Coin Flipper

Latest flip

{{ totalFlips }} flip{{ totalFlips === 1 ? '' : 's' }} recorded

{{ headCount }} Heads {{ tailCount }} Tails {{ headPercent }}% H / {{ tailPercent }}% T {{ rngBadge }} P(H) {{ pHeadsPercent }}% {{ streak.currentFace ? `${streak.currentFace} streak ${streak.current}` : 'No streak yet' }}

RNG mode:

Choose System for one-off flips or Seeded when the order must be reproducible.

Bias toward Heads: P(H) {{ pHeadsPercent }}%

Use -100 to 100; 0 keeps a 50/50 Heads/Tails draw.

Seed:

Any text is accepted, for example demo-seed.

Celebrate Heads:

Turn on before using vibration or sound cues.

Vibrate on reveal:

Requires Celebrate Heads and supported hardware.

Audio cue volume: {{ beep_volume }}%

Use 0 to 100%; browsers may require a user gesture before audio.

Tone frequency:

Enter 100 Hz or higher; 880 Hz is the default.

Tone duration:

Use 20 ms or more; 120 ms is the default.

Auto-flip run:

Enter 1 to 5000 flips, then run Flip xN.

Clear the ledger and start a fresh one-flip run.

Metric	Value	Copy
{{ row.label }}	{{ row.display }}

Check	Current reading	Interpretation	Copy
{{ row.check }}	{{ row.reading }}	{{ row.interpretation }}

Flip	Result	Running share	Copy
{{ row.flip }}	{{ row.result }}	{{ row.runningShare }}

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Coin flipping is the simplest useful model for a two-outcome random trial. Heads and tails are easy to name, but the result only makes sense after the probability model is clear. A fair model gives each face the same chance. A biased model deliberately shifts that chance. A recorded run shows the sequence that happened, not a promise about the next face.

The same flip can serve different jobs. A single toss can settle a low-stakes tiebreaker, while a longer run can show how observed percentages move around an expected probability. A seeded sequence helps a lesson, demo, or QA note replay the same order. A fresh random sequence is the better match when the point is an ordinary one-off draw.

Common coin flip concepts and how they affect interpretation
Concept	Plain meaning	Common mistake
Fair coin	Heads and tails each have probability `0.5`.	Expecting every short run to split exactly in half.
Biased coin	One face has a higher configured probability than the other.	Reading bias from a tiny sample instead of the chosen model.
Independent flip	Past results do not change the probability of the next draw.	Treating a streak as a sign that the opposite face is due.
Seeded sequence	A repeatable pseudo-random order made from the same seed and starting point.	Using repeatability when fresh unpredictability is the goal.

A fair probability does not promise an even-looking ledger. Ten flips can land six heads and four tails without anything unusual happening. A hundred flips often looks closer to the configured probability, yet the observed share can still miss by several percentage points. That gap is ordinary variation, not a correction mechanism.

Bias is a model choice rather than a finding. If heads is configured at 70%, each draw starts with that same heads chance. The running ledger may land near that share over time, but no individual flip remembers earlier outcomes. Keep the configured probability separate from the observed percentage when reading any session.

Digital coin flips are best treated as lightweight randomness for decisions, games, teaching, and demonstrations. They are not a substitute for audited lotteries, gambling systems, password generation, cryptographic keys, or any process where prizes, money, security, or compliance depend on the result.

How to Use This Tool:

Set the probability model first, then read the latest face and session record together. The first visible flip starts the ledger, and later flips add to the same session until you reset it.

Choose System RNG for ordinary browser-backed flips. Choose Seeded RNG and enter Seed text when the same replayable order is more important than fresh randomness.
Set Bias toward Heads. Leave it at 0 for a fair 50/50 model, move it above 0 to favor heads, or move it below 0 to favor tails.
Press Flip to add one result. The summary shows the latest face, total flips, heads and tails counts, percentage split, random mode, configured heads chance, and current streak.
Use Auto-flip run when you need many instant draws for a probability demonstration. Enter a positive whole number; a single batch is capped at 5,000 flips.
Open Flip Metrics for session totals, Expectation Gap for observed-versus-configured percentages, Probability Check for interpretation notes, Flip Distribution for the heads-versus-tails chart, and Flip Ledger for the ordered record.
Use the copy and download actions only after the settings and ledger match the session you want to keep.
Use Reset and flip to clear the ledger and immediately start a new one-flip session.

Interpreting Results:

The latest face answers the immediate choice. Counts, percentages, charts, and ledger rows describe the recorded session. Keep those readings separate: one flip can decide a tiebreaker, while a longer run is better for comparing observed frequency with the configured probability.

The Expectation Gap chart compares the session with the current model. A large gap after a few flips is normal. A large gap after hundreds of flips deserves a closer look at Bias toward Heads, RNG mode, seed text, and whether the session was reset before the comparison.

Coin flip result signals and practical reading
Signal	Check first	Practical reading
`Heads %` is far from `50.0`	`Total flips` and `Bias toward Heads`	Small samples wander. A biased setup may also make `50.0` the wrong expectation.
`Observed Heads gap` is positive	Configured heads chance	The session has more heads than the model's expected share, not proof that the next flip should be tails.
All flips show the same face	Bias boundary	`100` forces heads and `-100` forces tails after probability clamping.
A seeded replay differs from another run	`Seed`, `RNG mode`, and starting point	The same seed must start from the same draw position. Consuming extra flips changes the later order.
No sound or vibration occurs	`Celebrate Heads`, latest face, volume, and device support	Optional cues fire only on heads when the settings and browser or device allow them.

Technical Details:

A coin flip is a Bernoulli trial when it has two possible outcomes and a fixed probability for the outcome being counted. Repeating that trial under the same probability creates a binomial setting: the heads count after n flips varies around n x p, where p is the probability of heads.

Independence is the main reading rule. A streak changes the ledger, not the probability of the next draw. If the configured heads probability is 0.5, the next independent flip still uses 0.5 after five heads in a row. If the probability is 0.7, the next flip still uses 0.7 after a tails streak.

Formula Core

Configured heads probability

p_{H} = \min (1, \max (0, 0.5 + \frac{b}{200}))

b is Bias toward Heads as a percentage from -100 to 100. A random draw u in the range [0, 1) records heads when u < pH; otherwise it records tails.

Observed share and expectation gap

Heads % = \frac{Heads count}{Total flips} \times 100

Observed Heads gap = Heads % - (p_{H} \times 100)

Displayed percentages round to one decimal place. Expected counts use the configured probability multiplied by the current flip count.

Bias values and resulting heads probability
`Bias toward Heads`	Heads probability	Resulting model
`-100`	`0.00`	Tails is forced because all valid draws fail the heads test.
`-40`	`0.30`	Tails is favored, but heads can still appear.
`0`	`0.50`	The fair model gives both faces equal probability.
`40`	`0.70`	Heads is favored, but tails can still appear.
`100`	`1.00`	Heads is forced because every valid draw passes the heads test.

System RNG uses browser-provided random values and prefers browser cryptographic randomness when it is available. If that source is unavailable, the random mode label shows a pseudo-random fallback. Seeded RNG turns seed text into a deterministic pseudo-random sequence, which is useful for repeatable lessons and QA examples but not for security-sensitive unpredictability.

Sample size labels used by the probability check
Flip count	Displayed label	How to read it
`1` to `9`	`Tiny sample`	Useful for a choice, too small for reading percentage balance.
`10` to `99`	`Short run`	Good for showing variation, still likely to swing after new flips.
`100` to `999`	`Teaching sample`	Large enough for a clearer observed-versus-configured comparison.
`1,000` or more	`Large session`	Better for demonstrations, though still not audited randomness evidence.

The charts, tables, ledger, and JSON all describe the same recorded session. Exporting a chart image or table preserves the current record; it does not rerun the flips or change the probability model.

Privacy, Accuracy, and Safety Notes:

The flip calculation happens in the browser after the page loads. No account, uploaded file, or server-side lookup is needed for the coin result itself. Saved reports can include visible settings, seed text, counts, charts, and ledger rows, so treat them as records of the session you chose to keep or share.

Browser randomness is appropriate for casual use and teaching demonstrations, but regulated drawings and security tasks need stronger process controls than a web-page result can provide. For passwords, tokens, raffles, sweepstakes, financial games, or compliance-sensitive selections, use a purpose-built system with audit logs and the required legal or security safeguards.

Worked Examples:

One-flip tiebreaker

Keep RNG mode on System RNG and Bias toward Heads at 0. Press Flip once and use the latest face as the tiebreaker. The session counts are just the record of what has happened so far.

Weighted classroom run

Set Bias toward Heads to 40. The Formula Core gives pH = 0.70, so heads is favored on each draw. A run of 100 flips may land near 70 heads, but a visible gap is still possible because the run is random.

Forced-face boundary

Set Bias toward Heads to -100 and run a batch. The ledger records tails for every flip, Heads remains 0, and Tails % reads 100.0 %. That result comes from the configured boundary, not from luck.

Seeded replay check

Switch to Seeded RNG, enter the same Seed, reset, and start from the same point before comparing two runs. A seeded sequence that has already consumed draws will continue from its current position, so later flips can differ even when the seed text matches.

FAQ:

How do I make the coin fair?

Set Bias toward Heads to 0. That makes the configured heads probability 50.0% and the configured tails probability 50.0%.

Why is there already a flip in the ledger?

A starting flip is recorded on load when no previous flip history is present, so the summary and result views have an initial session instead of an empty display.

Why does a fair run look unbalanced?

Fair means equal probability before each draw, not equal counts after every small sample. Short runs often have visible gaps, and even longer runs can miss the expected share by chance.

Can a streak predict the next flip?

No. The current streak counts matching results at the end of the ledger. It does not change the configured probability used by the next independent flip.

Why will Flip xN not run?

Auto-flip run must be a positive whole number. A single batch is capped at 5,000 flips.

Can I use the result for prizes, passwords, or gambling?

No. Use the result for casual decisions, games without monetary stakes, and teaching. Security, regulated drawings, and gambling require purpose-built systems with stronger controls.

Glossary:

Bernoulli trial: A random trial with two possible outcomes and a fixed probability for the outcome being counted.
Binomial setting: A fixed number of independent Bernoulli trials with the same probability, summarized by the count of one outcome.
Bias: The configured shift that raises or lowers the heads probability before a draw is resolved.
Expected count: The flip count multiplied by the configured probability, such as expected heads after a given session size.
Expectation gap: The difference between the observed heads percentage and the configured heads percentage.
Seeded sequence: A repeatable pseudo-random order produced from seed text and a matching starting point.

References:

4.3 Binomial Distribution, OpenStax Introductory Statistics 2e.
Crypto: getRandomValues() method, MDN Web Docs.
Math.random(), MDN Web Docs.