# 賭徒謬誤

## 數學背景

• ${\displaystyle P(A)}$  做「${\displaystyle A}$  發生嘅或然率」
• ${\displaystyle P(B)}$  做「${\displaystyle B}$  發生嘅或然率」

${\displaystyle P(A\mid B)=P(A)}$
${\displaystyle P(B\mid A)=P(B)}$

—已知 ${\displaystyle B}$  發生咗，${\displaystyle A}$  發生嘅或然率依然係 ${\displaystyle P(A)}$  咁多，而且將兩件事件位置掉轉，上述講嘅嘢依然成立[2]。如果事件嘅數量超過兩件—有 ${\displaystyle n}$  咁多件事件，而 ${\displaystyle n>2}$  —都可以用同一道理想像：如果喺嗰 ${\displaystyle n}$  件事件入邊是但抽兩件出嚟，佢哋彼此之間都係獨立嘅，噉呢 ${\displaystyle n}$  件事件之間就算係彼此獨立[3]

• 10,000 次「之前連續十次出紅」嘅情況，同埋
• 10,000 次「之前五次紅五次黑」嘅情況，

## 註解

1. 可以睇睇大數定律嘅概念。

## 參考

• 賭徒謬誤：gambler's fallacy
• 蒙地卡羅謬誤：Monte Carlo fallacy
• 機率成熟謬誤：fallacy of the maturity of chances
• 或然率論：probability theory
• 統計獨立：statistically independent
• 蒙地卡羅賭場：Casino de Monte-Carlo

• Barron, G., & Leider, S. (2010). The role of experience in the Gambler's Fallacy (PDF). Journal of Behavioral Decision Making, 23(1), 117-129，講到過去經驗「點樣呈現」可以影響一個人對機率嘅判斷。將過往紀錄一次過展示出嚟嘅話，似乎能夠減低賭徒謬誤出現嘅機率（相對畀受試者親身體驗啲事件）。
• Goodie, A. S., & Fortune, E. E. (2013). Measuring cognitive distortions in pathological gambling: review and meta-analyses. Psychology of addictive behaviors, 27(3), 730，佢哋做咗元分析，講到爛賭嘅人特別傾向會有賭徒謬誤等嘅心態。
• Hon-Snir, S., Kudryavtsev, A., & Cohen, G. (2012). Stock market investors: Who is more rational, and who relies on intuition. International Journal of Economics and Finance, 4(5), 56-72，呢篇文討論啲人投資嗰陣好多時都會持有賭徒謬誤噉嘅心態，經驗老到啲嘅投資者被指係冇咁易喺判斷上出現偏差。

1. Russell, Stuart; Norvig, Peter (2002). Artificial Intelligence: A Modern Approach. Prentice Hall. p. 478.
2. Dawid, A. P. (1979). "Conditional Independence in Statistical Theory". Journal of the Royal Statistical Society, Series B. 41 (1): 1-31.
3. Feller, W (1971). "Stochastic Independence". An Introduction to Probability Theory and Its Applications. Wiley.
4. The Gambler's Fallacy: On the Danger of Misunderstanding Simple Probabilities (PDF), University of Wisconsin.
5. Clotfelter, C. T., & Cook, P. J. (1993). The "gambler's fallacy" in lottery play. Management Science, 39(12), 1521-1525，第一頁就有講賭徒謬誤係乜。
6. Hon-Snir, S., Kudryavtsev, A., & Cohen, G. (2012). Stock market investors: Who is more rational, and who relies on intuition. International Journal of Economics and Finance, 4(5), 56-72, 2.4 Gambler's Fallacy, 2.5 Hot Hand Fallacy.
7. Owen, A. M. (2011). The Monte Carlo fallacy. Medical Journal of Australia, 195(7), 421-421.