Coin Flip

How to use it

1. Choose how many coinsLeave the box at 1 for a classic toss, or enter up to 20 to flip a handful together and count the heads.
2. Press Flip or hit SpaceThe coin spins and shows the result. With several coins you see each outcome in a list and the number of heads on the face.
3. Read the tallyHeads and tails are counted under the coin and saved on this device. Reset clears the count whenever you want a fresh start.

What the coin flipper does

• Tosses one virtual coin or up to twenty at once. Each coin toss is decided by the browser's cryptographic random numbers, heads or tails with the same chance.
• Gives a heads or tails coin flip in one click or one press of Space, for the times you just flip a coin and move on.
• Turns a two-way choice into a quick coin flip game: name the caller, toss a coin, accept what lands.
• Works as a heads or tails generator for majority votes: set three coins and whichever side shows at least twice wins.
• Keeps a tally of every virtual coin flip on this device, so an experiment can carry on tomorrow.

What makes an online flip fair

Each flip asks the browser for a number from its cryptographic random generator and uses it to choose between two outcomes with exactly the same chance. The request is made in a way that cannot lean toward either side, and the result is decided before the little animation plays. The spin you see is decoration that lands on the answer.

Every flip is independent. The page does not remember what came up last, so there is no hidden correction that pulls the next toss toward the other side. Flip twenty coins at once and each of them is a separate fair choice, drawn one after another from the same generator, which makes the multi-coin option a quick way to run a majority vote.

Timing your click does nothing. The number comes from the browser's random generator, not from a clock or from where the pointer was, so pressing at a clever moment, holding Space, or flipping slowly cannot nudge the outcome. The same generator drives the wheel, the dice roller and every other picker on this site.

What a tally should look like

People expect a fair coin to deliver an even split every time. It rarely does. Take ten coins: the single most likely outcome is five heads, and even that happens only about a quarter of the time. Six heads and four tails, or the reverse, together come up about 41 percent of the time, so a lopsided-looking split is the usual result. The table counts every way ten coins can land, out of 1,024 equally likely patterns.

Over longer runs the share of heads settles toward half, but the raw gap tends to grow. A hundred flips typically land within about five of an even split, and a gap of ten is common enough not to worry about. A gap that stays large across thousands of flips would be worth investigating; one that appears after a hundred is just chance.

Streaks: why five in a row is not suspicious

Long runs feel like evidence that something is wrong. The arithmetic says otherwise. Once you have a long sequence, a stretch of the same face somewhere in it is normal. The table gives the chance that a run of at least a given length, of either heads or tails, appears somewhere in a series of flips.

Notice that in 20 flips, a run of five has about a 46% chance. People asked to invent a coin sequence tend to avoid runs that long, which is why a made-up series often looks too tidy next to a real one. The other half of the lesson: after five heads, the next flip is still fifty-fifty. A coin has no memory and nothing is due.

Using several coins and the tally

Set Coins to 3 for a majority vote: whichever side shows at least twice wins, and the matter is settled without a rematch. Set it to 20 and it becomes a coin flip simulator for a probability lesson. Each student flips twenty, writes down the heads, and the class compares counts that scatter around ten, typically within about two either way. The spread across a class is usually more convincing than any explanation, and it shows why nobody should expect exactly ten heads from twenty flips.

The tally counts every coin ever flipped on this device with this page, not just the last toss, and it is stored in local storage on this device. The tally is not uploaded. Press Reset between experiments so the totals describe only the one you are running. If several people share the device, write down their numbers before the next person starts, because the tally has no per-person view. For more than two outcomes, the dice roller handles d4 to d100.

How big a gap is normal

If you want to use the tally as a sanity check, compare the gap between heads and the expected half with what chance alone produces. For n fair flips, the number of heads typically strays from n/2 by about half the square root of n. In roughly 95 of 100 runs it stays within twice that distance.

So 62 heads in 100 flips, 12 above expected, is a little unusual but happens now and then, while 12 above expected after 10,000 flips is wonderfully close to even. The percentages tighten as the count grows even though the raw difference does not.

Coin flips in class, at home and on the field

A teacher can use one coin on the projector to decide which row answers first, then run a ten-minute experiment in pairs: each pair flips twenty coins at once, notes the heads, and the class plots the numbers on the board. The bell-shaped pile that forms is the tidiest introduction to chance most students see.

At home, a flip settles who chooses the movie or who takes the first turn, with the caller named before the toss. In sport, the flip sets kick-off or serve, where the loser of the toss often picks the end or the order. If the result is binding, say so before it appears, then accept it. A flip is only useful as a tiebreaker when everyone agreed to it first, and the person who called heads should say so out loud before the coin lands.

Deciding something with a coin

Agree who calls it before the flip, and what each side means. Decide in advance whether one toss settles it or whether you play best of three, because arguing about the format after a result is how disputes start. For a best-of-three or best-of-five series with a question attached, the yes or no wheel counts the series for you.

A real coin is not quite perfect: a large experiment published in 2023, with hundreds of thousands of physical tosses, reported a slight lean, about 51 in 100, toward the side that started facing up. A digital coin has no starting side, so that quirk does not apply. For more than two outcomes, use the dice roller or the decision wheel instead. With more than two options, the yes or no wheel or a decision wheel handles it.