Dave's Stupid Rule is a regulation that is in effect at most tournaments. While there are minor variations of the rule, they all have the same intention: to prevent a player from having an unfair advantage by playing the same stage multiple times in a set. The rule is named after the smasher Scamp.
At the rule's simplest level, no stage that has already been played in a set may be picked for another game in the same set. For example, a random pick chooses Final Destination for the first game of a Falco vs. Ike match. The Falco player loses, so they get to pick the next stage. They want to choose Final Destination again, because it's a strong stage for Falco. However, Dave's Stupid Rule states that Final Destination cannot be played again in that round, so the Falco player must pick a different stage.
The most common variation of Dave's Stupid Rule is that a player cannot pick a stage they have won on during the set in question. Therefore, under this variation, the Falco player would be free to pick Final Destination for the second game. However, imagine that Final Destination was the randomly selected starter stage. The Falco player wins, so the Ike player counterpicks Battlefield. Ike wins game two. Now, the Falco player gets to pick the next stage, but because they won on Final Destination, they cannot pick it again.
Another variation says that if the player counterpicking chooses Random for the stage, a stage may be played twice. In some tournaments, where only three or four stages are allowed, this is often a viable strategy to get the same stage twice in one match.
The newest variation, known as "Modified DSR", states that a player cannot pick the last stage they have won on during the set, while any stages of previous wins are fair game.
As of late there was much displeasure with "Modified DSR" because of the so called Mew2King effect where a player wins on the counterpick stage of his opponent and is able to pick his own counterpick stage again (in M2Ks case FD with Marth against Fox and Falco). Therefore the german community initiated by tournament organizer Tero acted as a pioneer and changed the rule to "you can not pick your counterpick stage again if you won on it", called Teros Smart Rule at first. This idea was picked up by Scar and Armada in an episode of the Melee it on me podcast and later adopted by other european countries.