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Coin flipping

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Coin flipping is a method of sortition used to choose between two alternatives. Sortition is a way of making decisions by using chance rather than skill or voting. In a typical toss, a person uses their thumb to launch a coin into the air. The coin rotates edge-over-edge an unpredictable number of times while it is in flight.

Coin Toss (3635981474)
Coin Toss (3635981474)

Before the coin lands, an interested party declares "heads" or "tails." The second party is assigned the opposite side. Once the coin comes to rest, the person who called correctly is the winner. This process provides a simple and unbiased way to settle disputes or choose between arbitrary options.

While most tosses result in one of two flat sides, other outcomes are possible. A coin can land on its edge if it hits an object like a shoe or gets stuck in the ground. For an American nickel, a computational model suggests the chance of landing on the edge is about 1 in 6,000.

1970 Anglo-Italian Cup - Juventus v Sheffield Weds - Coin toss
1970 Anglo-Italian Cup - Juventus v Sheffield Weds - Coin toss

Scientists have used statistical mechanics to study the thickness of a fair coin. They look at the ratio of the coin's thickness to its diameter. This ratio is thought to be between 0.577 and 0.866. This research considers the edge of the coin as a potential third option for landing.

There are also methods to conduct a three-way coin flip to choose between three options. To choose two out of three, a person flips three coins at once. If two coins show the same side and one is different, the different coin loses. To choose only one winner out of three, the process can be reversed so the odd coin wins. This three-way method is 75% likely to work each time it is tried.

penney game graphs
penney game graphs

If all three coins show the same result, the flip is simply repeated. This specific method does not require the players to call "heads" or "tails" beforehand.

Humans have used coins for decision-making for centuries. The Romans practiced a version called "navia aut caput," which means "ship or head." This name came from coins that featured a ship on one side and an emperor's head on the other.

Pompey by Nasidius
Pompey by Nasidius

In England, the practice was known as "cross and pile." Even in the history of American cities, a coin flip was decisive. In the United States, Francis W. Pettygrove used a coin to win the right to name Portland, Oregon. The coin he used is preserved today as the Portland Penny.

Sports rely heavily on the coin toss to ensure fairness and prevent escalation. In the NFL, a specially minted coin is used to decide which team starts with the ball.

In cricket, the toss is very significant because it determines if a captain chooses to bat or bowl first. This decision can influence the entire outcome of the match.

BradmanAllenToss
BradmanAllenToss

In tennis, the winner decides whether to serve or return first. Association football also uses the toss to decide which goal a team will attack in the first half.

Coin tossing has even decided major international tournament outcomes. In the 1968 European Championship semifinal, Italy and the Soviet Union finished in a 0–0 tie. A coin toss was used to decide the winner, and Italy went on to become the champions. In the United States, coin tosses are used to determine the class of senators when a new state is added to the Union. In the Philippines, a candidate can be chosen through a coin flip if an election results in a tie. These examples show how chance can resolve high-stakes legal and competitive moments.

Beyond games, coin flipping serves as a symbol of the democratic principle of equal opportunity. It represents a commitment to impartiality when two parties reach an impasse. Using a coin shows a willingness to accept an arbitrary outcome to avoid a struggle. This can be applied to business negotiations, interpersonal conflicts, and even scientific authorship. Scientists sometimes use a coin toss to decide the order of names on a scholarly paper. By accepting the result of the toss, all parties agree to move forward together.

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🖼️ Images & Media (6)
File:Coin Toss (3635981474).jpg
Coin Toss (3635981474).jpg
File:Pompey by Nasidius.jpg
Pompey by Nasidius.jpg
File:Coin toss at Super Bowl 43 1.jpg
Coin toss at Super Bowl 43 1.jpg
File:1970 Anglo-Italian Cup - Juventus v Sheffield Weds - Coin toss.jpg
1970 Anglo-Italian Cup - Juventus v...
File:BradmanAllenToss.jpg
BradmanAllenToss.jpg
File:penney_game_graphs.svg
penney_game_graphs.svg
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