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In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. It is also important to note that the LLN only applies to the average. Therefore, while other formulas that look similar are not verified, such as the raw deviation from "theoretical results":

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• In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. Importantly, the law applies (as the name indicates) only when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced" by the others (see the gambler's fallacy). It is also important to note that the LLN only applies to the average. Therefore, while other formulas that look similar are not verified, such as the raw deviation from "theoretical results": not only does it not converge toward zero as n increases, but it tends to increase in absolute value as n increases. (en)
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• Simulation illustrating the law of large numbers. Each frame, a coin that is red on one side and blue on the other is flipped, and a dot is added in the corresponding column. A pie chart shows the proportion of red and blue so far. Notice that while the proportion varies significantly at first, it approaches 50% as the number of trials increases. (en)
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• Law of large numbers (en)
• Strong Law of Large Numbers (en)
• Weak Law of Large Numbers (en)
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• StrongLawofLargeNumbers (en)
• WeakLawofLargeNumbers (en)
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• In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. It is also important to note that the LLN only applies to the average. Therefore, while other formulas that look similar are not verified, such as the raw deviation from "theoretical results": (en)
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• Law of large numbers (en)
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