"Husband Store Joke" or "Mystery Box Dillema"

I've never been a big fan of the Monty Hall Problem. Everyone either already knows it or try to recite it to make themselves sound smart. And there's also the small matter neither Monty Hall nor Wayne Brady have ever played that game on Let's Make a Del.

The other day I re-came across (as you often do with well known jokes) with the Husband Store joke which is, in one way or another, an interpretation of several Let's Make a Deal games.

Inventing a game on that premise:
You are shown 6 numbered boxes (1-6) and are shown the content of the first box.
The first box always contains some amount of money.
The next box either contains a greater amount of money or nothing (nothing resulting in a loss, presumably all subsequent boxes also contain nothing).
You must forfeit your current prize to open the next box.

Assuming both greed and an aversion to losing, what strategy would you use?

Depends on how much $$$ I want and how averse to losing I am.

If I am entirely 100% averse to losing, then I would take the $$ in the first box, every time. But I don't think many people are completely averse to losing.

The other is -- how much $$$ I'm willing to go for. Do I know how much $$ is in the other boxes?

There's no way to answer this with any degree of certitude given this little information.

It reminds me of the GSN show How Much is Enough? (or, as I liked to call it, "the show that makes Deal or No Deal look like Jeopardy! in comparison"). On the first show, one of the contestants said she needed $5000 for something - I think it was a college fund for her child. She made it to the final round, which works like this; there are two contestants, and a prize amount of money that slowly increases from zero; the first person to buzz in gets the money. The prize got up to $5000, but she let it keep going up, and the other player buzzed in first. Apparently, she didn't "need" the $5000 as much as she did 30 minutes earlier.

Money vault games on the radio work like this... choose to take an amount or hope it goes up. Not sure how you would analyze it without some idea of potential amounts in the next box.

If you listen enough to the radio shows, and I'm sure some people have, you get an idea for how much is in the boxes and how often there is nothing. Then you can create an empirical strategy.

But just being asked to play this game blind by a new host, there isn't a workable strategy. They could just as easily have $1M in the next box as nothing, and we can't know without more info. So, in the OP case, you wing it.