Statistics and Probability
Flip once or run a batch experiment. Compare observed heads and tails with the 50/50 expectation, and see how streaks appear in ordinary random-looking sequences.
Choose 1 to 1000 flips, then flip.
For an ideal fair coin, calculate the theoretical chance of exactly k heads in n flips.
Probability: —
No flips yet.
H = heads, T = tails. Recent outcomes show at most 40 flips; totals include the whole open session. Results are simulated in your browser and are not a source of secure randomness.
An ideal fair coin has a theoretical 50% chance of heads on each independent toss. That does not mean a batch of 10 flips must contain exactly five heads. The displayed heads rate is an observed frequency: heads divided by all flips in this open session.
A run or streak is a series of identical outcomes in a row. H-H-H-T contains a three-head run. A long streak can occur without indicating that the next outcome is more likely to be tails; for independent fair flips, the next toss still has a 50% theoretical chance of heads.
Batch flips append to the existing session rather than replacing it. The visible recent-outcome list is capped at 40 symbols to keep the page readable, while summary counts include all flips until Reset session. Refreshing the page clears the session because outcomes are not stored on a server.
This tool uses browser pseudorandom values to simulate a two-sided fair coin. It does not test the bias of a real physical coin or provide a cryptographically secure draw. If money, legal selection or scientific sampling is involved, use a procedure suited to that purpose.
Observed heads rate = heads / total flips × 100%. For 53 heads in 100 flips, the displayed rate is 53%, although the model's theoretical probability remains 50% per flip.
For a fair coin, the chance of exactly k heads in n independent flips is C(n,k) × (1/2)^n. For three flips, exactly two heads can occur in HHT, HTH or THH: 3 / 8 = 37.5%.
The expected number of heads in n flips is n / 2, but expectation is an average over repeated experiments, not a guarantee for one particular run.
Try 10 flips, then 100 and 1,000 to discuss observed frequency and variability without assuming every short run balances perfectly.
A single virtual toss offers a lightweight heads-or-tails choice when no physical coin is available.
Compare the longest same-side run with your intuition; sequences of H or T are possible even with independent flips.
Pseudorandom simulation is not a physical coin, a secure lottery or a guarantee of fairness for consequential decisions.
The simulator samples a fresh browser pseudorandom value for every flip. Earlier outcomes are not used to change the next flip's 50/50 rule.
Short samples fluctuate. A 50% chance for each toss does not force exact balance in any particular batch.
No. In the independent fair-coin model, a past run does not change the probability of the next toss.
No. Counts and the latest outcomes exist in the open page only and reset when you reload or press Reset session.
Last reviewed: October 23, 2026. Calculations and simulations run in your browser; verify important decisions independently.
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