Coin Flipper

You want to flip a coin but don't have any — with our coin flipper, you'll always have a coin to hand.

Our heads or tails generator simulates a coin toss. Each time you click on Flip, you have a 50/50 chance of getting heads or tails.

If you toss a (balanced) coin a very large number of times (say, a million times), then the average number of heads and tails should be very close to 50%. Or so we thought! Keep reading to discover that it may not be entirely accurate.

In the following article, you will learn:

• How to use our flipping coin generator;
• The probability theory behind coin flipping; and
• The origins of "heads or tails".

Are you tired of reaching into your wallet for a coin? The coin flip calculator is just a few clicks away from your phone or computer. Try it now!

Coin flipping, coin tossing, or heads or tails is an ancient game of chance in which you throw a coin in the air and guess which side it will land on — heads or tails.

It has been used in many contexts, including:

• Making decisions;
• Playing bets; or
• Determining who should perform a specific task.

Speaking of betting, we bet that after using our heads and tails generator, you'd like to know, let's say, the probability of flipping 3 heads in a row. Today's your lucky day because we've got precisely what you need. Continue to read or check out our coin flip streak calculator.

Want to play heads or tails with friends? It's never been easier! With our coin flipper, you can make lots of tosses without downtime. With our tool, you can flip a coin in two different ways. First, you can:

1. Click on the Flip button, and a randomly generated image of a coin appears: either heads or tails.
2. To flip a coin again, simply uncheck the Flip button. A new coin image will appear. Unsurprisingly, it will be heads or tails.
3. Ready to flip coins ad infinitum?

With the other way of using our coin flipper, it doesn't matter whether the Flip button is checked or unchecked. To generate another image, press the reload calculator button. A new coin will appear: heads or tails.

If you'd like to know the probability of getting a given number of heads (or tails) from a given number of throws, check out our coin flip probability calculator.

Flipping a coin is a Bernoulli trial, i.e., a random event is performed, and the result is either a success or a failure. This result is represented by a random variable of Bernoulli distribution, whose possible values are 0 and 1 (associated with heads and tails, or vice versa).

If the coin is balanced, the parameter of Bernoulli distribution is p = 1/2, i.e., heads and tails have the same probability of appearing. If the coin is unbalanced, the parameter p of the Bernoulli distribution is not 1/2, and one side of the coin is more likely to occur than the other.

When the same coin, or coins with the same balance, is tossed several times, it is assumed that the tosses are independent. The number of times tails (or heads) appear out of a certain number of throws follows a binomial distribution.

As mentioned in the previous section, the probability of winning a coin toss is 50/50 because there are two options: heads or tails.

Nonetheless, a recent study suggests that calling the visible side of the coin before the toss will increase your chances of winning. Researchers carried out 350,757 coin tosses and found that the initial side of the coin, which is up before the toss, slightly tends to fall back to the same side. Frantisek Bartos, from the University of Amsterdam in the Netherlands, reports that this technique will give you a 50.8% chance of winning.

But, the effect is not uniform for all. Some throwers have a much higher success rate than the average of 50.8%. Furthermore, this phenomenon does not occur if heads or tails are randomly selected before each toss. To eliminate any advantage, ensure that the person calling heads or tails does not see the initial face of the coin before the toss, or use our online coin-flipping calculator. You're guaranteed random coin tosses!

The expression "heads or tails" dates back to Roman antiquity, when coins were engraved on one side with the face of Janus — the god of beginnings and ends, entrances, exits, and passages — and on the other side with a ship.

When the Church came to power in Europe, it forbade the depiction of pagan divinities on coins and demanded that they be minted with Christian symbols. Thus, the side with the face of Janus was replaced by a cross, and the other side became the "pile". The pile takes its name from the indentation from the hammer used to press the metal as the coin was struck. People then began to say "cross or pile" to designate the random choice between the two sides of the coin.

The current name of "heads or tails" is in keeping with this tradition. The tails side of a coin is so called simply because it lies opposite the "head", by analogy with an animal that has a head at one end and a tail at the other.

Today, the expression is widely used in games of chance, sports, and competitions to determine who goes first or to assign random advantages or disadvantages.