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The movie "Groundhog Day," a science fiction film released in 1993, portrays the main character, played by Bill Murray, waking up every morning to find that it is still February 2nd, reliving the same day repeatedly. He conducts a series of decision-making experiments, including seducing women, drunk driving, and even suicide, gradually learning to make better choices. Unlike the movie's premise, life seldom provides us with the opportunity to go back to the beginning and make better decisions. If only life were like a video game, where we could undo our mistakes and restart! In 2005, when I first joined the workforce, I frequently took the bus to and from work. If you've ever taken a bus, you may have encountered the dilemma of waiting for an extended period or choosing an alternative when the bus does not arrive. At that time, there was no way to use apps or social media to obtain information about what was happening with the buses on that route, so we had to make decisions with limited information. Should we leave and risk missing the bus or continue to wait and risk the bus never coming? Thanks to technological advancements, I believe this waiting-for-the-bus problem has been perfectly solved. When faced with this issue, all we need to do is use our smartphones to search for relevant vehicle information and make the best decision for ourselves. Just when I thought the inner struggle that had troubled me for years had been resolved, I seem to have encountered a new situation.
On a sunny morning, I was walking from home to the office when suddenly dark clouds covered the sky and a heavy rainstorm began without warning. Since I didn't have an umbrella, I had to take shelter under the eaves of a building. As I was feeling helpless, the weather suddenly changed. Although it was still raining, the rain had noticeably decreased. At that moment, I faced a dilemma: should I assume that it was just a temporary relief and that the rain would get worse, or should I believe that the rainclouds had passed and continue to wait until the rain stopped completely before walking again?
In the preceding text, the belief that the rain had decreased was only a brief reprieve, and it would continue to worsen in the future. This is a trend-oriented thinking, while the opposite belief that the rain will gradually stop after heavy rain is oscillation-oriented thinking. In reality, the problem I faced in both scenarios is the same, which I refer to as a transitional problem. Transitional problems have two key elements: first, the selection of two or more completely different modes of thinking; second, the results of choosing one mode of thinking are precisely opposite to those of choosing another mode of thinking. For instance, if I choose Plan A and end up losing 100 million , I could have made a profit of 100 million if I had chosen Plan B at that time.

The image presented above illustrates two different modes of thought that individuals may employ when making decisions. In the realm of trading, it is often the case that available information is incomplete, leaving traders unsure about whether to buy on dips or sell on rallies.
To begin our discussion on transformation problems, I would like to introduce two phenomena: the hot-hand effect and the gambler's fallacy. The hot-hand/>