Magic is doing without knowing —— Gustav Meyrink

The Monty Hall problem involves three doors, one with a grand prize behind it. After the contestant makes their choice, the host opens a door without the prize and lets the contestant decide whether to change their selection. The conclusion is that changing the initial choice is the most rational approach.

This problem can be thought of this way: if there are a hundred doors, the initial chance of winning is one percent. As doors without prizes are continuously opened, leaving only two doors, the probability of winning by random choice becomes fifty percent. The counterintuitive thing is that when only two doors remain, it seems like the initially chosen door and the remaining door create a fifty-fifty illusion. In reality, the door that was left behind has been reinforced by countless pieces of information and has transformed into a super door that’s almost certain to win.

Let’s stop the mathematical discussion here. There’s a psychological issue called Loss aversion, which refers to people’s tendency to prefer avoiding losses over acquiring equivalent gains. The negative utility of losses is 2 to 2.5 times greater than the positive utility of gains. Loss aversion reflects that people’s risk preferences are not consistent: when it involves gains, people show risk aversion; when it involves losses, people show risk-seeking behavior.

Returning to the problem above, if the contestant follows rationality and makes the change but doesn’t win, the psychological loss would probably require winning two more grand prizes to compensate.

The first-level meaning of this matter is that people should try to eliminate the influence of loss aversion as much as possible and make rational choices more often. The metaphorical meaning of this entire problem is that people should open more doors for themselves, increase their knowledge and information reserves, and based on this foundation, bravely make choices, take action, and muster the courage to face all consequences.

Postscript: This might be my closest approach to a short essay from “Reader’s Digest.”