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Parallelism between thoughts and the double-split experiment
In the early 1800s, experiments that later became known as the Double-slit experiment revealed something strange about the world. Electrons don’t always behave like solid little particles. Sometimes they behave like waves — spread out, probabilistic, not clearly in one place. And then something interesting happens: when you measure them, the ambiguity disappears. Suddenly the…
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Simulations of the German “DFB-Pokal”: Evaluating Tournament Outcomes with a Stochastic Model
In the last season 2023/2024 of the German cup in football, the so-called “DFB-Pokal”, a team from the 3rd league, 1. FC Saarbrücken, made it to the semi-finals. Not only does this seem to be a rare event, but they also eliminated three Bundesliga clubs in previous rounds. By the semi-finals, Bayer Leverkusen was the…
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Why You Should Think (at least) Twice: A Scientific Approach to Decision-Making
The world bestseller “Thinking, Fast and Slow” by Daniel Kahneman explores two systems of thought: We will look at System 2. It is responsible for complex judgments and decisions requiring effort and concentration. It addresses how this deliberate thought process can be influenced by biases and overconfidence, often leading to errors in decision-making. But what does…
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Hypothesis testing on football players consciously getting yellow cards to get suspended
When I recently watched the Saturday afternoon football games of the first German Bundesliga (the highest league in Germany), I noticed something that I have been observing for many years. Players seem to get yellow cards on purpose to get suspended for the next away game. Why is that? In a season, the yellow cards of…


