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Variable ratio is a psychological concept used in operant behavioral conditioning that describes how often a "reward" is delivered in relation to a discriminative stimulus. It is by far the most powerful reward schedule discovered, and the one that creates the greatest response to the stimulus, the quickest rate of learning the connection between the reward and the stimulus, and is the most resistant to extinction when the reward is no longer paired with the stimulus. It also has the interesting side effect of creating the most "ghost" stimulus - known in humans as "superstitions" or "magical thinking".
The classic example of a variable ratio reward schedule is the slot machine. In this case rather an action (or response) is conditioned. The action is putting your money in the machine and pulling the lever, while the reward is "winning" more money than you put in. The reward is delivered based on the number of times the action is performed, but the number of times needed to get a reward is variable not fixed.
The overwhelming power of this reward schedule is thought to have developed in response to it ecological validity. The mechanisms that underlie conditioned responses developed in order to facilitate survival by linking salient cues with appropriate actions. Conditioned responses are often sub-conscious and very quick. For appropriately conditioned responses this facilitates survival, but for badly conditioned responses it can be detrimental. Therefore, you want conditioned responses to build up most readily to true predictors of consequence. In nature, cues that predict future events are most often going to follow a variable ratio.
Beyond being capitalized on by casinos the power of the variable ratio has a role to play in magical thinking. While logically it is easy to see that correlation does not imply causation, our underlying psychology is constantly forming just such inferences about the world around us. Superstitions often develop my thinking that certain events predict certain outcomes, when in fact the relationship is random or only loosely related. However, "random" co-variation, or variation due to third variables mimic "variable ratio" reward scheduling. This means that the conditioned response to superstitions and magical thinking becomes highly ingrained very quickly, and is highly resistant to change.