulli.github.io/2048/
function [m, p] = moves2048(score, board)
    board = board(:)';
    lowerbound = max(log2(board)-2,0) * board';
    
    moves2 = (score-lowerbound)/2 + sum(board==2);
    moves4 = (sum(board)-moves2*2)/4;
    moves = moves2+moves4;
    
    m = moves;
    p = moves2/moves;
end