Instead of having radio buttons (white to move/black to move) and one button, change the GUI to have two buttons: [Black next move] [White next move] and remove the radio buttons. Now that you have prev button, you should automatically apply the move after the calculation is done. This way it will take one click to make a black move and see it. Right now I have to make three clicks - chose the black radio, click on the button and click on the move when it is done.