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Intro — Probability in Python: The Best Choice Problem — Part 2
- The article discusses the mathematical model behind the 37% rule strategy in the Best Choice Problem.
- It builds upon the simulation-based methods from the previous article to explain the theoretical values through probability theory.
- The focus is on guessing the position of the largest number in a sequence rather than its actual value.
- The strategy involves observing a range of numbers, using the largest seen as a benchmark, and deciding based on available information.
- Probability calculations are used to quantify the success rate of this strategy across different observation ranges.
- The optimal observation range is found to be 37% for a 100-element sequence, resulting in a 37% success rate.
- The mathematical derivation leads to the key value of 1/e (approximately 37%) as the optimal observation range for maximizing success.
- The article explains how the 37% rule is a common occurrence in mathematical models and converges to e or 1/e in various contexts.
- The theoretical rates based on the calculation align closely with simulation-based results for different sequence sizes.
- As the sequence size increases, the success rate converges more closely towards 1/e, demonstrating the universality of the 37% rule.
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