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Two Hypotheses In the contemporary discussion about artificial intelligence, two distinct hypotheses intersect and are often conflated. The first hypothesis describes AI as a thin client between intention and result. Historically, a chain of translators existed between a concept and an artifact. A person formulated a task for a programmer, the programmer wrote code, the code became a program. A screenwriter passed an idea to a studio, the studio hired a VFX team, the team produced a film. A composer worked with musicians and a studio to record a track. AI shortens this chain, allowing a result to be obtained directly from a natural language prompt. The second hypothesis is more radical. It asserts that AI washes out not only performers but also apprentices. The main function of many professions was not the production of the current result, but the reproduction of knowledge. A junior was needed not because he is useful today, but because in five years he will become a senior. A student was needed not to create value now, but to become an engineer. A doctoral candidate was needed not for brilliant papers, but to undergo the school of scientific thinking. The Destruction of the Apprenticeship Mechanism The classical model of competence growth was built on review. A junior wrote code, a senior dissected it, extracted the substrate of experience, and transmitted professional intuition. Each review was an act of knowledge transfer. The new model looks different. A person formulates a prompt, AI generates the result. If code of acceptable quality appears immediately, the economic need for a junior declines. Along with it, the mechanism through which knowledge was transmitted disappears. A structural question arises that goes beyond the labor market. Where will the next seniors come from if the intermediate link does not undergo the path of learning through mistakes and reviews. This is a problem of competence reproduction, not simply automation. The Transformation of Educa

In This Article The Question The Intuition Trap Building the State Machine for HH Solving the System: E[HH] = 6 Building the State Machine for HTH Solving the System: E[HTH] = 10 Why Overlapping Patterns Change Everything Python Simulation: 100,000 Trials Business Application: Credit Migration & Web Ranking The Question You flip a fair coin — one with probability 1/2 of landing heads and 1/2 of landing tails — repeatedly, recording every result. What is the expected number of flips required until the sequence HH appears for the first time as consecutive results? What is the expected number of flips required until HTH appears for the first time? Both questions have the same surface structure: you want a specific consecutive pattern, and you want to know, on average, how many flips it takes to observe it. The coin is fair, the flips are independent, and the patterns are short. These seem like they should yield similar answers. They do not. HH takes exactly 6 flips on average. HTH takes exactly 10. The four-flip gap between those two answers is not a rounding artifact or a computational error — it is a precise consequence of the internal structure of each pattern, and deriving it rigorously is one of the cleanest demonstrations of absorbing Markov chain analysis you will encounter. This problem appears frequently in quantitative finance interviews — at firms like Jane Street, Citadel, and Two Sigma — precisely because it separates candidates who understand Markov structure from those who rely on heuristic reasoning. Getting the answer right, and being able to explain it, requires building a state machine, writing the system of first-step equations, and solving it algebraically. That is exactly what we will do. The Intuition Trap Before the formal derivation, it is worth examining why intuition fails here. The most common wrong answer from candidates is that both expected values should be "similar" because the patterns are comparable in length. This intuition imports th