Besides that you need to predict where the next number can and should spawn. If you don't figure out the strategy for that you will never get a decent score.

Board history does not matter.

    Grid.prototype.randomAvailableCell = function () {
      var cells = this.availableCells();

      if (cells.length) {
        return cells[Math.floor(Math.random() * cells.length)];
      }
    };

Yes, but that's _state_, not _history_.