Thought Experiment

In front of you there are two seemingly identical envelops. Both contain real cash. One envelop has exactly double the amount of dollars that the other one has. You get to choose one envelop to open. After opening that envelop and seeing how much cash is inside, you are given a choice: keep the amount in your hand, or forfeit it and take the other envelop.

Note: there's no silly trickery or anything, nor is there a right or wrong answer.
Note: the envelops can have up to, let's say, a million dollars.

Most people would forfeit the first envelop if it contained only twenty bucks. Because the probability (50%) of getting either $10 or $40 bucks instead of your guaranteed $20 is not really a big deal.

Assuming you would switch the envelop with a small sum of money, at which dollar amount would you keep the first envelop? Or would you always switch?

Me: Any amount up to $1000 and I would forfeit it for the second envelop. I would keep the first envelop if it had $1000 or more in it.

Second note: I kinda came up with this just in a conversation a few months back. In asking a few people since then, I've been told game shows such as "Deal or No Deal" are similar. Though, this game there's less pressure and no hype. You always know there's a 50% chance of halving your money, and a 50% chance of doubling it. I also don't watch television.