It's funny how this "all the contestants were stupid" stereotype is so prevalent, as many of the contestants on this show actually did very well; it's just that we as humans tend to remember negative outcomes more often than positive outcomes, so people disregard the large number of contestants that won six-figures in favor of the relatively small number that walked out with pocket change, like the contestant you described.
Otherwise, I pretty much agree with your post. This is a game that is dependent on risk/reward, and evaluating the expected value of the remaining amounts in comparison to the offer is also an important aspect of the game; I would personally cash out on most offers that are 80% of the expected value or more (especially if there is only one amount available that is higher than the offer), but I could certainly accept a lower percentage based on how volatile the board is. If there is only one higher amount on the board, I honestly wouldn't care if my case held that amount or not; my only regret would probably be not opening one more case in order to get a higher offer, and even then, I know an offer that's too good to refuse when I see one, so that regret could also be eliminated in certain instances.
I'm not entirely sure what I would do in your example scenario since 67% of the expected value ($80,000/$120,000) is not exactly the type of percentage I would readily accept; my decision would definitely depend on the amounts I was offered earlier (due to both the possibility/inability to match a higher offer by opening one more case in addition to studying the offer trends; if the earlier offers were also lacking in generosity, an offer close to the expected value seems highly unlikely one case later), but in all likelihood, I would accept the $80,000 because it's relatively close to the second-highest amount, and a board like $1/$5/$100/$100,000 or even $1/$5/$100/$500,000 could potentially open the door for the Banker to lowball the consequential offer since the contestant will have a much greater fear of walking away with almost nothing (although this was far more common on the daytime syndicated version rather than the primetime network version that is the subject of discussion here).
Going back to what I was saying about the offer trends, I would predict that the next offer would be 80% of the expected value assuming that there were similar increases in generosity between the earlier offers, so you'd essentially be looking at a 60% chance of gaining $40,000 vs. a 20% chance of gaining $20,000 vs. a 20% chance of losing $60,000. I wouldn't consider that an ideal gamble, which is why I would probably take the deal, but it is arguable either way if you are prepared for the 20% chance of the offer being divided by 4 in an attempt to take advantage of the 80% chance of an increase. It's all in the eye of the beholder, and while there is certainly an element of greed that is required in making the decision, it all comes down to whether you personally feel comfortable taking the risk or not.
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