What is a weighted coin?
A weighted (or biased, or loaded) coin is one that lands on one side more often than chance allows โ classically achieved by shaving metal from one face or embedding dense material under the other. In textbooks the weighted coin is the standard first example of unfair probability: instead of 50/50, the split might be 70/30, and every calculation changes accordingly.
This page gives you a slider instead of a metal file. Set the heads probability anywhere from 0% (a double-tailed coin) to 100% (double-headed), and every flip of the golden coin follows your chosen bias, generated with cryptographic randomness. The default is a fair 50%.
Experiments to try
Set the slider to 70% and flip ten times: the result usually looks unremarkable, because small samples hide bias โ this is exactly why ten flips can never prove a coin unfair. Then watch the statistics as you keep flipping: the running percentage creeps toward 70%, and the dot history starts showing the imbalance in color.
Push the slider to the extremes to build intuition for edge cases. At 100% heads you have the classic two-headed coin of con artists and philosophy seminars; at 50% you have the fair coin from the rest of this site; and at intermediate values you can hunt for the point where a biased coin becomes indistinguishable from a fair one in a handful of flips.
Why bias matters
Biased coins make the abstract parts of probability concrete: expected value, hypothesis testing and the difference between 'unlikely' and 'impossible' all become visible when you can turn the fairness dial yourself. Detecting a 60/40 coin reliably takes hundreds of flips โ a fact that explains everything from skeptical auditors to why small A/B tests mislead.
And if you leave the slider at 50%, you simply have the fairest coin on the internet โ no thumb, no shave, no asterisk. The statistics page tracks everything you flip either way.