Summary Evidence of Fair Coin Tossing Experiment arxiv.org
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Bartos et al. conducted a study with 350,757 coin flips, confirming a 51% chance of the coin landing on the same side.
Slides
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Key Points
- The study collected data from 350,757 coin flips to test the prediction from a physics model of human coin tossing developed by Persi Diaconis.
- The data strongly support the prediction that when people flip a fair coin, it tends to land on the same side it started.
- The probability of a same-side outcome was estimated to be about 51%.
- There was considerable variation in the degree of same-side bias between individuals.
- The data confirmed that when people flip a fair coin with the initial side randomly determined, it is equally likely to land heads or tails.
- The lack of heads-tails bias does not appear to vary across different coins.
- The study provides strong empirical confirmation of Diaconis' model of human coin tossing.
- The findings have implications for decision-making processes that rely on coin flips.
Summaries
17 word summary
Bartos et al. tested Diaconis' model with 350,757 coin flips, confirming a 51% probability of same-side landing.
84 word summary
Frantisek Bartos and colleagues conducted a study using 350,757 coin flips to test Persi Diaconis' physics model of coin tossing. The data supports Diaconis' prediction that a fair coin tends to land on the same side it started, with a 51% probability. The study found variation in same-side bias between individuals but no variation in heads-tails bias across different coins. Despite limitations, the study provides strong empirical confirmation of Diaconis' model. Concealing the starting position of the coin may be advisable in high-stakes situations.
123 word summary
A study by Frantisek Bartos and colleagues collected data from 350,757 coin flips to test Persi Diaconis' physics model of human coin tossing. The data strongly support Diaconis' prediction that a fair coin tends to land on the same side it started, with a probability of about 51%. The study also found variation in same-side bias between individuals but no significant variation in heads-tails bias across different coins. The researchers accounted for uncertainty in the model structure and used Bayesian model averaging to quantify evidence for different hypotheses. Despite limitations, such as the potential for manipulation, the study provides strong empirical confirmation of Diaconis' model. Concealing the starting position of the coin may be advisable in high-stakes situations that rely on coin flips.
442 word summary
A study conducted by Frantisek Bartos and colleagues collected data from 350,757 coin flips to test the prediction from a physics model of human coin tossing developed by Persi Diaconis. The data strongly support Diaconis' prediction that when people flip a fair coin, it tends to land on the same side it started. The probability of a same-side outcome was estimated to be about 51%. There was also variation in the degree of same-side bias between individuals. The data confirmed that when people flip a fair coin with the initial side randomly determined, it is equally likely to land heads or tails. The lack of heads-tails bias does not appear to vary across different coins. Overall, the data provide strong evidence in support of Diaconis' physics model of coin tossing.
Coin flipping is often used as a chance event for decision-making, but it follows the laws of Newtonian physics and is not random. The standard model of coin flipping predicts that the probability of a fair coin landing heads is 50% with no heads-tails bias. However, Diaconis' extended model proposes that people introduce a small degree of "precession" or wobble when flipping an ordinary coin, leading to a higher chance of the coin landing on the same side as it started.
Previous studies on coin flipping did not record whether the coin landed on the same side it started. In this study, researchers collected 350,757 coin flips, providing strong confirmation of Diaconis' prediction. The probability of a same-side outcome was estimated to be 0.508, close to Diaconis' prediction of approximately 51%. There was no heads-tails bias observed in the data.
The study also revealed variation in same-side bias between individuals, with some people showing little or no bias and others displaying varying degrees of bias. However, there was no significant variation in heads-tails bias across different coins. The study accounted for uncertainty in the model structure and used Bayesian model averaging to quantify evidence for different hypotheses.
While there are limitations to the study, such as the potential for participants to manipulate the coin flip outcomes, the nature of the coin tossing process and video recordings make this possibility unlikely. Further research could explore whether individuals with a higher degree of "wobbliness" exhibit a more pronounced same-side bias.
In conclusion, the study provides strong empirical confirmation of Diaconis' model of human coin tossing. The data support the prediction that when people flip a fair coin, it tends to land on the same side it started. These findings have implications for decision-making processes that rely on coin flips, suggesting that concealing the starting position of the coin may be advisable in high-stakes situations.
665 word summary
A study conducted by Frantisek Bartos and colleagues collected data from 350,757 coin flips to test the prediction from a physics model of human coin tossing developed by Persi Diaconis. The model suggests that when people flip a fair coin, it tends to land on the same side it started. The data from the study strongly support this prediction, with the coins landing on the same side more often than not. The probability of a same-side outcome was estimated to be about 51%. There was also considerable variation in the degree of same-side bias between individuals. The data also confirmed that when people flip a fair coin with the initial side randomly determined, it is equally likely to land heads or tails. The lack of heads-tails bias does not appear to vary across different coins. Overall, the data provide strong evidence in support of Diaconis' physics model of coin tossing.
Coin flipping is often considered a chance event, but few people consider the statistical and physical intricacies involved. The simplicity and perceived fairness of a coin flip, coupled with its widespread availability, make it a commonly used method for making decisions. Despite its popularity, the outcome of a coin flip is not random but follows the laws of Newtonian physics. According to the standard model of coin flipping, the flip is a deterministic process, and the perceived randomness comes from small fluctuations in initial conditions combined with narrow boundaries on the outcome space. The standard model predicts that when people flip a fair coin, the probability of it landing heads is 50%, with no heads-tails bias. However, Persi Diaconis extended this model by proposing that when people flip an ordinary coin, they introduce a small degree of "precession" or wobble, causing the coin to spend more time in the air with the initial side facing up. This leads to a higher chance of the coin landing on the same side as it started.
Previous studies on coin flipping have collected thousands of coin flips, but they did not record whether the coin landed on the same side it started. In this study, the researchers collected a total of 350,757 coin flips, which is a significantly larger sample size than previous efforts. The data confirmed the prediction from the Diaconis model, with the coins landing on the same side more often than 50%. The probability of a same-side outcome was estimated to be 0.508, which is remarkably close to Diaconis' prediction of approximately 51%. The data also showed no trace of a heads-tails bias, with an equal likelihood of the coin landing heads or tails. The Bayesian analyses provided strong evidence for the presence of same-side bias and moderate evidence against the presence of heads-tails bias.
The researchers also investigated between-people variation in the same-side bias and between-coin variation in the heads-tails bias. The data revealed substantial heterogeneity in the degree of same-side bias between individuals, with some people showing little or no bias and others displaying a varying degree of bias. There was no significant variation in the heads-tails bias across different coins. The analysis also accounted for uncertainty in the model structure and used Bayesian model averaging to quantify evidence for the different hypotheses.
The study has some limitations, including the possibility of participants manipulating the coin flip outcomes to produce the same-side bias. However, based on the nature of the coin tossing process, the evidence from video recordings, and the correspondence between the data and Diaconis' predictions, this possibility is deemed unlikely. Future research could explore whether individuals with a higher degree of "wobbliness" show a more pronounced same-side bias.
In conclusion, the study provides strong empirical confirmation of Diaconis' model of human coin tossing. The data support the prediction that when people flip a fair coin, it tends to land on the same side it started. The findings have implications for decision-making processes that rely on coin flips, suggesting that concealing the starting position of the coin may be advisable in high