Final answer:
The reinforcement schedule that rewards gamblers with money in a slot machine is the variable ratio schedule. The player experienced positive reinforcement initially but then underwent extinction when pulling the handle no longer resulted in a payout.
Step-by-step explanation:
The reinforcement schedule that rewards gamblers with money in a slot machine is the variable ratio schedule. This means that the payouts are unpredictable and occur after an average number of responses. In this scenario, the player initially won three times, which provided positive reinforcement and increased their interest in continuing to play. However, after pulling the handle 30 more times without a payout, the player experienced extinction, as the behavior of pulling the handle no longer resulted in reinforcement.