Quote Originally Posted by FunkyDexter View Post
if you ran that same simulation 1000 times
That's the key... you CAN'T play the (actual) game 1000 times. You only get to play once, and at least in the US version, you're generally dealing with life-altering quantities of money. This is why there is a huge difference for the player between a $400,000 offer when the two cases left are $1 and $1,000,000, as opposed to a $400,000 offer when the two cases contain $250,000 and $750,000. Their expected values are only 50 cents apart, but I would advise the former to always make that deal, knowing he has been low-balled by $100,000, while the latter has much better reason to press his luck.

It sounds like in the UK and Australian versions the cases contain less money relative to the typical contestants income (it makes sense, assuming the audience sizes are proportional to the national populations). Is £50,000 a life-altering amount for the typical Brit? If not, then we might as well be talking about different games entirely.

This is kind of similar to prisoner dilemma scenarios. Tit-for-tat is almost always the best strategy when there is repetition, but for the actual prisoner himself, he only gets one shot, so tit-for-tat doesn't even make sense for him.

That said, your suggestion to the OP is a good one, with the caveat that the game goes longer, the banker's offers should approach the expected value (since that is what happens in the actual game).

And for what it's worth, I don't like this show either, but mostly because of the over-dramatization. I find the mechanics pretty interesting, but am not willing to burn an hour for just 10 minutes of actual entertainment.