The Drunkard's Walk Summary

The Chapter Five in "The Drunkard's Walk" is "The Dueling Laws of Large and Small Numbers". At first, it discusses the problem about what is the connection between probability and observed results, however, true randomness does occur in nature. To learn more about the randomness, people found that nature's perfect quantum dice. According to Benford's law, numbers cumulative biased towards lower digits. This law can be used to identify fraud in dollar amounts. Then, the writer introduces two definitions of randomness, one is Frequency interpretation: a number is random if comes up in frequency one way or another with expected frequency (judge sample by the way it turned out); another is Subjective interpretation: number coming up can be predicted (judge sample by way it was produced). Dice throwing in the real
world is random from subjective interpretation but not from frequency, and dice throwing in perfect knowledge and throwing world is random in frequency but not in subjective since could predict it. Moshe pointed out that complete chaos is a kind of perfection.
Next, Jagger beating Monte Carlo casino by tracking bias of roulette wheel for favored numbers. After that, it points out that the invention of calculus required to know what observations expected for certain probabilities. Then, the writer describes how Bernoulli made contributes to the calculus, and the Principia by Newton and Leibniz. The Sequence, Series, Limit, Xeno's paradox, 1 meter is limit of series, and the Weak law of large numbers was been found. In the end, it says that Bernoulli binary outcome process, which must specify an underlying tolerance for error in measured probability (accuracy) and specify confidence level required, he was trying to know how many observations needed to see expected probability within some tolerance. Bernoulli formula will give the number of trials necessary, however, the mistaken intuition that a small sample reflects underlying probabilities, which is the law of small numbers misguided. On the other hand, more reliable to judge ppl by abilities than by glancing at the scoreboard. Finally, the writer states the Gamblers fallacy which is luck won't catch
up.

In this chapter, the most interesting for me is that the real danger is making assumptions based on a small number of events. For example, if a teenage boy decides that it’s safe to jump out of a third story window because he didn’t break a bone the first time he did it, that’s a mistake. Similarly, to decide that the world is out to “get” you because you didn’t get the first job you applied for is a similar mistake on the other end. Unless there are significant drawbacks to repetition (like the potential for seriously hurting yourself), you’re better off trying things multiple times.