Question

The gambler’s fallacy suggests that in the cases of independent events such as coin tosses, the next coin toss’s probability does not depend upon previous ones.

But there are different definitions and interpretations of probability. If you go the Bayesian/subjective route, your subjective credence is your probability. So if you feel 80% sure that the next coin toss will land on heads, how can someone prove you wrong within that same Bayesian framework? It would be subjectivity vs subjectivity.

So are these fallacies only applicable in a frequentist sense?

Answer 1

The gambler's fallacy and subjective probability in a Bayesian framework.

Step-by-step explanation:

The gambler’s fallacy suggests that in the cases of independent events such as coin tosses, the next coin toss’s probability does not depend upon previous ones.

However, in a Bayesian framework, probability can be interpreted subjectively. If you feel 80% confident that the next coin toss will land on heads, someone else's subjective opinion cannot prove you wrong within that same Bayesian framework, as it would be subjectivity versus subjectivity.

These fallacies are often discussed in a frequentist sense, which focuses on the long-term relative frequency of obtaining a certain outcome. In a frequentist interpretation, each coin toss is considered statistically independent, and the probability of heads or tails remains the same for each toss.