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每一次决策背后的隐秘数学

用期望值、基准率、贝叶斯等六个数学模型系统纠正直觉决策的系统性偏差，但作者在计算、证据和适用边界上都有明显漏洞，且存在预测市场宣传意图。
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2026-03-09 原文链接 ↗
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核心观点

  • 期望值（EV）是决策的基础，但人类被损失厌恶扭曲了判断 人对损失的感受是收益的2倍，导致即使EV为正的机会也被拒绝；问题不在公式，而在于大多数人从不算这笔账，凭感觉就决定了。
  • 基准率被系统性忽视，让你高估小概率事件 创业成功率6%、独角兽0.00006%、医生诊断准确率99%但患病真实概率只有9%——这些数字揭示了人们如何被单个故事洗脑，而忽视真实的分母。
  • 沉没成本谬误是人生决策里最常见的陷阱 已投入的时间、金钱、情感都已经过去，唯一的问题是"如果今天从零开始，我还会选这条路吗"；大多数人却在用过去的投入为错误决定辩护。
  • 贝叶斯思维让你像科学家而非政客一样更新信念 不是"肯定会"或"肯定不会"的二元跳变，而是根据证据强度按比例微调概率；这是预测市场能精准定价的原因，也是顶级决策者的共同特征。
  • 幸存者偏差让你只看赢家，极度高估成功概率 Polymarket 87%的钱包亏损但你从不看到他们发帖、餐厅80%五年内倒闭但你只知道爆红的那家、Spotify每天90000首歌上传但你听到的都是爆火的——信息流天然隐藏尸体。
  • 凯利准则告诉你有优势时该下注多少，而非梭哈或保守 即使判断正确，下注规模错了也会输；现实中顶级交易者用1/4到1/2凯利而非满凯利，因为方差会在数学回报兑现前先摧毁你的心理和现金流。

跟我们的关联

  • 对ATou的意义：海外增长决策中，别被头部案例带节奏 每个"某AI社交爆了"的故事都是幸存者偏差；下一步应该追问真实基准率——这类产品跨文化复制成功率多少、社交产品留存基准率多少、AI伴侣真正付费用户比例多少，而不是拿个别爆款当战略依据。
  • 对Neta的意义：用EV框架替代"凭气氛决策" 任何>2周、>1人、>1万美元机会成本的决策都强制过六步检查表（EV、基准率、沉没成本、贝叶斯、幸存者偏差、凯利），这能显著降低对的方向被错误杠杆毁掉的概率。
  • 对Uota的意义：成为能指挥AI的top 0.0001%的核心不是写prompt 而是设计可校准的决策回路——人负责定义问题、赔率、约束和下注规模，AI负责生成方案、补充分母、持续更新概率；顶级使用者把AI当概率校准器和反偏见装置，而非答案机。
  • 对通用的意义：识别"确信"本身就是bug 当你对某个决定感到绝对确信时，这往往是大脑在为直觉找补而非做数学计算；这是高认知人群最危险的问题——不是无知，而是带着强自信犯系统性错误。

讨论引子

  • 你最近做过的一个重大决策，如果用EV框架重新算一遍，结论会改变吗？那些让你"感觉确信"的决定，真的经得起数学检验吗？
  • 在你的行业或领域里，基准率是多少？你是否在用个别成功故事高估了自己的成功概率，而从未真正追问过分母？
  • 凯利准则说即使判断正确也不该满仓，但现实中你见过多少创业者或投资者真的只用1/4凯利？这种"理性的保守"为什么这么难执行？

你每天大约要做 35,000 个决定。

吃什么。要不要现在回复那封邮件，还是晚点再回。走高速还是走小路。接受工作 offer 还是继续谈条件。继续持有那只股票还是卖掉。

我花了 3 个月决定要不要搬去巴黎：凌晨两点在脑子里列利弊清单。一次都没写下来。全凭感觉。搬了。结果一周之内就讨厌到不行。

对于小事：午饭吃什么、Netflix 看哪部剧——凭感觉当然没问题。谁在乎。

但对于那些真正塑造你人生的决定呢？职业选择、投资、关系、健康？凭感觉就是灾难。而且我能用数学证明。

顺带说一句，这不是数学课。没有微积分。我保证。这讲的是 6 个心智模型，它们改变了我对几乎一切事情的思考方式——一旦你看见了，就再也“看不回去”。

提前预警：有些内容会让你不舒服。你会意识到自己可能已经做了很多年糟糕的决定。我就有过。

1. 期望值（Expected Value）——支配一切的那一个公式

好，这就是最重要的一条。就算你从这篇文章里只学到一件事，也请学这个。

你做的任何决定，都有若干可能结果。每个结果都有一个概率和一个回报（或代价）。把它们相乘，再把所有结果加起来，你就得到了期望值（expected value）。

就这么简单。这就是公式。我是在过去五年里在加密圈把机会一次次亏到体无完肤之后，才开始用它认真思考。

朋友给你一个赌局：抛硬币。正面，他给你 $150。反面，你给他 $100。

大多数人会犹豫：“我可能会亏 $100！”没错，你确实可能亏。但把数学算一遍：

EV = (50% × $150) + (50% × -$100) = $75 - $50 = +$25

每次你接受这个赌局，平均下来你赚 $25。要是有人给你这个机会 100 次，你拒绝才是真的离谱——你大概能赚 $2,500。

但奇怪的是——在研究里，大多数人会拒绝这个赌局。即便数学在大喊“YES”。因为人类对损失的感受大约是同等收益的 2 倍。亏 $100 的痛，远大于赢 $150 的爽。心理学家把这叫做“损失厌恶”（loss aversion），它几乎会把你做的每一个决定都搅乱。

现实例子：你的老板给你两条路。

选项 A：留在当前岗位。保证年薪 $120K。
选项 B：去一家初创公司做更冒险的岗位（只是举例）。60% 概率成了，你在 2 年内赚到 $250K（股权 + 薪水）。40% 概率失败，你在同样时间里赚 $70K。

大多数人选 A。感觉更安全。我们算算：

A 的 EV = $120K（保证） B 的 EV = (0.60 × $350K) + (0.40 × $70K) = $150K + $28K = $178K

B 的价值高出 $58K。但 40% 的概率“只”拿到 $70K 听起来太吓人，所以人们不敢选。

我不是说要盲目追逐每一个期望值为正的机会。方差（波动）很重要。如果输了这把你就付不起房租，那就算 EV 为正也别上。但至少在你决定之前，要先知道 EV 是多少。大多数人甚至都不算——只凭直觉，然后纳闷自己为什么卡住不动。

2. 忽视基准率（Base Rate Neglect）——你比自己想的更常出错的原因

这一条很阴险，因为它直觉上特别反直觉。

假设有一种疾病，发生率是 1/1,000。你做了一个准确率 99% 的检测，结果显示阳性。

你真的患病的概率是多少？

如果你说 99%……你错了。而且你并不孤单——大多数医生也会算错。

想一想：在 1,000 个人里：

  • 其中 1 个真的有病。检测能抓到他（99% 准确），这就是 1 个真阳性。

  • 另外 999 个没病。但检测有 1% 的假阳性率，也就是大约 10 个假阳性。

于是总共有 11 个阳性结果，其中只有 1 个是真的。

不是 99%。是 9%。基准率（1/1,000）极其重要，而人们每次都会忽略它。

它如何毁掉现实决策：

  • “我的创业点子很棒——你看 Uber 做得多好！”创业成功的基准率：约 6%。成为独角兽的基准率：0.00006%。我从 2017 年开始一直想做自己的创业项目。我大多数朋友也一样（而且他们父母更有钱）。我以为自己是例外。并不是。

  • “这个投资去年涨了 40%，我应该加仓。”任何基金连续 3 年跑赢市场的基准率：约 15%。去年的表现对明年几乎没什么说明力。

  • “推特上这个人预测到了崩盘，他一定是天才。”基准率：如果有 10,000 个人随机瞎预测，大约会有 100 个能精准蒙中。他们不是天才。他们只是大样本里的幸存者。

每当有人用一个具体的成功故事来证明“这事可行”，问问自己：基准率是什么？这种事现实里到底多常发生？如果答案是“很少”——那无论故事听起来多么有说服力，都要保持强烈怀疑。

3. 沉没成本谬误——把好钱往坏钱里砸（而且不止是钱）

你花 $15 买了电影票。看了 30 分钟，发现这电影烂得要命。

你是走，还是继续坐着？

从经济学角度答案很明显：走。那 $15 无论如何都已经没了——你继续坐也拿不回来。唯一的问题是：“接下来的 90 分钟，是继续看这部烂片更值得，还是去做任何别的事情更值得？”

但几乎所有人都会留下来：“我都付钱了。”

这就是沉没成本谬误。而它毁掉人生的方式，比烂电影严重得多。

  • 在一份没有前途的工作里再熬 3 年，只因为“我已经在这里投入了 5 年”。那 5 年已经过去了。唯一的问题是：接下来的 3 年怎么用最好？

  • 抱着一只亏损的股票，或者任何山寨币/迷因币不放，因为“都跌 50% 了，现在卖就亏大了”。股票不知道你的成本价。市场也不在乎你买入时付了多少。唯一的问题是：如果你现在手里是现金，你会按今天的价格买入这只股票吗？

  • 维持一段关系，只因为“我们在一起 6 年了”。那 6 年已经发生了。唯一的问题是接下来的 6 年会不会好。

修复方式简单到近乎粗暴：做任何决定时，假装你现在就是从零开始。忽略你已经付出的所有东西——时间、金钱、情绪。只看未来。以你现在掌握的信息，你今天还会选择这条路吗？

如果答案是否，离开。无论如何，过去都回不来。

4. 贝叶斯思维——像科学家（而不是政客）一样更新你的信念

大多数人先形成观点，然后就终身捍卫。新证据来了？无所谓——他早就决定了。

这恰恰是你不该有的思考方式。

贝叶斯定理给了你一个在数学上正确的“改变主意”的方法：

看起来很吓人。其实不吓人。我把它翻译成大白话：

你更新后的信念 = 证据与理论的吻合程度 × 你在此之前相信该理论的可能性 ÷ 这种证据在总体里出现的常见程度。

例子：你觉得同事可能要辞职。在没有任何证据前，你会说只有 10% 的概率（大多数人不会在某一个月突然辞职）。这就是你的先验（prior）。

然后你发现她更新了 LinkedIn 主页。嗯。

  • 如果她确实快要辞职了，她更新 LinkedIn 的概率有多大？挺高——比如 70%。

  • 如果她并不打算辞职，她更新 LinkedIn 的概率有多大？人们也会随手更新——比如 15%。

P(辞职 | LinkedIn 更新) = (0.70 × 0.10) / ((0.70 × 0.10) + (0.15 × 0.90)) = 0.07 / (0.07 + 0.135) = 0.07 / 0.205 ≈ 34%

一条证据就把你从 10% 推到了 34%。不是 90%——那是过度反应；也不是还停在 10%——那是在无视证据。34% 才是数学上理性的更新。

接着她开始在办公室外接电话。再更新一次。也许变成 55%。她突然对长期项目含糊其辞。70%。

每一条证据都会把概率轻轻推一下：慢慢地、按比例地。没有戏剧性。不会在“肯定会”与“肯定不会”之间突然翻转。

这也是预测市场的运作方式。合约的价格就是贝叶斯后验（posterior）——随着新信息不断流入而持续更新。所以 Polymarket 能在 CNN 之前预测伊朗的打击行动：成千上万的人把零碎证据喂进价格里，每条证据可能只把它推 0.5% 或 2%。汇总起来就诡异地准确。

要点是：对观点保持松弛。持续更新。你更新的力度，应该与证据的力度成正比。大多数人要么完全忽略证据，要么疯狂过度纠正。两种都错。

5. 幸存者偏差——你看到的只有赢家

你读到一个大学辍学的人，建立了十亿美元公司。很励志，对吧？也许上大学就是浪费时间？

但你从来听不到另外 10,000 个辍学后穷困潦倒的人。他们不上杂志封面，不会上播客访谈。他们只是默默挣扎，而一个幸存者拿走了全部注意力。

这就是幸存者偏差。你只看见赢家，于是会极度高估“赢”的概率。

它无处不在：

  • 加密圈的 Twitter。人人晒收益，没人晒亏损。把 $500 变成 $50K 的那个人拿到 200K 点赞。把 $500 亏到 $0 的那 500 个人删号跑路。你的信息流让你以为大家都在赢。并没有。Polymarket 的钱包里有 87% 是亏钱的——只是你从来没看到他们发帖。

  • 餐饮建议。“跟随热爱，开家餐厅就行！”60% 的餐厅在第一年内倒闭。80% 在五年内倒闭。活下来的那些，才会成为你最爱的店。死掉的都不可见。如果你无视坟场，“跟随热爱”当然听起来像绝佳建议。

  • 音乐行业。“上传到 Spotify，直接爆火！”Spotify 每天都有 90,000 首歌被上传。中位数歌曲总播放量只有 30 次。你听到的都是爆火的，因为……它们爆火了。剩下的 89,990 首是沉默。

修复方式：每当有人用一个成功故事证明“这事可行”，去找分母。到底有多少人试过？成功率是多少？如果你找不到分母，就默认成功率很低。因为世界只会把分子展示给你。

6. 凯利准则（Kelly Criterion）——当你确实有优势时，该下注多少

好，假设你把上面都做到了：你算了 EV，查了基准率，用贝叶斯更新了信念，把幸存者偏差考虑进去了，而且你真的找到了一个好机会。

那你该下注多少？

大多数人只有两种模式：押太多或押太少。要么因为“自信”就梭哈（yolo），要么因为害怕只投一点点。两种都错——而且有一个公式告诉你“恰到好处”的量。

f* = (p × b - q) / b

p = 胜出的概率（你诚实的估计）
q = 输的概率（= 1 - p）
b = 每风险 1 美元，你能赢多少美元

例子：你找到一个赌局，你认为自己有 60% 的胜率。如果赢了，你的钱翻倍（b = 1）。

f* = (0.60 × 1 - 0.40) / 1 = 0.20

凯利说：下注你本金的 20%。

但过去 50 年的现实应用告诉我们：对人类来说，满凯利太激进了。方差会在数学回报兑现之前，先把你的情绪摧毁。每一个我研究过的职业赌徒和交易员，都会用四分之一凯利到二分之一凯利。

所以别下注 20%，下注 5–10%。不够刺激。你明天不会暴富。但你下周也不会爆仓。

顺带说一句，这适用于一切——不只是钱：

  • 职业：别为了一个副业直接辞职 all-in。把工作缩到每周 4 天，用 1 天做项目。这大概就是“四分之一凯利”。

  • 学习：别一次学 5 项新技能。选 EV 最高的那一个，深挖下去。

  • 关系：别把精力摊在 20 段浅层友谊上。把投资集中在真正重要的 4–5 个人身上。

原则是：当你有优势时，要集中。但不要太集中。给自己留出犯错的空间。

这 6 个模型如何串起来（以及为什么预测市场是终极训练场）

它们不是零散的数学小把戏，而是一整套“清晰思考系统”：

  1. EV 告诉你要不要行动

  2. 基准率 让你的估计贴近现实

  3. 沉没成本 告诉你该忽略什么

  4. 贝叶斯 告诉你如何更新

  5. 幸存者偏差 告诉你画面里缺了什么

  6. 凯利 告诉你该投入多少

像 Polymarket 这样的预测市场，奇妙地成了训练这 6 点的最佳场地。每一张合约都逼你给出一个概率。市场价格展示人群的概率。如果你不同意——并且你有理由——你就交易。你的盈亏会告诉你，你的思考到底对不对。

它像是决策能力的健身房。只不过你做的不是重复次数，而是下注；你得到的不是酸痛，而是一个不会说谎的钱包余额。

我分析过的 Polymarket 交易者里，排名前 1.2% 的那群人？他们都用这种方式思考。不是因为他们读了同样的书——而是市场把这套思维硬生生敲进了他们的骨头里。概率估得差，就亏钱；学到教训；重复。500 次之后，这就是课程大纲。

那个让人不舒服的部分

我第一次学会这些东西时，最困扰我的是这一点：

我意识到，在我人生里几乎所有重要的事情上，我都在做错决定。工作待太久（沉没成本）。不敢谈薪水，因为“他们可能会拒绝我”（损失厌恶 + 错误的 EV 计算）。跟随加密圈 KOL，只因为他们有过一次大胜（幸存者偏差）。有些事情改主意太快，有些事情改得太慢（糟糕的贝叶斯更新）。把自己摊在太多项目上（反凯利）。

最糟糕的是？我一直以为自己很理性。我对每个决定都有“理由”。只是那些理由，刚好都是大脑为了给直觉的决定找补而编出来的错误理由。

这就是陷阱：当你不理性时，你并不会感觉到“不理性”。你会感觉到“确信”。这种确信本身，就是 bug。

上面这 6 个模型不会让你完美。没有任何东西能。但它们能给你一个结构化的方法来检查自己的思考。就像飞行员在起飞前逐项检查——不是因为他们不会飞，而是因为即便是专家，在只靠直觉时也会漏掉东西。

开始用它们吧。先从一个开始。下次你遇到一个真正的决定——职业、金钱、关系，随便什么——先停 5 分钟，把 EV 算一遍。只做这一件事就好。

你会震惊：答案会和你的直觉告诉你的，完全不同。

阅读清单（想更深入的话）

按它们改变我思考方式的程度排序：

  1. Thinking, Fast and Slow - Daniel Kahneman。堪称圣经。几乎涵盖了本文的一切，还额外讲了 200 个你不知道自己有的偏差。

  2. Superforecasting - Philip Tetlock。世界上最强的预测者如何思考。对预测市场直接有用。

  3. The Signal and the Noise --Nate Silver。如何找到真实模式、忽略伪模式。

  4. Fooled by Randomness -Nassim Taleb。为什么大多数“技能”其实是披着外衣的运气。

  5. Fortune's Formula - William Poundstone。凯利准则的狂野历史。读起来像惊悚小说。

You make roughly 35,000 decisions a day.

你每天大约要做 35,000 个决定。

What to eat. Whether to reply to that email now or later. Take the highway or side streets. Accept the job offer or negotiate. Hold the stock or sell.

吃什么。要不要现在回复那封邮件，还是晚点再回。走高速还是走小路。接受工作 offer 还是继续谈条件。继续持有那只股票还是卖掉。

I spent 3 months deciding whether to move to Paris by making pro/con lists in my head at 2am. Never wrote anything down. Just vibes. Moved. Hated it within a week

我花了 3 个月决定要不要搬去巴黎：凌晨两点在脑子里列利弊清单。一次都没写下来。全凭感觉。搬了。结果一周之内就讨厌到不行。

And for small stuff: what to have for lunch, which Netflix show to watch, vibes are fine. Who cares.

对于小事：午饭吃什么、Netflix 看哪部剧——凭感觉当然没问题。谁在乎。

But for the decisions that actually shape your life? Career moves, investments, relationships, health? Vibes are a disaster. And I can prove it with math.

但对于那些真正塑造你人生的决定呢？职业选择、投资、关系、健康？凭感觉就是灾难。而且我能用数学证明。

This isn't a math lecture btw. No calculus. I promise. This is about 6 mental models that changed how I think about literally everything - and once you see them you can't unsee them.

顺带说一句，这不是数学课。没有微积分。我保证。这讲的是 6 个心智模型，它们改变了我对几乎一切事情的思考方式——一旦你看见了，就再也“看不回去”。

Fair warning: some of this will make you uncomfortable. You'll realize you've been making bad decisions for years. I know I did.

提前预警：有些内容会让你不舒服。你会意识到自己可能已经做了很多年糟糕的决定。我就有过。

1. Expected Value — the one formula that runs everything

1. 期望值（Expected Value）——支配一切的那一个公式

Ok so this is the big one. If you learn nothing else from this article, learn this.

好，这就是最重要的一条。就算你从这篇文章里只学到一件事，也请学这个。

Any decision you make has possible outcomes. Each outcome has a probability and a payoff. Multiply them together, add them up, and you get the expected value.

你做的任何决定，都有若干可能结果。每个结果都有一个概率和一个回报（或代价）。把它们相乘，再把所有结果加起来，你就得到了期望值（expected value）。

That's it. That's the formula. I started thinking about this after I endless rekt opportunities in crypto space over last 5 years of my experience.

就这么简单。这就是公式。我是在过去五年里在加密圈把机会一次次亏到体无完肤之后，才开始用它认真思考。

Your friend offers you a bet. Flip a coin. Heads, he pays you $150. Tails, you pay him $100.

朋友给你一个赌局：抛硬币。正面，他给你 $150。反面，你给他 $100。

Most people hesitate. "I could lose $100!" And yeah, you could. But run the math:

大多数人会犹豫：“我可能会亏 $100！”没错，你确实可能亏。但把数学算一遍：

EV = (50% × $150) + (50% × -$100) = $75 - $50 = +$25

EV = (50% × $150) + (50% × -$100) = $75 - $50 = +$25

Every time you take this bet, you make $25 on average. If someone offered you this 100 times you'd be insane to say no. You'd make roughly $2,500.

每次你接受这个赌局，平均下来你赚 $25。要是有人给你这个机会 100 次，你拒绝才是真的离谱——你大概能赚 $2,500。

But here's the weird thing - in studies, most people reject this bet. Even when the math screams YES. Because humans feel losses about 2x more than equivalent gains. Losing $100 hurts way more than winning $150 feels good. Psychologists call this loss aversion and it screws up almost every decision you make.

但奇怪的是——在研究里，大多数人会拒绝这个赌局。即便数学在大喊“YES”。因为人类对损失的感受大约是同等收益的 2 倍。亏 $100 的痛，远大于赢 $150 的爽。心理学家把这叫做“损失厌恶”（loss aversion），它几乎会把你做的每一个决定都搅乱。

Real world example. Your boss offers you two paths:

现实例子：你的老板给你两条路。

Option A: Stay in your current role. Guaranteed $120K salary. Option B: Take a riskier role at a startup (just an example). 60% chance it works and you make $250K in 2 years (equity + salary). 40% chance it fails and you make $70K for the same period.

选项 A：留在当前岗位。保证年薪 $120K。
选项 B：去一家初创公司做更冒险的岗位（只是举例）。60% 概率成了，你在 2 年内赚到 $250K（股权 + 薪水）。40% 概率失败，你在同样时间里赚 $70K。

Most people pick A. Feels safe. Let's check:

大多数人选 A。感觉更安全。我们算算：

EV of A = $120K (guaranteed) EV of B = (0.60 × $350K) + (0.40 × $70K) = $150K + $28K = $178K

A 的 EV = $120K（保证） B 的 EV = (0.60 × $350K) + (0.40 × $70K) = $150K + $28K = $178K

Option B is worth $58K more. But 40% chance of "only" $70K feels terrifying so people don't take it.

B 的价值高出 $58K。但 40% 的概率“只”拿到 $70K 听起来太吓人，所以人们不敢选。

I'm not saying blindly chase every positive EV opportunity. Variance matters. If losing the bet means you can't pay rent, don't take it even if EV is positive. But at least KNOW the EV before you decide. Most people don't even calculate it. They just go with their gut and wonder why they're stuck.

我不是说要盲目追逐每一个期望值为正的机会。方差（波动）很重要。如果输了这把你就付不起房租，那就算 EV 为正也别上。但至少在你决定之前，要先知道 EV 是多少。大多数人甚至都不算——只凭直觉，然后纳闷自己为什么卡住不动。

2. Base Rate Neglect — the reason you're wrong more than you think

2. 忽视基准率（Base Rate Neglect）——你比自己想的更常出错的原因

This one is sneaky because it feels so counterintuitive.

这一条很阴险，因为它直觉上特别反直觉。

Let's say there's a disease that affects 1 in 1,000 people. You take a test that's 99% accurate. It comes back positive.

假设有一种疾病，发生率是 1/1,000。你做了一个准确率 99% 的检测，结果显示阳性。

What's the probability you actually have the disease?

你真的患病的概率是多少？

If you said 99%... you're wrong. And you're in good company — most doctors get this wrong too.

如果你说 99%……你错了。而且你并不孤单——大多数医生也会算错。

Let's think about it. Out of 1,000 people:

想一想：在 1,000 个人里：

  • 1 actually has the disease. The test catches them (99% accurate). That's 1 true positive.
  • 其中 1 个真的有病。检测能抓到他（99% 准确），这就是 1 个真阳性。
  • 999 don't have it. But the test has a 1% false positive rate. That's ~10 false positives.
  • 另外 999 个没病。但检测有 1% 的假阳性率，也就是大约 10 个假阳性。

So there are 11 positive results total. Only 1 is real.

于是总共有 11 个阳性结果，其中只有 1 个是真的。

Not 99%. Nine percent. The base rate (1 in 1,000) matters enormously, and people ignore it every single time.

不是 99%。是 9%。基准率（1/1,000）极其重要，而人们每次都会忽略它。

How this ruins real decisions:

它如何毁掉现实决策：

  • "My startup idea is great - look at how well Uber did!" Base rate of startup success: ~6%. Base rate of becoming a unicorn: 0.00006%. I have been trying to do my own startups since 2017. Most of my friends had as well (whose parents were way richer). Thought I was the exception. I wasn't.
  • “我的创业点子很棒——你看 Uber 做得多好！”创业成功的基准率：约 6%。成为独角兽的基准率：0.00006%。我从 2017 年开始一直想做自己的创业项目。我大多数朋友也一样（而且他们父母更有钱）。我以为自己是例外。并不是。
  • "This investment returned 40% last year, I should buy more." Base rate of any fund beating the market 3 years in a row: ~15%. Last year's performance tells you almost nothing about next year.
  • “这个投资去年涨了 40%，我应该加仓。”任何基金连续 3 年跑赢市场的基准率：约 15%。去年的表现对明年几乎没什么说明力。
  • "This guy on Twitter predicted the crash, he must be a genius." Base rate: if 10,000 people make random predictions, ~100 will nail it perfectly. They are not geniuses. They're survivors of a large sample.
  • “推特上这个人预测到了崩盘，他一定是天才。”基准率：如果有 10,000 个人随机瞎预测，大约会有 100 个能精准蒙中。他们不是天才。他们只是大样本里的幸存者。

Whenever someone tells you about a specific success story, ask yourself: what's the base rate? How often does this type of thing actually work? If the answer is "rarely" — be very skeptical, no matter how convincing the story sounds.

每当有人用一个具体的成功故事来证明“这事可行”，问问自己：基准率是什么？这种事现实里到底多常发生？如果答案是“很少”——那无论故事听起来多么有说服力，都要保持强烈怀疑。

3. Sunk Cost Fallacy — throwing good money after bad (and not just money)

3. 沉没成本谬误——把好钱往坏钱里砸（而且不止是钱）

You bought a movie ticket for $15. Thirty minutes in, the movie is terrible.

你花 $15 买了电影票。看了 30 分钟，发现这电影烂得要命。

Do you leave or stay?

你是走，还是继续坐着？

Economically, the answer is obvious: leave. The $15 is gone either way- staying doesn't get it back. The only question is: "Will the next 90 minutes be better spent watching this bad movie or doing literally anything else?"

从经济学角度答案很明显：走。那 $15 无论如何都已经没了——你继续坐也拿不回来。唯一的问题是：“接下来的 90 分钟，是继续看这部烂片更值得，还是去做任何别的事情更值得？”

But almost everyone stays. "I already paid for it."

但几乎所有人都会留下来：“我都付钱了。”

That's the sunk cost fallacy. And it wrecks people's lives in ways far worse than bad movies.

这就是沉没成本谬误。而它毁掉人生的方式，比烂电影严重得多。

  • Staying in a dead-end job for 3 more years because "I already invested 5 years here." Those 5 years are gone. The only question is: what's the best use of the NEXT 3?
  • 在一份没有前途的工作里再熬 3 年，只因为“我已经在这里投入了 5 年”。那 5 年已经过去了。唯一的问题是：接下来的 3 年怎么用最好？
  • Holding a losing stock or any altcoin / memecoin because "Already down 50%, I can't sell now." The stock doesn't know your entry. The market doesn't care what you paid. The only question is: if you had cash right now, would you buy this stock at today's price?
  • 抱着一只亏损的股票，或者任何山寨币/迷因币不放，因为“都跌 50% 了，现在卖就亏大了”。股票不知道你的成本价。市场也不在乎你买入时付了多少。唯一的问题是：如果你现在手里是现金，你会按今天的价格买入这只股票吗？
  • Staying in a relationship because "we've been together for 6 years." Those 6 years happened. The only question is whether the NEXT 6 will be good.
  • 维持一段关系，只因为“我们在一起 6 年了”。那 6 年已经发生了。唯一的问题是接下来的 6 年会不会好。

The fix is aggressively simple: when making any decision, pretend you're starting from scratch right now. Ignore everything you've already spent - time, money, emotion. Only look forward. Would you choose this path today, knowing what you know?

修复方式简单到近乎粗暴：做任何决定时，假装你现在就是从零开始。忽略你已经付出的所有东西——时间、金钱、情绪。只看未来。以你现在掌握的信息，你今天还会选择这条路吗？

If the answer is no, get out. The past is not coming back regardless.

如果答案是否，离开。无论如何，过去都回不来。

4. Bayesian Thinking — how to update your beliefs like a scientist (not a politician)

4. 贝叶斯思维——像科学家（而不是政客）一样更新你的信念

Most people form an opinion and then defend it forever. New evidence comes in? Doesn't matter - they already decided.

大多数人先形成观点，然后就终身捍卫。新证据来了？无所谓——他早就决定了。

This is the opposite of how you should think.

这恰恰是你不该有的思考方式。

Bayes' theorem gives you the mathematically correct way to change your mind:

贝叶斯定理给了你一个在数学上正确的“改变主意”的方法：

Looks scary. It's not. Let me translate it to English:

看起来很吓人。其实不吓人。我把它翻译成大白话：

Your updated belief = how well the evidence fits your theory × how likely your theory was before ÷ how common the evidence is in general.

你更新后的信念 = 证据与理论的吻合程度 × 你在此之前相信该理论的可能性 ÷ 这种证据在总体里出现的常见程度。

Example. You think your coworker is going to quit. Before any evidence, you'd say there's a 10% chance (most people don't quit in any given month). That's your prior.

例子：你觉得同事可能要辞职。在没有任何证据前，你会说只有 10% 的概率（大多数人不会在某一个月突然辞职）。这就是你的先验（prior）。

Then you notice she updated her LinkedIn profile. Hm.

然后你发现她更新了 LinkedIn 主页。嗯。

  • If she IS about to quit, what's the probability she'd update LinkedIn? Pretty high — say 70%.
  • 如果她确实快要辞职了，她更新 LinkedIn 的概率有多大？挺高——比如 70%。
  • If she's NOT about to quit, what's the probability she'd update LinkedIn? People do it randomly all the time — say 15%.
  • 如果她并不打算辞职，她更新 LinkedIn 的概率有多大？人们也会随手更新——比如 15%。

P(quitting | LinkedIn update) = (0.70 × 0.10) / ((0.70 × 0.10) + (0.15 × 0.90)) = 0.07 / (0.07 + 0.135) = 0.07 / 0.205 ≈ 34%

P(辞职 | LinkedIn 更新) = (0.70 × 0.10) / ((0.70 × 0.10) + (0.15 × 0.90)) = 0.07 / (0.07 + 0.135) = 0.07 / 0.205 ≈ 34%

One piece of evidence moved you from 10% to 34%. Not to 90% -that would be overreacting. Not staying at 10% - that would be ignoring evidence. 34% is the mathematically rational update.

一条证据就把你从 10% 推到了 34%。不是 90%——那是过度反应；也不是还停在 10%——那是在无视证据。34% 才是数学上理性的更新。

Now she also starts taking calls outside the office. Another update. Maybe goes to 55%. She's suddenly vague about long-term projects. 70%.

接着她开始在办公室外接电话。再更新一次。也许变成 55%。她突然对长期项目含糊其辞。70%。

Each piece of evidence nudges the probability. Gradually. Proportionally. No drama. No sudden flipping between "definitely yes" and "definitely no."

每一条证据都会把概率轻轻推一下：慢慢地、按比例地。没有戏剧性。不会在“肯定会”与“肯定不会”之间突然翻转。

This is how prediction markets work btw. The price of a contract IS the Bayesian posterior- constantly updating as new information flows in. That's why Polymarket predicted the Iran strikes before CNN. Thousands of people feeding tiny pieces of evidence into a price. Each one nudging it 0.5% this way or 2% that way. The aggregate is spookily accurate.

这也是预测市场的运作方式。合约的价格就是贝叶斯后验（posterior）——随着新信息不断流入而持续更新。所以 Polymarket 能在 CNN 之前预测伊朗的打击行动：成千上万的人把零碎证据喂进价格里，每条证据可能只把它推 0.5% 或 2%。汇总起来就诡异地准确。

The takeaway: hold opinions loosely. Update them constantly. The strength of your update should be proportional to the strength of the evidence. Most people either ignore evidence entirely or overcorrect wildly. Both are wrong.

要点是：对观点保持松弛。持续更新。你更新的力度，应该与证据的力度成正比。大多数人要么完全忽略证据，要么疯狂过度纠正。两种都错。

5. Survivorship Bias — you're only seeing the winners

5. 幸存者偏差——你看到的只有赢家

You read about a college dropout who built a billion-dollar company. Inspiring, right? Maybe college is a waste of time?

你读到一个大学辍学的人，建立了十亿美元公司。很励志，对吧？也许上大学就是浪费时间？

Except you never hear about the 10,000 other dropouts who are broke. They don't get magazine covers. They don't get podcast interviews. They just quietly struggle while one survivor gets all the attention.

但你从来听不到另外 10,000 个辍学后穷困潦倒的人。他们不上杂志封面，不会上播客访谈。他们只是默默挣扎，而一个幸存者拿走了全部注意力。

This is survivorship bias. You only see the winners, so you massively overestimate the probability of winning.

这就是幸存者偏差。你只看见赢家，于是会极度高估“赢”的概率。

It's everywhere:

它无处不在：

  • Crypto Twitter. Everyone posting gains. Nobody posting losses. The guy who turned $500 into $50K gets 200K likes. The 500 guys who turned $500 into $0 deleted their accounts. Your feed makes it look like everyone's winning. They're not. 87% of Polymarket wallets lose money. You just never see them post about it.
  • 加密圈的 Twitter。人人晒收益，没人晒亏损。把 $500 变成 $50K 的那个人拿到 200K 点赞。把 $500 亏到 $0 的那 500 个人删号跑路。你的信息流让你以为大家都在赢。并没有。Polymarket 的钱包里有 87% 是亏钱的——只是你从来没看到他们发帖。
  • Restaurant advice. "Just follow your passion and open a restaurant!" 60% of restaurants close within the first year. 80% close within five. The ones that survive become your favorite spots. The dead ones are invisible. Following your passion is great advice if you ignore the graveyard.
  • 餐饮建议。“跟随热爱，开家餐厅就行！”60% 的餐厅在第一年内倒闭。80% 在五年内倒闭。活下来的那些，才会成为你最爱的店。死掉的都不可见。如果你无视坟场，“跟随热爱”当然听起来像绝佳建议。
  • Music industry. "Just upload to Spotify and go viral!" 90,000 tracks are uploaded to Spotify every single day. The median track gets 30 plays total. You hear about the ones that go viral because... they went viral. The other 89,990 are silence.
  • 音乐行业。“上传到 Spotify，直接爆火！”Spotify 每天都有 90,000 首歌被上传。中位数歌曲总播放量只有 30 次。你听到的都是爆火的，因为……它们爆火了。剩下的 89,990 首是沉默。

The fix: whenever someone shows you a success story as proof that something works, look for the denominator. How many people tried this? What percentage succeeded? If you can't find the denominator, assume the success rate is very low. Because the world only shows you numerators.

修复方式：每当有人用一个成功故事证明“这事可行”，去找分母。到底有多少人试过？成功率是多少？如果你找不到分母，就默认成功率很低。因为世界只会把分子展示给你。

6. The Kelly Criterion — how much to bet when you DO have an edge

6. 凯利准则（Kelly Criterion）——当你确实有优势时，该下注多少

Ok so let's say you've done everything above. You calculated the EV. Checked the base rate. Updated your beliefs with Bayes. Accounted for survivorship bias. And you've found a genuinely good opportunity.

好，假设你把上面都做到了：你算了 EV，查了基准率，用贝叶斯更新了信念，把幸存者偏差考虑进去了，而且你真的找到了一个好机会。

How much should you bet?

那你该下注多少？

Most people have two modes: too much or too little. Either they yolo everything because they're "confident" or they put in a tiny amount because they're scared. Both are wrong and there's a formula for exactly the right amount.

大多数人只有两种模式：押太多或押太少。要么因为“自信”就梭哈（yolo），要么因为害怕只投一点点。两种都错——而且有一个公式告诉你“恰到好处”的量。

f* = (p × b - q) / b

f* = (p × b - q) / b

p = probability of winning (your honest estimate) q = probability of losing (= 1 - p) b = how much you win per dollar risked

p = 胜出的概率（你诚实的估计）
q = 输的概率（= 1 - p）
b = 每风险 1 美元，你能赢多少美元

Example. You find a bet where you think you have a 60% chance of winning. If you win, you double your money (b = 1).

例子：你找到一个赌局，你认为自己有 60% 的胜率。如果赢了，你的钱翻倍（b = 1）。

f* = (0.60 × 1 - 0.40) / 1 = 0.20

f* = (0.60 × 1 - 0.40) / 1 = 0.20

Kelly says: bet 20% of your bankroll.

凯利说：下注你本金的 20%。

But here's what 50 years of real-world application has taught us: full Kelly is way too aggressive for humans. The variance will destroy you emotionally long before the math pays off. Every professional gambler and trader I've studied uses quarter-Kelly to half-Kelly.

但过去 50 年的现实应用告诉我们：对人类来说，满凯利太激进了。方差会在数学回报兑现之前，先把你的情绪摧毁。每一个我研究过的职业赌徒和交易员，都会用四分之一凯利到二分之一凯利。

So instead of 20%, bet 5-10%. It's not as exciting. You won't get rich tomorrow. But you also won't blow up next week.

所以别下注 20%，下注 5–10%。不够刺激。你明天不会暴富。但你下周也不会爆仓。

This applies to everything btw. Not just money:

顺带说一句，这适用于一切——不只是钱：

  • Career: Don't quit your job to go all-in on a side project. Reduce to 4 days/week and spend 1 day on the project. That's ~quarter-Kelly.
  • 职业：别为了一个副业直接辞职 all-in。把工作缩到每周 4 天，用 1 天做项目。这大概就是“四分之一凯利”。
  • Learning: Don't try to learn 5 new skills at once. Pick the one with the highest EV and go deep.
  • 学习：别一次学 5 项新技能。选 EV 最高的那一个，深挖下去。
  • Relationships: Don't spread yourself thin across 20 shallow friendships. Invest deeply in 4-5 people who actually matter.
  • 关系：别把精力摊在 20 段浅层友谊上。把投资集中在真正重要的 4–5 个人身上。

The principle: when you have edge, concentrate. But not too much. Leave room to be wrong.

原则是：当你有优势时，要集中。但不要太集中。给自己留出犯错的空间。

How all 6 connect (and why prediction markets are the ultimate training ground)

这 6 个模型如何串起来（以及为什么预测市场是终极训练场）

These aren't random math tricks. They're a complete system for thinking clearly:

它们不是零散的数学小把戏，而是一整套“清晰思考系统”：

  1. EV tells you whether to act
  1. EV 告诉你要不要行动
  1. Base rates ground your estimates in reality
  1. 基准率 让你的估计贴近现实
  1. Sunk costs tell you what to ignore
  1. 沉没成本 告诉你该忽略什么
  1. Bayes tells you how to update
  1. 贝叶斯 告诉你如何更新
  1. Survivorship bias tells you what's missing from the picture
  1. 幸存者偏差 告诉你画面里缺了什么
  1. Kelly tells you how much to commit
  1. 凯利 告诉你该投入多少

Prediction markets like Polymarket are weirdly the best training ground for all 6. Every contract forces you to assign a probability. The market price shows you the crowd's probability. If you disagree — and you have a reason to — you trade. Your P&L tells you whether your thinking was right.

像 Polymarket 这样的预测市场，奇妙地成了训练这 6 点的最佳场地。每一张合约都逼你给出一个概率。市场价格展示人群的概率。如果你不同意——并且你有理由——你就交易。你的盈亏会告诉你，你的思考到底对不对。

It's like a gym for your decision-making. Except instead of reps, you're placing bets. And instead of soreness, you get a wallet balance that doesn't lie.

它像是决策能力的健身房。只不过你做的不是重复次数，而是下注；你得到的不是酸痛，而是一个不会说谎的钱包余额。

The top 1.2% of Polymarket traders I analyzed? They all think this way. Not because they read the same books — because the market beat it into them. Make a bad probability estimate, lose money, learn. Repeat 500 times. That's the curriculum.

我分析过的 Polymarket 交易者里，排名前 1.2% 的那群人？他们都用这种方式思考。不是因为他们读了同样的书——而是市场把这套思维硬生生敲进了他们的骨头里。概率估得差，就亏钱；学到教训；重复。500 次之后，这就是课程大纲。

The uncomfortable part

那个让人不舒服的部分

Here's what bugged me the most when I first learned this stuff.

我第一次学会这些东西时，最困扰我的是这一点：

I realized I have been making the WRONG decision on basically everything important in my life. Stayed in a job way too long (sunk cost). Didn't negotiate my salary because "they might say no" (loss aversion + wrong EV calculation). Followed crypto influencers because they had one big win (survivorship bias). Changed my mind too fast on some things, too slow on others (bad Bayesian updating). Spread myself across too many projects (anti-Kelly).

我意识到，在我人生里几乎所有重要的事情上，我都在做错决定。工作待太久（沉没成本）。不敢谈薪水，因为“他们可能会拒绝我”（损失厌恶 + 错误的 EV 计算）。跟随加密圈 KOL，只因为他们有过一次大胜（幸存者偏差）。有些事情改主意太快，有些事情改得太慢（糟糕的贝叶斯更新）。把自己摊在太多项目上（反凯利）。

And the worst part? I thought I was being rational the whole time. I had "reasons" for every decision. They just happened to be the wrong reasons that my brain invented to justify what my gut already decided.

最糟糕的是？我一直以为自己很理性。我对每个决定都有“理由”。只是那些理由，刚好都是大脑为了给直觉的决定找补而编出来的错误理由。

That's the trap. You don't feel irrational when you're being irrational. You feel certain. The certainty IS the bug.

这就是陷阱：当你不理性时，你并不会感觉到“不理性”。你会感觉到“确信”。这种确信本身，就是 bug。

The 6 models above don't make you perfect. Nothing does. But they give you a structured way to check your own thinking. Like a pilot going through a pre-flight checklist — not because they don't know how to fly, but because even experts miss things when they rely purely on instinct.

上面这 6 个模型不会让你完美。没有任何东西能。但它们能给你一个结构化的方法来检查自己的思考。就像飞行员在起飞前逐项检查——不是因为他们不会飞，而是因为即便是专家，在只靠直觉时也会漏掉东西。

Start using them. Start with one. Next time you face a real decision — career, money, relationship, whatever — pause for 5 minutes and run through the EV calculation. Just that one thing.

开始用它们吧。先从一个开始。下次你遇到一个真正的决定——职业、金钱、关系，随便什么——先停 5 分钟，把 EV 算一遍。只做这一件事就好。

You'll be shocked how different the answer is from what your gut tells you.

你会震惊：答案会和你的直觉告诉你的，完全不同。

Reading list (if you want to go deeper)

阅读清单（想更深入的话）

In order of how much they changed my thinking:

按它们改变我思考方式的程度排序：

  1. Thinking, Fast and Slow - Daniel Kahneman. The Bible. Covers almost everything in this article and 200 more biases you didn't know you had.
  1. Thinking, Fast and Slow - Daniel Kahneman。堪称圣经。几乎涵盖了本文的一切，还额外讲了 200 个你不知道自己有的偏差。
  1. Superforecasting - Philip Tetlock. How the world's best predictors think. Directly applicable to prediction markets.
  1. Superforecasting - Philip Tetlock。世界上最强的预测者如何思考。对预测市场直接有用。
  1. The Signal and the Noise --Nate Silver. How to find real patterns and ignore fake ones.
  1. The Signal and the Noise --Nate Silver。如何找到真实模式、忽略伪模式。
  1. Fooled by Randomness -Nassim Taleb. Why most "skill" is luck in disguise.
  1. Fooled by Randomness -Nassim Taleb。为什么大多数“技能”其实是披着外衣的运气。
  1. Fortune's Formula - William Poundstone. The wild history of Kelly criterion. Reads like a thriller.
  1. Fortune's Formula - William Poundstone。凯利准则的狂野历史。读起来像惊悚小说。
  1. Annie Duke - Thinking in Bets. Poker player turned decision consultant. Very practical.
  1. Annie Duke - Thinking in Bets. 从扑克选手到决策顾问。非常实用。

One more thing.

还有一件事。

The fact that you read to the end of an article about expected value and Bayesian updating puts you in a tiny minority. Most people scroll past anything with a formula. You didn't.

你能把一篇讲期望值和贝叶斯更新的文章读到最后，这让你属于极小的少数。大多数人看到公式就滑走了。你没有。

That is your edge. Not information - everyone has access to the same books and formulas. The edge is actually caring enough to learn this stuff and apply it.

这就是你的优势。不是信息——所有人都能接触到同样的书和公式。真正的优势，是你愿意在乎到去学、去用。

Now go make a better decision than you would have made an hour ago.

现在，去做一个比一小时前更好的决定。

Thanks for reading!

感谢阅读！

More articles about decision-making / statistics / prediction markets in my TG channel ! 🧠 https://t.me/+1R_LZ0EZuXsxOWM0

更多关于决策 / 统计 / 预测市场的文章在我的 TG 频道！🧠
https://t.me/+1R_LZ0EZuXsxOWM0

Link: http://x.com/i/article/2030259380055126016

链接：http://x.com/i/article/2030259380055126016

相关笔记

You make roughly 35,000 decisions a day.

What to eat. Whether to reply to that email now or later. Take the highway or side streets. Accept the job offer or negotiate. Hold the stock or sell.

I spent 3 months deciding whether to move to Paris by making pro/con lists in my head at 2am. Never wrote anything down. Just vibes. Moved. Hated it within a week

And for small stuff: what to have for lunch, which Netflix show to watch, vibes are fine. Who cares.

But for the decisions that actually shape your life? Career moves, investments, relationships, health? Vibes are a disaster. And I can prove it with math.

This isn't a math lecture btw. No calculus. I promise. This is about 6 mental models that changed how I think about literally everything - and once you see them you can't unsee them.

Fair warning: some of this will make you uncomfortable. You'll realize you've been making bad decisions for years. I know I did.

1. Expected Value — the one formula that runs everything

Ok so this is the big one. If you learn nothing else from this article, learn this.

Any decision you make has possible outcomes. Each outcome has a probability and a payoff. Multiply them together, add them up, and you get the expected value.

That's it. That's the formula. I started thinking about this after I endless rekt opportunities in crypto space over last 5 years of my experience.

Your friend offers you a bet. Flip a coin. Heads, he pays you $150. Tails, you pay him $100.

Most people hesitate. "I could lose $100!" And yeah, you could. But run the math:

EV = (50% × $150) + (50% × -$100) = $75 - $50 = +$25

Every time you take this bet, you make $25 on average. If someone offered you this 100 times you'd be insane to say no. You'd make roughly $2,500.

But here's the weird thing - in studies, most people reject this bet. Even when the math screams YES. Because humans feel losses about 2x more than equivalent gains. Losing $100 hurts way more than winning $150 feels good. Psychologists call this loss aversion and it screws up almost every decision you make.

Real world example. Your boss offers you two paths:

Option A: Stay in your current role. Guaranteed $120K salary. Option B: Take a riskier role at a startup (just an example). 60% chance it works and you make $250K in 2 years (equity + salary). 40% chance it fails and you make $70K for the same period.

Most people pick A. Feels safe. Let's check:

EV of A = $120K (guaranteed) EV of B = (0.60 × $350K) + (0.40 × $70K) = $150K + $28K = $178K

Option B is worth $58K more. But 40% chance of "only" $70K feels terrifying so people don't take it.

I'm not saying blindly chase every positive EV opportunity. Variance matters. If losing the bet means you can't pay rent, don't take it even if EV is positive. But at least KNOW the EV before you decide. Most people don't even calculate it. They just go with their gut and wonder why they're stuck.

2. Base Rate Neglect — the reason you're wrong more than you think

This one is sneaky because it feels so counterintuitive.

Let's say there's a disease that affects 1 in 1,000 people. You take a test that's 99% accurate. It comes back positive.

What's the probability you actually have the disease?

If you said 99%... you're wrong. And you're in good company — most doctors get this wrong too.

Let's think about it. Out of 1,000 people:

  • 1 actually has the disease. The test catches them (99% accurate). That's 1 true positive.

  • 999 don't have it. But the test has a 1% false positive rate. That's ~10 false positives.

So there are 11 positive results total. Only 1 is real.

Not 99%. Nine percent. The base rate (1 in 1,000) matters enormously, and people ignore it every single time.

How this ruins real decisions:

  • "My startup idea is great - look at how well Uber did!" Base rate of startup success: ~6%. Base rate of becoming a unicorn: 0.00006%. I have been trying to do my own startups since 2017. Most of my friends had as well (whose parents were way richer). Thought I was the exception. I wasn't.

  • "This investment returned 40% last year, I should buy more." Base rate of any fund beating the market 3 years in a row: ~15%. Last year's performance tells you almost nothing about next year.

  • "This guy on Twitter predicted the crash, he must be a genius." Base rate: if 10,000 people make random predictions, ~100 will nail it perfectly. They are not geniuses. They're survivors of a large sample.

Whenever someone tells you about a specific success story, ask yourself: what's the base rate? How often does this type of thing actually work? If the answer is "rarely" — be very skeptical, no matter how convincing the story sounds.

3. Sunk Cost Fallacy — throwing good money after bad (and not just money)

You bought a movie ticket for $15. Thirty minutes in, the movie is terrible.

Do you leave or stay?

Economically, the answer is obvious: leave. The $15 is gone either way- staying doesn't get it back. The only question is: "Will the next 90 minutes be better spent watching this bad movie or doing literally anything else?"

But almost everyone stays. "I already paid for it."

That's the sunk cost fallacy. And it wrecks people's lives in ways far worse than bad movies.

  • Staying in a dead-end job for 3 more years because "I already invested 5 years here." Those 5 years are gone. The only question is: what's the best use of the NEXT 3?

  • Holding a losing stock or any altcoin / memecoin because "Already down 50%, I can't sell now." The stock doesn't know your entry. The market doesn't care what you paid. The only question is: if you had cash right now, would you buy this stock at today's price?

  • Staying in a relationship because "we've been together for 6 years." Those 6 years happened. The only question is whether the NEXT 6 will be good.

The fix is aggressively simple: when making any decision, pretend you're starting from scratch right now. Ignore everything you've already spent - time, money, emotion. Only look forward. Would you choose this path today, knowing what you know?

If the answer is no, get out. The past is not coming back regardless.

4. Bayesian Thinking — how to update your beliefs like a scientist (not a politician)

Most people form an opinion and then defend it forever. New evidence comes in? Doesn't matter - they already decided.

This is the opposite of how you should think.

Bayes' theorem gives you the mathematically correct way to change your mind:

Looks scary. It's not. Let me translate it to English:

Your updated belief = how well the evidence fits your theory × how likely your theory was before ÷ how common the evidence is in general.

Example. You think your coworker is going to quit. Before any evidence, you'd say there's a 10% chance (most people don't quit in any given month). That's your prior.

Then you notice she updated her LinkedIn profile. Hm.

  • If she IS about to quit, what's the probability she'd update LinkedIn? Pretty high — say 70%.

  • If she's NOT about to quit, what's the probability she'd update LinkedIn? People do it randomly all the time — say 15%.

P(quitting | LinkedIn update) = (0.70 × 0.10) / ((0.70 × 0.10) + (0.15 × 0.90)) = 0.07 / (0.07 + 0.135) = 0.07 / 0.205 ≈ 34%

One piece of evidence moved you from 10% to 34%. Not to 90% -that would be overreacting. Not staying at 10% - that would be ignoring evidence. 34% is the mathematically rational update.

Now she also starts taking calls outside the office. Another update. Maybe goes to 55%. She's suddenly vague about long-term projects. 70%.

Each piece of evidence nudges the probability. Gradually. Proportionally. No drama. No sudden flipping between "definitely yes" and "definitely no."

This is how prediction markets work btw. The price of a contract IS the Bayesian posterior- constantly updating as new information flows in. That's why Polymarket predicted the Iran strikes before CNN. Thousands of people feeding tiny pieces of evidence into a price. Each one nudging it 0.5% this way or 2% that way. The aggregate is spookily accurate.

The takeaway: hold opinions loosely. Update them constantly. The strength of your update should be proportional to the strength of the evidence. Most people either ignore evidence entirely or overcorrect wildly. Both are wrong.

5. Survivorship Bias — you're only seeing the winners

You read about a college dropout who built a billion-dollar company. Inspiring, right? Maybe college is a waste of time?

Except you never hear about the 10,000 other dropouts who are broke. They don't get magazine covers. They don't get podcast interviews. They just quietly struggle while one survivor gets all the attention.

This is survivorship bias. You only see the winners, so you massively overestimate the probability of winning.

It's everywhere:

  • Crypto Twitter. Everyone posting gains. Nobody posting losses. The guy who turned $500 into $50K gets 200K likes. The 500 guys who turned $500 into $0 deleted their accounts. Your feed makes it look like everyone's winning. They're not. 87% of Polymarket wallets lose money. You just never see them post about it.

  • Restaurant advice. "Just follow your passion and open a restaurant!" 60% of restaurants close within the first year. 80% close within five. The ones that survive become your favorite spots. The dead ones are invisible. Following your passion is great advice if you ignore the graveyard.

  • Music industry. "Just upload to Spotify and go viral!" 90,000 tracks are uploaded to Spotify every single day. The median track gets 30 plays total. You hear about the ones that go viral because... they went viral. The other 89,990 are silence.

The fix: whenever someone shows you a success story as proof that something works, look for the denominator. How many people tried this? What percentage succeeded? If you can't find the denominator, assume the success rate is very low. Because the world only shows you numerators.

6. The Kelly Criterion — how much to bet when you DO have an edge

Ok so let's say you've done everything above. You calculated the EV. Checked the base rate. Updated your beliefs with Bayes. Accounted for survivorship bias. And you've found a genuinely good opportunity.

How much should you bet?

Most people have two modes: too much or too little. Either they yolo everything because they're "confident" or they put in a tiny amount because they're scared. Both are wrong and there's a formula for exactly the right amount.

f* = (p × b - q) / b

p = probability of winning (your honest estimate) q = probability of losing (= 1 - p) b = how much you win per dollar risked

Example. You find a bet where you think you have a 60% chance of winning. If you win, you double your money (b = 1).

f* = (0.60 × 1 - 0.40) / 1 = 0.20

Kelly says: bet 20% of your bankroll.

But here's what 50 years of real-world application has taught us: full Kelly is way too aggressive for humans. The variance will destroy you emotionally long before the math pays off. Every professional gambler and trader I've studied uses quarter-Kelly to half-Kelly.

So instead of 20%, bet 5-10%. It's not as exciting. You won't get rich tomorrow. But you also won't blow up next week.

This applies to everything btw. Not just money:

  • Career: Don't quit your job to go all-in on a side project. Reduce to 4 days/week and spend 1 day on the project. That's ~quarter-Kelly.

  • Learning: Don't try to learn 5 new skills at once. Pick the one with the highest EV and go deep.

  • Relationships: Don't spread yourself thin across 20 shallow friendships. Invest deeply in 4-5 people who actually matter.

The principle: when you have edge, concentrate. But not too much. Leave room to be wrong.

How all 6 connect (and why prediction markets are the ultimate training ground)

These aren't random math tricks. They're a complete system for thinking clearly:

  1. EV tells you whether to act

  2. Base rates ground your estimates in reality

  3. Sunk costs tell you what to ignore

  4. Bayes tells you how to update

  5. Survivorship bias tells you what's missing from the picture

  6. Kelly tells you how much to commit

Prediction markets like Polymarket are weirdly the best training ground for all 6. Every contract forces you to assign a probability. The market price shows you the crowd's probability. If you disagree — and you have a reason to — you trade. Your P&L tells you whether your thinking was right.

It's like a gym for your decision-making. Except instead of reps, you're placing bets. And instead of soreness, you get a wallet balance that doesn't lie.

The top 1.2% of Polymarket traders I analyzed? They all think this way. Not because they read the same books — because the market beat it into them. Make a bad probability estimate, lose money, learn. Repeat 500 times. That's the curriculum.

The uncomfortable part

Here's what bugged me the most when I first learned this stuff.

I realized I have been making the WRONG decision on basically everything important in my life. Stayed in a job way too long (sunk cost). Didn't negotiate my salary because "they might say no" (loss aversion + wrong EV calculation). Followed crypto influencers because they had one big win (survivorship bias). Changed my mind too fast on some things, too slow on others (bad Bayesian updating). Spread myself across too many projects (anti-Kelly).

And the worst part? I thought I was being rational the whole time. I had "reasons" for every decision. They just happened to be the wrong reasons that my brain invented to justify what my gut already decided.

That's the trap. You don't feel irrational when you're being irrational. You feel certain. The certainty IS the bug.

The 6 models above don't make you perfect. Nothing does. But they give you a structured way to check your own thinking. Like a pilot going through a pre-flight checklist — not because they don't know how to fly, but because even experts miss things when they rely purely on instinct.

Start using them. Start with one. Next time you face a real decision — career, money, relationship, whatever — pause for 5 minutes and run through the EV calculation. Just that one thing.

You'll be shocked how different the answer is from what your gut tells you.

Reading list (if you want to go deeper)

In order of how much they changed my thinking:

  1. Thinking, Fast and Slow - Daniel Kahneman. The Bible. Covers almost everything in this article and 200 more biases you didn't know you had.

  2. Superforecasting - Philip Tetlock. How the world's best predictors think. Directly applicable to prediction markets.

  3. The Signal and the Noise --Nate Silver. How to find real patterns and ignore fake ones.

  4. Fooled by Randomness -Nassim Taleb. Why most "skill" is luck in disguise.

  5. Fortune's Formula - William Poundstone. The wild history of Kelly criterion. Reads like a thriller.

  6. Annie Duke - Thinking in Bets. Poker player turned decision consultant. Very practical.

One more thing.

The fact that you read to the end of an article about expected value and Bayesian updating puts you in a tiny minority. Most people scroll past anything with a formula. You didn't.

That is your edge. Not information - everyone has access to the same books and formulas. The edge is actually caring enough to learn this stuff and apply it.

Now go make a better decision than you would have made an hour ago.

Thanks for reading!

More articles about decision-making / statistics / prediction markets in my TG channel ! 🧠 https://t.me/+1R_LZ0EZuXsxOWM0

Link: http://x.com/i/article/2030259380055126016

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