CoinFlipSim

Weighted Coin Simulator โ€” Bias the Odds

Slide the probability anywhere from always-tails to always-heads and experiment with biased flips.

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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.

Frequently Asked Questions

๏ผ‹How does the weighted coin simulator work?

Use the slider to set the probability of heads anywhere from 0% to 100%. Each flip is then generated with cryptographic randomness against your chosen threshold โ€” at 70%, for example, seven out of ten flips will land heads on average.

๏ผ‹Can you tell a coin is weighted by flipping it a few times?

Not reliably. Ten flips of a 70% coin often look perfectly ordinary, because small samples scatter widely. Detecting a modest bias reliably takes hundreds of flips โ€” try it with the slider and the statistics page.

๏ผ‹What is a double-headed coin?

A trick coin with heads on both faces โ€” in this simulator, the slider set to 100%. It always lands heads, which makes it the extreme case of a weighted coin and a classic prop in probability puzzles.