So what does this have to do with investing?
Quite often we see the same sort of behavior in the stock market: always trying to do better than the average, folks will use all kinds of methods (including paying extra to get the top dog stock picker's advice) because they're sure they can beat the market. If a chosen stock shoots up in value the investor hangs on, "knowing" that if it went up 10% it is bound to go up another 10%. And what happens when the stock goes on up to 20%? Yep, they hang in there again.
Then suddenly the stock pulls back, and now is down 5% from the original investment -- what happens now? This is just like when the banker on the show reduces his offer: Investors feel like they've lost something already in hand, so they begin to take more risks, perhaps buying more of the stock -- again, "knowing" they'll "make it up." But it rarely works out.
The problem is that the investor didn't go into the investment with a plan -- and the same would hold true for a contestant on the game show. If you decided you were shooting for a 10% return from this particular stock, you'd have sold out at that level and could have gone looking for the next great option. Without a plan, you never know when to get out of the position.
If contestants were to go into the show with a plan to do better than average: The first time the banker offered more than $131,477.50 (the average of all the amounts in suitcases), they would take it. It's an excellent strategy, especially when you consider that 20 of the 26 cases have less than the average amount inside.