The Drunkard's Walk

• The right hemisphere of the brain is more tied to primitive instinct, while the left is more tied to reason.
• To improve your odds of beating randomness, rely on repetition.
• Availability bias: when we base a decision on our most vivid memories (they are more "available" to us). What we've lived through most doesn't necessarily reflect reality.
• Law of combined probabilities: if event A and event B are independent (NO relation between them), the probability of both happening is the product A*B. For the probability of A or B, we add A + B.
• Girolamo Cardano was one of the fathers of probability theory.
• Cardano's rule: in a random process, the probability of something happening is its share of all the possible outcomes. All those outcomes together are called the sample space.
• Short-term results are extremely unreliable as proof of skill.
• Any artificial device is bound to be biased (like a die), because humans have no access to perfection.
• "Complete chaos is, ironically, a kind of perfection".
• Law of large numbers (Bernoulli's theorem): results reflect the underlying probabilities when run at large scale.
• Law of small numbers: a small sample probably doesn't reflect the underlying probabilities.
• We shouldn't judge people's actions by the outcome but by their skill (fundamental analysis).
• An event is NOT more or less likely to happen because it happened recently.
• The chance that several events happen because they come from one cause is different from the chance that something happens because it comes from several events (conspiracy theories).
• According to Bayes, the probability of A given B is usually different from the probability of B given A.
• Measurements always carry uncertainty.
• A standard-deviation normal curve (the normal distribution, the law of errors) is a signature of a random process.
• Much of the order we find in nature hides an underlying disorder.
• Humans can't intuitively grasp randomness.
• In real life we have a certain illusion of control, but chance decides much more than we realise.
• Confirmation bias: we always try to prove our ideas right, never wrong.
• Preconceptions can make us believe a pattern isn't random, even when it is.
• We should give more weight to our impression of someone than to their results.
• We underestimate the role of chance in the lives of the successful and the unsuccessful alike.

First law of probability: the probability that two events both occur can never be greater than the probability that each event occurs on its own.