Coin flipping was known to the Romans as navia aut caput ("ship or head"), as some coins had a ship on one side and the head of the emperor on the other. In England, this was referred to as cross and pile.
The mathematical abstraction of the statistics of coin flipping is described by means of the Bernoulli process. A single flip of a coin is a Bernoulli trial. In the study of statistics, coin-flipping plays the role of being an introductory example of the complexities of statistics. A commonly treated textbook topic is that of checking if a coin is fair.
Predicting the outcome of a coin toss using artificial intelligence (AI) is a relatively simple task, as it involves a random binary choice between two possible outcomes: heads or tails. AI can't predict the outcome of a fair coin toss with more than 50% accuracy because it is inherently random and not influenced by any external factors that AI could analyze.
Randomness
A fair coin toss is designed to be completely random, and the outcome is not influenced by any external factors. AI relies on data and patterns to make predictions, but there are no patterns or data points to analyze in a coin toss.
Lack of Information
In a fair coin toss, you have no information about the initial conditions, such as the force with which the coin is flipped, the air resistance, or the initial orientation of the coin. Without this information, it's impossible to predict the outcome accurately.
Limited Predictive Power
AI algorithms are only as good as the data they are trained on. Since coin tosses are fundamentally unpredictable, there's no meaningful training data that can be used to create a predictive model.
Randomness
If the coin is fair and not tampered with, the outcome is determined by true randomness, which means that it cannot be predicted even with advanced AI models.
While AI can be used for a wide range of predictive tasks based on data and patterns, predicting the outcome of a fair coin toss is not one of them due to the inherent randomness of the process. If you want to predict the outcome of a coin toss, you would need to rely on chance alone, as there are no reliable AI methods to do so.
So, AI cannot predict the outcome of a fair coin toss with 100% accuracy. A fair coin toss is designed to be a completely random process, and the outcome is not influenced by any external factors or patterns that AI could analyze. It is fundamentally unpredictable.
QUESTION I: Does the prediction power improve if we work with a biased coin?
QUESTION II: Could we axiomatize the limitations of AI?
REFERENCE: Wikipedia, ChatGPT