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Coin Flips Are Biased – Schneier on Security

A groundbreaking study has revealed that coin flips are not as random as previously believed. The study, which collected 350,757 coin flips, aimed to test the predictions of a physics model developed by Persi Diaconis. The model suggested that when people flip a regular coin, it is more likely to land on the same side it started. In fact, Diaconis estimated the probability of a same-side outcome to be around 51%.

The implications of this bias in coin flipping are significant. It raises the question of whether future coin tossers could exploit this bias to their advantage. To illustrate the magnitude of the observed bias, the study used a betting scenario. If a person were to bet a dollar on the outcome of a coin toss, knowing the starting position of the coin toss would earn them an average of 19 dollars if they repeated the bet 1,000 times. This advantage is greater than the casino advantage in a game of 6 deck blackjack against an optimal-strategy player, where the casino would make 5 dollars on a comparable bet. However, it is less than the casino advantage in single-zero roulette, where the casino would make 27 dollars on average. These findings suggest that when coin flips are used for high-stakes decision-making, it is best to conceal the starting position of the coin.

This study challenges the notion that coin flips are random and unbiased. It sheds light on the statistical and physical intricacies of the coin flipping process that many people overlook. The findings have implications not only in gambling but also in any scenario where coin flips are used to make important decisions. The study urges caution in relying on coin flips for high-stakes situations and highlights the need to conceal the starting position of the coin to mitigate the bias.

In conclusion, a comprehensive study has revealed that coin flips are not as random as commonly assumed. The study, which collected a large dataset of coin flips, showed that there is a bias towards the coin landing on the same side it started. This bias can be exploited in betting scenarios, where knowing the starting position of the coin can give an advantage. However, it is important to be cautious when using coin flips for high-stakes decision-making and to conceal the starting position of the coin to counteract the bias. These findings challenge our understanding of coin flips and highlight the need for further research in this area.

Key points:
– A study with a large dataset of coin flips has shown that there is a bias towards the coin landing on the same side it started.
– This bias can be exploited in betting scenarios, where knowing the starting position of the coin can give an advantage.
– Caution should be exercised when using coin flips for high-stakes decision-making.
– Concealing the starting position of the coin can help mitigate the bias.
– Further research is needed to better understand the intricacies of coin flips and their implications.

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