It's like a casino they are not going to give you a fair deal if they can help it.
...not
if they can help it -- they DESIGN the game that way: it's ALWAYS in their favour.
The difference is, this is a TV game and the thing in 'their favour', is advertising. That's how they can 'afford' to give away money every game.
Thus, the US has a $1m prize because the bigger audience means more advertising revenue. In other countries (mentioned above), max win is 1/5 of that... because they're smaller markets.
Most people are way to stupid to realize they are getting a deal and pass, but by far most of the time it is a bad deal. It's like a casino they are not going to give you a fair deal if they can help it.
The 'rational' approach should be:
Let Expected value = sum of (probability * value of case i)
Decision rule for this game should be where expected value < offer, accept.
But I don't think many people run this calculation. They try to approximate it, which leads to what Rage talks about in the above quote.
...But 'stupid', (or, more formally, 'irrational') decisions are interesting things: you can't judge someone else's decision, because they've got their own risk orientations. To THEM, while standing there thinking about the tradeoff, taking the risk is 'worth it'.
Wow it's like my psych classes all over again.