Probability bench
What should happen—and what happened this time?
Probability describes the source. A sample is one noisy piece of evidence from it. Load the coin to feel the difference.
Hands-on evidence
Load the coin
Change the odds, then compare what the source promises with what a short run happens to produce.
Expected heads50%The source model
Observed heads49.0%49 of 100 flips
Shannon entropy1.000Average surprise, bits/flip
Min-entropy1.000Worst-case guess, bits/flip
Sample closeness to the expected share: 95%
Observed gap: 1.0 percentage points. The bar is a teaching scale, not statistical confidence.
- Tails
- Tails
- Tails
- Heads
- Heads
- Heads
- Tails
- Heads
- Tails
- Tails
- Tails
- Tails
- Tails
- Tails
- Heads
- Tails
- Heads
- Heads
- Heads
- Heads
- Tails
- Tails
- Tails
- Heads
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Tails
- Heads
- Heads
- Heads
- Tails
- Heads
- Tails
- Heads
- Heads
- Tails
- Tails
- Heads
- Tails
- Tails
- Heads
- Tails
- Heads
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Heads
- Tails
- Tails
- Heads
- Heads
- Heads
- Tails
- Heads
- Tails
- Tails
- Heads
- Tails
- Tails
- Heads
- Heads
- Heads
- Heads
- Heads
- Tails
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Tails
- Tails
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Tails
- Heads
- Heads
- Heads
- Tails
- Heads
- Heads
- Tails
- Tails
Balanced source
A fair source gives both outcomes equal weight. Bias lowers min-entropy because an attacker will always try the more likely answer first.