Question 1

Is this coin flip really random?

Accepted Answer

Yes. Each flip uses Math.random() (a cryptographically strong PRNG in modern browsers) and is independent of previous flips. Over large samples (10,000+), the distribution will converge to a near-perfect 50/50. Short runs can be skewed by chance, which is exactly what makes the analysis interesting.

Question 2

What is the longest streak I should expect?

Accepted Answer

The probability of a streak of k heads in a row is (1/2)^k. In 100 flips you will typically see one streak of 4-5. In 1,000 flips, expect a streak of 7-8. In 10,000 flips, expect a streak of 10-12. The longest streak you see is well described by the formula log₂(N) where N is the number of flips.

Question 3

What is a runs test?

Accepted Answer

A runs test counts how many 'runs' (consecutive identical outcomes) appear in a sequence. For a fair coin, the expected number of runs in N flips is (N+1)/2. The standard deviation is sqrt((N-1)/4). If your sequence has too few runs, the coin may not be fair; too many runs suggests alternation. It's a quick statistical test for randomness.

Question 4

Can I use this for a class or experiment?

Accepted Answer

Yes. The tool is perfect for teaching probability, the law of large numbers, and the gambler's fallacy. You can flip thousands of coins at once to demonstrate convergence to 50/50, and use the runs test and streak analysis to show that even fair coins can produce long streaks by chance.

👑 Longest H-streak: 0

👑 Longest T-streak: 0

📊 Runs Test

📈 Chi-Square vs 50/50