you CAN'T play the (actual) game 1000 times. You only get to play once
We're dealing with probablity maths so that's irrelevent. Logically you should alwasy make the decision that has the best prospective outcome. I understand what you're saying but you're essentially advising the player to make their decision based on emotion rather than logic. $400,000 dollars may be a life changing amount of money but $1,000,000 is two and a half times as life changing. The right decision in life is to always, ALWAYS play the odds. You may lose out today but you'll win back tomorrow. (Which is the same reason you're better off not buying insurance if you can help it, collectivise your own risk, as part of a wider collective if necessary - it's cheaper).

It sounds like in the UK and Australian versions the cases contain less money
From memory I think they run from £1 to £100,000 in the UK but I don't watch it enough to be sure. It's certainly enough to be life changing if they win the jackpot though I don't think you'd retire on it. Realistically, most people win somewhere less than £20,000 which is a deposit on a flat. Nice, but not life changing.

This is kind of similar to prisoner dilemma scenarios. Tit-for-tat is almost always the best strategy
I don't know anything about that but it sounds quite interesting. Can you expand on it?

mostly because of the over-dramatization
Yeah, I blame Chris Tarrant. No quiz show since Who Wants to be a Millionaire has been able to go to a commercial break without a 5 minute suspense build up at the end of which the host declares "and we'll find out after this..." As a formula it's getting pretty old at this point. I watched a great episode of Who Wants to be a Millionaire once where the contestant had already won the Australian and US versions. He was utterly sure of himself in every answer he gave. Tarrant kept trying to do teh "Are you sure? it could be A." thing and this guy just shut him down cold every time. It was brilliant TV for all the wrong reasons.