Късметът на начинаещия
Beginner’s luck

Summary/Abstract: This article examines the “beginner’s luck” phenomenon in the light of Bernoulli scheme, the mathematical model for repeated experiments with two possible outcomes. The definition and conditions for applying the scheme are presented, along with Bernoulli’s formula for the probability that a given event occurs exactly k times in n trials. Through three illustrative problems, it is demonstrated that when the number of trials is even, the probability of achieving success in half of them decreases as the total number of trials increases. First, this is shown empirically through two specific numerical examples suitable for 11th grade students, and then theoretically using the Cauchy inequality, which is studied in the 12th grade. The main conclusion is that the more frequently a person participates in games, including gambling, the lower is the probability of winning half of them, regardless of the probability of success in each individual game.

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