The thumb around trick is the pen making a complete 360 degree circle around the thumb. First you must find the pen's center of gravity by balancing it on one finger. Hold the pen just to the left of the center of gravity between your thumb and index finger. Your middle finger will be in the center. Push the pen away sending it towards your thumb. Your middle finger should get out of the way by folding down. Your thumb does not move during this trick.
Catch the pen on the other side with your index finger. This trick will take a lot of practice. You will need to vary the speed and strength at which the pen moves until you figure out the force needed to send it all the way around without losing control of it.
This trick starts with your pen between the middle and ring fingers with the top of the pen resting between your thumb and index finger, or thumbflap. By pressing the top of the pen into the thumbflap you are creating pressure that will provide momentum for the pen. Move your ring finger away from your body and your middle finger towards your body. This will release the pressure from your thumbflap and create the rotation.
Keep your index finger straight and out of the way until the pen moves towards your thumb when you can use the thumb and index finger to catch it. You can also do this trick by starting between different fingers like the pinky and ring finger or the index finger and middle finger.
For the half tap the pen rests on top of your hand and does a half spin so it starts with its tip pointing out towards your fingertips but finishes pointing in the opposite direction. Start with the top of your pen resting on the thumbflap. The pen does not need pressure like in the previous trick.
Extend your index finger straight out with the bottom of the pen resting on your middle finger. Your thumb is extended on the other side of the pen. Push, or tap, the pen with your index finger. The pen should skim along the top of your thumb and index finger as it rotates. When it has gone halfway around lift your index finger to stop the motion and the pen will fall back into position. Once you have mastered the half tap you can do the full tap by allowing the pen to rotate 360 degrees.