Bayesian Coin Flip - Interactive Probability Learning

🪙 Bayesian Coin Flip

Learn Bayesian Probability

Welcome to the Bayesian Coin Flip! This interactive game teaches you how Bayesian inference works by updating probabilities as new evidence arrives.

Instead of assuming each coin flip is independent (50/50), Bayesian probability considers your prior beliefs and updates them based on observed evidence. Watch how the probabilities change with each flip!

Bayes' Theorem

P(H|E) = P(E|H) × P(H) / P(E)

Where:
P(H|E) = Probability of hypothesis given evidence (posterior)
P(E|H) = Probability of evidence given hypothesis (likelihood)
P(H) = Prior probability
P(E) = Total probability of evidence

How Bayesian Coin Flipping Works

Step 1: Prior Beliefs

We start with a prior belief that the coin is fair: 50% heads, 50% tails. This is our initial hypothesis before seeing any data.

Step 2: Observe Evidence

Each coin flip provides new evidence. If we flip 3 heads in a row, we might start to suspect the coin isn't fair!

Step 3: Update Probabilities

Using Bayes' Theorem, we calculate the posterior probability - our updated belief after seeing the evidence. The formula weights our prior belief with the new evidence.

Posterior ∝ Likelihood × Prior

Step 4: Make Predictions

Try to predict each flip! Watch how the Bayesian probabilities change and see if you can beat the algorithm's predictions.

🪙 Bayesian Coin Flip

Learn Bayesian Probability

Bayes' Theorem

Make Your Prediction

📊 Statistics

🎲 Bayesian Probabilities

📜 Flip History

How Bayesian Coin Flipping Works

Step 1: Prior Beliefs

Step 2: Observe Evidence

Step 3: Update Probabilities

Step 4: Make Predictions