研究揭示拋硬幣的同側偏差，挑戰隨機性假設

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

開創性的研究揭示了拋硬幣中令人驚訝的偏差：「公平」的硬幣有利於同側著陸

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（合眾國際社）—在一項突破性的研究中，阿姆斯特丹大學的研究人員仔細分析了超過350,000 次硬幣拋擲結果，挑戰了長期以來人們所持有的50/50硬幣拋擲結果的觀念，揭示了一個顯著的偏差：硬幣有輕微的偏差。降落在他們出發的同一側的可能性更高。

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.

在著名研究員 František Bartoš 的帶領下，該團隊對 48 個人使用 46 種不同貨幣進行的 350,757 次拋硬幣進行了細緻的分析。他們的研究結果發表在同行評審期刊《科學報告》上，顛覆了拋硬幣產生完全隨機結果的普遍假設。

"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."

巴托什在社交媒體聲明中表示：“我們詳盡的分析為‘同方’偏見提供了壓倒性的證據，正如 Diaconis 及其同事在 2007 年所預測的那樣。” “當一枚硬幣最初正面朝上翻轉時，它會表現出更大的再次​​正面朝上落地的趨勢，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.

該研究採用了細緻的方法，包括分析拋硬幣，參與者將硬幣拋向空中並接在手中。團隊的嚴格分析顯示，硬幣有 50.8% 的機率落在其出發的同一側。

"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."

巴托什強調：“這種微妙但具有統計意義的偏差對於機會遊戲和其他依賴拋硬幣的應用具有深遠的影響。” 「例如，假設您對拋硬幣的結果下注 1 美元，並重複下注 1,000 次，如果知道硬幣的第一面，您的平均利潤將為 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."

研究人員的發現超越了對偏見的簡單觀察。他們也發現，不同的拋硬幣者同側落地的幾率差異很大。巴托什解釋說：“一些腳蹼者對同側著陸表現出明顯的偏好，而另一些則沒有表現出明顯的偏好。” “這些差異可以歸因於翻轉技術的細微差別。”

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."

這項研究的意義不僅在於它對隨機拋硬幣概念的挑戰，還在於它的潛在應用。巴托什說：“我們的發現為進一步研究開闢了令人興奮的途徑，特別是在硬幣設計、賭博和概率論領域。” “‘同邊’偏見可能會對一切產生影響，從賭博策略到用於科學實驗的公平、公正的硬幣設計。”

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.

阿姆斯特丹大學的開創性研究引發了科學界內外的強烈興趣和爭論。其精心收集和分析的數據提供了無可辯駁的證據，表明即使像拋硬幣這樣看似簡單的事件也可能隱藏著微妙但重大的偏見。隨著研究人員繼續探索這一令人著迷的現象，人們長期以來認為硬幣真正翻轉 50/50 的觀點可能需要重新評估。