Do absolutely not "encourage them to let go on their own". When discovered use tweezers or a tick-removal tool to remove it as soon as possible. Make sure to pull as close to the skin as possible.

All old folk-remedy things with butter and alcohol only risks the tick to go into shock and spew saliva into you, increasing the risk for lyme disease/tbe or borrelia.

Just pull it straight out, it's safe and easy, done it a dozen times.

Also get vaccine for lyme disease if you are in an area where ticks pass it on, it is a horribly crippling disease and not worth the risk however low.