研究揭示抛硬币的同侧偏差，挑战随机性假设

Groundbreaking Study Unveils Surprising Bias in Coin Flips: 'Fair' Coins Favor Same-Side Landings

开创性的研究揭示了抛硬币中令人惊讶的偏差：“公平”的硬币有利于同侧着陆

Amsterdam, April 2 (UPI) - In a groundbreaking study that challenges the long-held notion of 50/50 coin flip outcomes, researchers at the University of Amsterdam have meticulously analyzed over 350,000 coin tosses to reveal a remarkable bias: coins have a slightly higher probability of landing on the same side they started from.

阿姆斯特丹，4 月 2 日（合众国际社）——在一项突破性的研究中，阿姆斯特丹大学的研究人员仔细分析了超过 350,000 次硬币抛掷结果，挑战了长期以来人们所持有的 50/50 硬币抛掷结果的观念，揭示了一个显着的偏差：硬币有轻微的偏差。降落在他们出发的同一侧的可能性更高。

Led by renowned researcher František Bartoš, the team embarked on a painstaking analysis of 350,757 coin flips performed by 48 individuals using 46 different currencies. Their findings, published in the peer-reviewed journal "Scientific Reports," upend the prevailing assumption that coin flips yield perfectly random results.

在著名研究员 František Bartoš 的带领下，该团队对 48 个人使用 46 种不同货币进行的 350,757 次抛硬币进行了细致的分析。他们的研究结果发表在同行评审期刊《科学报告》上，颠覆了抛硬币产生完全随机结果的普遍假设。

"Our exhaustive analysis provides overwhelming evidence for a 'same-side' bias, as predicted by Diaconis and colleagues in 2007," Bartoš stated in a social media announcement. "When a coin is initially flipped heads-up, it exhibits a greater tendency to land heads-up again, and vice versa."

巴托什在社交媒体声明中表示：“我们详尽的分析为‘同方’偏见提供了压倒性的证据，正如 Diaconis 及其同事在 2007 年所预测的那样。” “当一枚硬币最初正面朝上翻转时，它会表现出更大的再次​​正面朝上落地的趋势，反之亦然。”

The study's meticulous methodology involved analyzing coin flips in which participants tossed the coins into the air and caught them in their hands. The team's rigorous analysis revealed that coins displayed a 50.8% probability of landing on the same side they started from.

该研究采用了细致的方法，包括分析抛硬币，参与者将硬币抛向空中并接在手中。该团队的严格分析显示，硬币有 50.8% 的概率落在其出发的同一侧。

"This subtle but statistically significant bias has profound implications for games of chance and other applications that rely on coin flips," Bartoš emphasized. "For instance, in a hypothetical scenario where you wager a dollar on the outcome of a coin toss and repeat the bet 1,000 times, knowing the initial side of the coin would provide you with an average profit of 19 dollars."

巴托什强调说：“这种微妙但具有统计学意义的偏差对于机会游戏和其他依赖于抛硬币的应用具有深远的影响。” “例如，假设您对抛硬币的结果下注 1 美元，并重复下注 1,000 次，如果知道硬币的第一面，您的平均利润将为 19 美元。”

The researchers' findings extend beyond a simple observation of bias. They also found that the odds of same-side landings varied considerably among individual coin flippers. "Some flippers exhibited a pronounced bias towards the same-side landing, while others showed no significant preference," Bartoš explained. "These variations can be attributed to subtle differences in flipping techniques."

研究人员的发现超出了对偏见的简单观察。他们还发现，不同的抛硬币者同侧落地的几率差异很大。巴托什解释说：“一些脚蹼者对同侧着陆表现出明显的偏好，而另一些则没有表现出明显的偏好。” “这些差异可以归因于翻转技术的细微差别。”

The study's significance lies not only in its challenge to the notion of random coin flips but also in its potential applications. "Our findings open up exciting avenues for further research, particularly in the fields of coin design, gambling, and probability theory," Bartoš said. "The 'same-side' bias could have implications for everything from gambling strategies to the design of fair and unbiased coins for use in scientific experiments."

这项研究的意义不仅在于它对随机抛硬币概念的挑战，还在于它的潜在应用。巴托什说：“我们的发现为进一步研究开辟了令人兴奋的途径，特别是在硬币设计、赌博和概率论领域。” “‘同边’偏见可能会对一切产生影响，从赌博策略到用于科学实验的公平、公正的硬币设计。”

The University of Amsterdam's groundbreaking study has sparked a surge of interest and debate within the scientific community and beyond. Its meticulously gathered and analyzed data provide irrefutable evidence that even seemingly simple events like coin flips can harbor subtle but significant biases. As researchers continue to explore this fascinating phenomenon, the long-held belief that coins truly flip 50/50 may need to be reassessed.

阿姆斯特丹大学的开创性研究引发了科学界内外的强烈兴趣和争论。其精心收集和分析的数据提供了无可辩驳的证据，表明即使像抛硬币这样看似简单的事件也可能隐藏着微妙但重大的偏见。随着研究人员继续探索这一令人着迷的现象，人们长期以来认为硬币真正翻转 50/50 的观点可能需要重新评估。