A Fair Coin When You Do Not Have One
Settling something by chance needs a source of randomness that nobody controls. A physical coin works, but only if one is to hand and everyone can see it; a person picking "a number between one and ten" is not random at all, since people avoid the ends and over-choose seven.
This roller produces coin flips and dice rolls from the browser’s cryptographic random number generator, which is the same source used for security keys rather than a predictable arithmetic sequence.
How to Flip or Roll
Everything is a single click, and the history is what makes it useful for more than one decision.
- Choose a coin or a die. Dice come in the standard tabletop sizes, from four sides up to twenty.
- Set how many to roll at once when you need several, three dice at a time rather than three separate rolls.
- Flip or roll. The result appears immediately along with a running history.
- Use the history to keep track across a game or a series of decisions, which is what a physical coin cannot do.
- For anything where fairness will be questioned, roll in front of the people affected rather than reporting a result afterwards.
What Makes This Random
Most software randomness comes from a pseudo-random generator: an arithmetic sequence that looks random but is fully determined by its starting value. That is fine for a game and unsuitable for anything where predicting the next value would matter. This tool uses the browser’s crypto random source instead, which draws on entropy the operating system gathers from unpredictable physical events.
The practical difference is that the sequence cannot be reproduced or predicted from the results you have already seen. For a coin flip that distinction rarely matters, but it costs nothing to use the stronger source, and it means the tool is honest about being random rather than merely appearing so.
Dice and Their Odds
Probability of any single face, and of common outcomes on two six-sided dice.
| Roll | Outcome | Probability |
|---|---|---|
| Coin | Heads or tails | 50% each |
| d6 | Any given face | 16.7% |
| d20 | Any given face | 5% |
| 2d6 | Total of 7 | 16.7%, the most likely |
| 2d6 | Total of 2 or 12 | 2.8% each, the least likely |
| 2d6 | Any double | 16.7% |
| 3 coins | All three the same | 25% |
Two dice do not give a flat distribution, which surprises people. Seven comes up six times more often than two, because there are six ways to make seven and only one way to make two. Any game that treats 2d6 as uniform is being scored wrongly.
The Gambler’s Fallacy
After five heads in a row, tails is not "due". The coin has no memory, and the sixth flip is fifty-fifty exactly as the first was. Long runs feel wrong because human intuition expects short sequences to look balanced, but in a hundred flips a run of five is entirely ordinary and a run of six or seven is likely.
The related error is reading meaning into a small sample. Ten flips landing seven heads is unremarkable, it happens about twelve per cent of the time with a fair coin, and proves nothing about the coin. Fairness only becomes visible over hundreds of trials, which is why a handful of results never settles an argument about whether something is rigged.