In what is perhaps the most affirming arcade discovery of our time, Vox writer Phil Edwards uncovered why claw machines are rigged and generally a total sham. Basically, the claw mechanism can be programmed to have different levels of "claw strength." That's why it will sometimes neatly clench itself around the neck of your desired teddy bear, only to graze back over the toy's head on the way back up, leaving you with nothing. The machines can be programmed by their owners to power up to full strength only when it's profitable based on the prizes inside. For example, "if it costs $0.50 to play the game, and the prize inside costs $7, [then] to make a profit of 50%, full power will be sent to the claw only about once every 21 games or so."
To make the odds infinitely more infuriating, the winning game is randomized inside a range of games, so you can't just play 21 times in a row and expect to win on the last try.
And there's an extra feature machine owners can program to manage profits, too — "dropping skill." So, in addition to the claws being programmed for strength, they can also be programmed for dropping-prize-in-the-slot accuracy.
If you've always dreamed of sweet, sweet closure for your childhood claw-related trauma and disappointment, all the answers you seek to find can be viewed below.