【Hacker News搬运】公平的硬币往往落在它们开始的一侧

hackernews

Title: Fair coins tend to land on the side they started

公平的硬币往往落在它们开始的一侧

Text:

Url: https://www.researchgate.net/publication/374700857_Fair_coins_tend_to_land_on_the_same_side_they_started_Evidence_from_350757_flips

首先，我将提供关于所提供链接的摘要，然后进行翻译和总结。

摘要：
该研究通过分析350,757次投掷硬币的结果，发现“公平的硬币倾向于落在它们开始的那一侧”。这种现象在统计学上显著，表明硬币的投掷结果可能受到初始投掷角度或表面摩擦等因素的影响，而非完全随机的。

翻译：
这项研究通过分析350,757次掷硬币的结果，发现“公平的硬币倾向于落在它们开始的那一侧”。这种效应在统计学上是显著的，表明硬币的投掷结果可能受到初始投掷角度或表面摩擦等因素的影响，而不是完全随机的。

总结：
这项研究挑战了硬币投掷结果应该是完全随机这一普遍观点。通过对大量硬币投掷数据进行分析，研究者发现硬币并不总是随机落在正面或反面，而是有倾向于落在初始投掷位置同侧的趋势。这一发现可能对心理学、统计学以及任何依赖随机性原理的领域产生影响。尽管如此，这一现象的具体原因还需进一步研究。

Post by: seanhunter

Comments:

fbartos: Hi, I'm the first author of the manuscript, so I thought I could answer some of the questions and clarify some issues (all details are in the manuscript, but who has the time to read it ;)Low RPM tosses: Most of the recordings are on crapy webcams with ~ 30FPS. The coin spin usually much faster than the sensor can record which results in often non-spinning-looking flips. Why did we take the videos in the first place? To check that everyone collected the data and to audit the results.Building a flipping matching: The study is concerned with human coin flips. Diaconis, Holmes, and Montgomery's (DHM, 2007) paper theorize that the imperfection of human flips causes the same-side bias. Building a machine completely defeats the purpose of the experiment.Many authors and wasted public funding: We did the experiment in our free time and we had no funding for the study = no money was wasted. Also, I don't understand why are so many people angry that students who contributed their free time and spent the whole day flipping coins with us were rewarded with co-authorship. The experiment would be impossible to do without them.Improper tosses: Not everyone flips coin perfectly and some people are much worse at flipping than others. We instructed everyone to flip the coin as if they were to settle a bet and that the coin has to flip at least once (at least one flip would create bias for the opposite side). We find that for most people, the bias decreased over time which suggests that people might get better at flipping by practice = decrease the bias and it also discredits the theory that they learned how to be biased on purpose. From my own experience - I flipped coins more than 20,000 times and I have no clue how to bias it. Also, we did a couple of sensitivity analyses excluding outliers - the effect decreased a bit but we still found plentiful evidence for DHM.If you doubt my stats background, you are more than welcome to re-analyze the data on your own. They are available on OSF: <a href="https://osf.io/mhvp7/" rel="nofollow">https://osf.io/mhvp7/</a> (including cleaning scripts etc).Frantisek Bartos

fbartos: 嗨，我；我是手稿的第一作者，所以我想我可以回答一些问题并澄清一些问题（所有细节都在手稿中，但谁有时间阅读它；）低转速：大多数录音都是在大约30FPS的疯狂网络摄像头上录制的。硬币的旋转速度通常比传感器记录的快得多，这通常会导致看起来不旋转的翻转。我们为什么一开始就拍这些视频？检查每个人是否收集了数据并审核了结果 建立翻转匹配：这项研究涉及人类硬币翻转。迪亚科尼斯、福尔摩斯和蒙哥马利；s（DHM，2007）的论文提出理论，认为人类翻转的不完美会导致相同的侧偏。制造一台机器完全违背了实验的目的 许多作者和浪费的公共资金：我们在空闲时间做了这个实验，但我们没有为这项研究提供资金=没有浪费任何钱。此外，我不知道；我不明白为什么这么多人对那些贡献空闲时间并花了一整天时间与我们一起抛硬币的学生获得合著奖感到愤怒。没有他们，这个实验是不可能的 投掷不当：并非每个人都能完美地抛硬币，有些人的抛硬币能力比其他人差得多。我们指示每个人像下注一样抛硬币，并且硬币必须至少翻转一次（至少一次翻转会对另一方产生偏见）。我们发现，对于大多数人来说，随着时间的推移，偏见会减少，这表明人们可能会通过练习变得更好=减少偏见，这也使他们学会如何故意偏见的理论不可信。根据我自己的经验，我抛硬币超过2万次，但我不知道如何对其进行偏置。此外，我们还进行了几次排除异常值的敏感性分析，效果略有下降，但我们仍然发现了大量DHM的证据 如果你怀疑我的统计背景，欢迎你自己重新分析数据。它们可以在OSF上找到：<a href=“https:&#x2F；OSF.io/ mhvp7&#x2F；rel=“nofollow”>https:&#x2F；osf.io；mhvp7x2F</a> （包括清洁脚本等） Frantisek Bartos

acyou: The paper looks like it has a large sample size, but it actually has a sample size of only 48 testers/flippers. Some of the videos of those testers show very low, low-rpm coin tosses, we're talking only 1-2 flips. Where they also flipped thousands of times, presumably in the same way. So there is actually a very small sample size in the study (N = 48), where testers that don't flip properly (low rpm, low height, few coin rotations) can affect the results disproportionately.Doesn't look like the study author backgrounds are particularly focused on statistics. I would presume with 48 authors (all but 3 of which flipped coins for the study), the role of some might have been more test subject than author. And isn't being the subject in your own study going to introduce some bias? Surely if you're trying to prove to yourself that the coins land on one side or another given some factor, you will learn the technique to do it, especially if you are doing a low-rpm, low flip. Based on the study results, some of the flippers appear to have learned this quite well.If the flippers (authors) had been convinced of the opposite (fair coins tend to land on the opposite side from which they started) and done the same study, I bet they could have collected data and written a paper with the results proving that outcome.

acyou: 这篇论文看起来样本量很大，但实际上只有48名测试人员；脚蹼。这些测试人员的一些视频显示了非常低的、低转速的硬币投掷，我们；你只会翻1-2次。在那里，它们也翻转了数千次，大概是以同样的方式。因此，研究中的样本量实际上非常小（N=48）；正确翻转（低转速、低高度、很少旋转硬币）会对结果产生不成比例的影响 不会；看起来研究作者的背景特别侧重于统计学。我假设有48位作者（除了3位之外，其余都为这项研究抛硬币），其中一些人的角色可能比作者更像是测试对象。而且不是；作为你自己研究的对象，不会引入一些偏见吗？当然，如果你；如果你试图向自己证明，在给定某种因素的情况下，硬币会落在一边或另一边，你会学习如何做到这一点，特别是如果你正在进行低转速、低翻转。根据研究结果，一些鳍状肢似乎已经很好地学会了这一点 如果鳍状肢（作者）确信相反的情况（公平的硬币往往落在它们开始的另一边）并做了同样的研究，我打赌他们本可以收集数据并写一篇论文，证明这一结果。

seanhunter: There's a nice presentation of the paper here <a href="https://www.youtube.com/watch?v=-QjgvbvFoQA" rel="nofollow">https://www.youtube.com/watch?v=-QjgvbvFoQA</a>In essence the effect comes from "precession" - the tendency of the flip to not be purely vertical but to have some wobble/angular momentum which causes it to flip in such a way as to spend longer on one side than the other. Depending on the technique this will have a greater or lesser effect on the fairness of the coin toss, ranging from about p_same = 0.508 for the best technique to one person in the study actually exhibiting 0.6 over a large sample which is staggeringly unlikely if the toss was purely fair. In the extreme, it shows in the video a magician doing a trick toss using precession that looks as if it's flipping but does not in fact change sides at all, purely rotating in the plane of the coin and wobbling a bit.The video is quite a nice one for setting out how hypothesis testing works.

seanhunter: 那里；这是一篇很好的论文介绍<a href=“https:”www.youtube.com“watch？v=-QjgvbvFoQA”rel=“nofollow”>https:”&#x2F；www.youtube.com；看？v=-QjgvbvFoQA</a>从本质上讲，效果来自于“；进动”-翻转的趋势不是纯粹垂直的，而是有一些摆动；角动量使其翻转，使其在一侧的停留时间比另一侧长。根据技术的不同，这将对抛硬币的公平性产生或多或少的影响，从最佳技术的p_same=0.508到研究中一个人在大样本上实际表现出0.6，如果抛硬币纯粹是公平的，这是不太可能的。在极端情况下，它在视频中显示了一个魔术师使用进动进行魔术投掷，看起来就像它在做魔术一样；s翻转，但实际上根本不会改变方向，纯粹是在硬币的平面上旋转并稍微摆动。这段视频很好地阐述了假设检验的工作原理。

quantadev: I'm not sure I believe this coin flip bias, but I would if lots of other researchers can reproduce it.If indeed it's happening, the only explanation can be something to do with very deep Quantum Mechanics including multiverse theory, where we're simply "more likely" to be in a universe where the coin ends where it starts. (But honestly it seems like it would take trillions of flips to detect, just as a hunch) So that would make this experiment, believe it or not, akin to the infamous Slit-Experiment in Particle Physics, where multiverses are one way that's theorized as an explanation. That is, we're sort of in "all universes" as s superposition until something interacts in a way forcing us into ONE universe. (i.e. wave collapse)Along the same multiverse theme, I also have this other wild conjecture (feel free to ridicule it!) which is that AI LLM (Large Language Models) are "tending towards intelligence" during training because at each quantum collapse (of which Model Training has astronomically high numbers, with powerful computer data centers running for months) we're nudged just slightly more probabilistically into a universe where LLMs are "smart" as compared to "dumb", and so when you multiply it all up over months of churning, that puts us into a universe with dramatically smarter AI, because of the sheer number of computations, adding all the probabilities. I realize the training of AI is "deterministic" but nonetheless only quantum probabilities "determine" which universe we collapse into at each QM decoherence. So you can ask WHY is there this 'nudge' towards universes with smart LLMs? Probably because in all future universes we only exist because LLMs save us, or help us in some way, so other timelines/universes are "less" likely.

quantadev: 我；我不确定我是否相信这种硬币翻转偏见，但如果很多其他研究人员能够复制它，我会相信的。如果真的是这样的话；如果发生这种情况，唯一的解释可能与非常深入的量子力学有关，包括多元宇宙理论，在那里我们；简单地说&quot；更有可能&quot；在一个硬币从起点到终点的宇宙中。（但老实说，这似乎需要数万亿次翻转才能检测到，就像一种预感一样）所以，不管你信不信，这将使这个实验类似于臭名昭著的粒子物理学中的狭缝实验，其中多重宇宙是一种方式；这被理论化为一种解释。也就是说，我们；重新排序&quot；所有宇宙&quot；就像叠加一样，直到有东西以某种方式相互作用，迫使我们进入一个宇宙。（即波浪崩塌）沿着同一个多元宇宙主题，我还有另一个疯狂的猜想（随意嘲笑吧！），那就是AI LLM（大型语言模型）是&quot；趋向智能化&quot；在训练期间，因为在每次量子坍缩（其中模型训练具有天文数字，强大的计算机数据中心运行数月）时，我们；重新推动只是稍微更有可能地进入LLMs所在的宇宙；智能”；与“；“愚蠢”；，因此，当你在数月的搅动中将其全部相乘时，这将使我们进入一个具有更智能的人工智能的宇宙，因为计算量巨大，加上所有的概率。我意识到人工智能的训练是&quot；确定性”；但尽管如此，只有量子概率”；确定&quot；在每次QM退相干时，我们会坍缩到哪个宇宙。所以你可以问为什么会有这个；轻推；用智能LLM走向宇宙？可能是因为在所有未来的宇宙中，我们之所以存在，只是因为LLM拯救了我们，或者以某种方式帮助了我们，所以其他时间线也是如此；宇宙是“；较少&quot；可能。

cgag: I wouldn't be surprised if there is something to it, but I suspected they didn't use legitimate coin flips (because it seems like a large amount of people can't really flip a coin), and looking at the videos confirms it, at least for the flips done by Bartos:<a href="https://osf.io/6a5hy/" rel="nofollow">https://osf.io/6a5hy/</a>They're very low RPM and very low time in the air. Nothing I would accept for any decision worth flipping a coin for.

cgag: 我会；如果有什么事情发生，请不要感到惊讶，但我怀疑他们没有；不要使用合法的硬币翻转（因为看起来很多人都不能真正翻转硬币），观看视频可以证实这一点，至少对于Bartos所做的翻转来说是这样：<a href=“https:&#x2F；osf.io&#6a5hy�”rel=“nofollow”>https:&#x2F；osf.io；6a5hy</a> 他们；转速非常低，在空气中停留的时间也很短。对于任何值得为之抛硬币的决定，我都不会接受。