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A coin toss models a simple chance event with two outcomes and a clear proportion over time. It helps demonstrate fairness and supports transparent choices in groups.
You can keep it neutral or add a bias and save a seed so sequences repeat. Many use it as a fair coin flip simulator for lessons and team picks.
Provide a bias if needed then flip and watch the running split between heads and tails. The display updates immediately and a compact chart summarizes the proportions.
A quick example helps set expectations. Ten flips with a 20 percent bias toward Heads might show six Heads and four Tails. The exact sequence can differ each time.
Short runs can swing widely so compare larger samples for steadier proportions. For reproducible comparisons reuse the same seed across sessions and devices.
A coin flip is modeled as independent Bernoulli trials that observe Heads or Tails per flip. The key quantity is the probability of Heads which can be neutral or adjusted by a user‑set bias. Results accumulate into proportions to show how often each outcome appears.
The computation transforms a bias percentage into a Heads probability then draws a random value each flip to decide the face. Proportions are the observed Heads and Tails counts divided by total flips and expressed as percentages for interpretation.
Interpretation centers on how close the observed proportion of Heads is to the configured probability. Values near the configured probability indicate typical sampling noise while small samples can sit far from the target. Long streaks can appear naturally in independent trials.
Comparisons are most meaningful when the same seed and configuration are used. Seeded mode reproduces the identical sequence for a given seed while system mode varies on each run.
| Symbol | Meaning | Unit/Datatype | Source |
|---|---|---|---|
| Probability of Heads | dimensionless | Derived | |
| Bias toward Heads | percent | Input | |
| Limits a value to 0 to 1 | function | Constant rule |
Set b to 20. Compute the Heads probability.
Run N = 10 flips and suppose you observe H = 6.
Interpretation: 60% aligns with a 0.6 target yet small samples can vary. Larger samples stabilize the proportion.
| Parameter | Meaning | Unit/Datatype | Typical Range | Notes |
|---|---|---|---|---|
| Bias toward Heads | Shifts probability toward Heads | percent | −100 to 100 | 0 is neutral |
| RNG mode | System randomness or seeded | enum | system | seeded | Seeded repeats sequences |
| Seed | Reproducibility key | string | any text | Same seed → same order |
| Auto‑flip ×N | Runs multiple flips quickly | integer | 1 to 5000 | Capped for performance |
| Animation time | Flip duration | ms | 80 to 2000+ | Defaults to 450 ms |
| Spin turns | Full rotations per flip | integer | 1 to 10 | Visual only |
| Tilt | 3D tilt angle | degrees | 0 to 30 | Default 8° |
| Celebrate Heads | Optional reveal cues | boolean | on | off | Gates haptics and audio |
| Vibrate on reveal | Haptic signal | boolean | on | off | Device‑dependent |
| Audio beep | Tone on Heads | Hz | ms | percent | ≥100 Hz · ≥20 ms · 0–100% | Volume 0% is silent |
| Field | Type | Min | Max | Step/Pattern | Error Text | Placeholder |
|---|---|---|---|---|---|---|
| Bias toward Heads | number | −100 | 100 | step 1 | — | — |
| RNG mode | select | — | — | system|seeded | — | — |
| Seed | text | — | — | any string | — | e.g. demo‑seed |
| Animation time | number | 0 | — | step 10 ms | — | — |
| Spin turns | number | 1 | 10 | step 1 | — | — |
| Tilt | number | 0 | 30 | step 1 | — | — |
| Auto‑flip ×N | number | 0 | 5000 | step 1 | — | — |
| Beep frequency | number | 100 | — | step 1 Hz | — | — |
| Beep duration | number | 20 | — | step 10 ms | — | — |
| Beep volume | range | 0 | 100 | step 1% | — | — |
Configure the probability model and view proportions for Heads and Tails.
Example: Bias 20 and seeded mode with seed “class‑A” over 100 flips should land near 60% Heads.
Pro tip: encode context in your seed such as “week3‑groupB” to keep runs organized.
No. All flips and stats are computed on your device. Files you save remain on your device unless you share them.
Clipboard and downloads require your action.It uses pseudo‑random sources. Seeded mode is deterministic and great for teaching. System mode varies naturally. Neither mode is designed for gambling or security.
Counts are integers. Percentages show one decimal place. Optional files use human‑readable text with standard number formatting.
Yes after the page loads. All computation runs on your device without a network connection.
Use follows the app’s availability settings. There is no payment flow in the interface.
Select seeded mode and enter a seed string. With the same settings and seed you will get the same sequence and proportions every time.
Values near the configured probability are expected. If your sample is small treat differences of a few percentage points as normal variation.
Independent trials can cluster. Long runs of the same face happen naturally and do not imply bias unless they persist across large samples.