When Flipping Coins, Fair Coins Tend to Land on the Side They Started
hubie writes:
An a short but interesting paper recently posted to arXiv finds when most people flip a coin, it tends to land on the same side from which the toss started. Their observations are based upon analysis of 350,757 coin flips.
A coin flip-the act of spinning a coin into the air with your thumb and then catching it in your hand-is often considered the epitome of a chance event. It features as a ubiquitous example in textbooks on probability theory and statistics and constituted a game of chance ('capita aut navia' - 'heads or ships') already in Roman times.
The simplicity and perceived fairness of a coin flip, coupled with the widespread availability of coins, may explain why it is often used to make even high-stakes decisions. For example, in 1903 a coin flip was used to determine which of the Wright brothers would attempt the first flight; in 1959, a coin flip decided who would get the last plane seat for the tour of rock star Buddy Holly (which crashed and left no survivors); in 1968, a coin flip determined the winner of the European Championship semi-final soccer match between Italy and the Soviet Union (an event which Italy went on to win); in 2003, a coin toss decided which of two companies would be awarded a public project in Toronto; and in 2004 and 2013, a coin flip was used to break the tie in local political elections in the Philippines.
[...] The standard model of coin flipping was extended by Diaconis, Holmes, and Montgomery (D-H-M) who proposed that when people flip an ordinary coin, they introduce a small degree of 'precession' or wobble-a change in the direction of the axis of rotation throughout the coin's trajectory. According to the D-H-M model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started (i.e., 'same-side bias').
Their analysis agrees with the D-H-M model that suggests a coin will land 51 percent of the time on the same side it started.
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