Clicker training is the same as positive reinforcement training, with the added benefit of a clicker. A clicker is simply a small mechanical noisemaker. The techniques are based on the science of animal learning, which says that behaviors that are rewarded are more likely to be repeated in the future.
Also known as incremental games or idle clickers, most idle games involve tapping on the screen to rack up currency of some sort. Tap enough and you'll level up, eventually unlocking new features and systems. The more you play, the more the game grows and many idle games will even keep playing while you're away.
