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Run the math again. This game should be called "Discounted Actuarial Tables: The Game Show." At any given point, average the remaining amounts on the board, reduce it by ten to twenty percent, and you'll have the "banker's" offer. Like, if the player is down to $200k, $1, and $1000, the offer will probably be something around $55k to $60k.
Over the long term, they get cost certainty and with some insurance they can run it like a casino and budget accordingly. It doesn't have to be rigged, and as someone else has said, American TV game shows are generally considered to be above-board in a "yes/no" sense due to the Quiz Show scandal of the late 1950s. However, this makes the game play for something like Deal or No Deal very, very boring, so they spice it up with fake drama and human interest.
And even then, the show is still incredibly boring.
Hence why it is on tv
You should DEFINITELY work in marketing 😄
It's been well over a decade since I've seen the show, but I remember the banker would sometimes throw in exceptionally high/ low offers to add to the "drama". Like they'd offer $2 after the contestant knocks out the million dollar case.
Yeah, I suppose the real answer is "what will make good TV without blowing the budget," but I would just about bet the trendline for actual offers would be skimming a little bit below expected value.