No, I’m not asking about the math. I understand the odds. This is a different topic.
Part of the set-up is that Monty knows what’s behind each door. Has anyone ever discussed the part of the problem? Did Monty already know before the contestant made their choice? If he did, did he have a tell? It occurs to me that you could watch past episodes of Let’s Make a Deal and observe Monty’s reactions. You might discover, for example, that Monty always raised his right eyebrow when you picked the wrong door or frowned when you picked the right door.
If the studio was concerned that Monty might be inadvertently tipping off the answers, they might have kept him in ignorance along with the contestant when the choice was made and then signaled to Monty which door he should open.
Another issue was whether the choice of the door with the prize was truly random. Did anybody ever keep records? Maybe the studio felt that the show was more dramatic when Monty opened the middle door so that door was left empty more often than the right or left doors.
Everyone treats this as an idealized math problem but I’m wondering how much the actual show differed from the idealized conditions.