Posterior

A hidden source is one of several candidate distributions. Each card you draw is a piece of evidence; your belief bars update according to Bayes' rule. You score for guessing right with as few draws as you can responsibly take, but stopping too early on a lucky streak is punished.

• Draw a card to reveal evidence and update the posterior over every hypothesis.
• Watch the confidence-interval width shrink as samples accumulate.
• Commit to a hypothesis once you're confident enough.
• Your score rewards a correct call balanced against how many cards you sampled and the round's target.

• Desktop: click Draw (or press Space / Enter) to reveal a card; click a hypothesis bar to commit; pick Daily/Practice and easy/medium/hard.
• Phone & tablet: tap to draw and tap a hypothesis to commit, fully touch-friendly.

• Don't anchor on the first card or two, a single draw barely moves a well-formed prior.
• Use the confidence-interval width as your stop signal rather than the leading bar alone.
• Higher difficulties make the candidate distributions more similar, so they demand more evidence.

Posterior turns Bayesian inference into a press-your-luck decision, balancing accuracy against the cost of more evidence.

• Skills: Bayesian inference, posterior probability, decision-making
• Best for: advanced high school / college
• For parents & teachers: Bayesian inference as a decision.

Drawing cards as evidence and updating belief bars over candidate distributions is Bayesian inference in its purest form: a prior, a likelihood, and a posterior that becomes the next prior.

Showing the belief bars move with every card is the original teaching device.

Watching the update happen repeatedly is the only good cure for the idea that evidence either proves or disproves something. A card consistent with two hypotheses shifts the balance between them slightly rather than settling anything, and enough slight shifts become certainty without any single one being decisive.

Posterior turns Bayesian inference into a press-your-luck decision: balance accuracy against the cost of more evidence. It's an original, free browser game with daily and practice rounds across three difficulty levels.

A free, original browser game on PlayPendium. No download, no install.