She could then compound her glee by being smart enough not to trade it all back for the old purse and whatever amount of cash Mr. Hall had slipped into it — maybe a hefty amount or maybe a measly $27. If she went for the deal that turned out to be a loser, she was, in the language of the show, zonked.

At the end of the show, the two biggest winners were given a shot at the Big Deal. They could trade their winnings for whatever was behind one of three doors: a new car, perhaps, or $15,000 in cash, or, if they were not so lucky, something worth less than what they had traded. All the while, the affable, smooth-talking Mr. Hall gave no hint of where the treasure might lie.

“Monty had to be a very likable con man; he had to convince people to give up a bird in the hand for what’s in the box,” David Schwartz, the author, with Fred Wostbrock and Steve Ryan, of “The Encyclopedia of TV Game Shows,” said in an interview.

Mr. Hall had other responsibilities, too, Mr. Schwartz added: “He had to be a traffic cop, to get a decision out of the contestant without taking a long time. With his great ability to ad-lib, he knew how to keep the show moving.”

Mr. Hall kept “Let’s Make a Deal” moving for most of almost 5,000 broadcasts on NBC, on ABC and in syndication. The show ended its original daytime run in 1976 on ABC. A concurrent syndicated nighttime version lasted until the next year. It occasionally resurfaced over the next decades and, after being off the air for a while, was revived in October 2009 on CBS, with Wayne Brady as host. That version is still on the air.

“Let’s Make a Deal” became such a pop-culture phenomenon that it gave birth to a well-known brain-twister in probability, called “the Monty Hall Problem.” This thought experiment involves three doors, two goats and a coveted prize and leads to a counterintuitive solution.