Book: The Perfect Bet
Author: Adam Kucharski
- Cardano was one of the first to understand that games of chance could be analyzed mathematically (“Cardamon’s formula” is known for calculating the correct odds in repeated games). He realized that navigating the world of chance meant understanding where its boundaries lay (what I think of as “corner cases”).
- Bernoulli solve the wager problem (why people prefer low-risk bets vs. theoretically more profitable bets) by thinking in terms of “expected utility” vs. the expected payoff (e.g. a single coin is more valuable to a person who is poor vs. someone who is rich). I also think of this in terms of the risks the money managers are willing to take (if I get only limited monetary/reputation benefit from making a higher-risk call vs. being remembered who lost money on an obvious risky bet, I would always take low-risk bets).
- Limitations of Kelly Criterion:
- First of all, it assume you know the true probabilities of the event
- Syndicates often bet 1/2 or 1/3 of the number Kelly Criterion would have one bet, to avoid having a “rough ride” and losing a large chunk of their wealth
- Researchers found that when the feeling of regret was missing from patients’ decision-making process, they struggled to master games involving an element of risk.
- During a game of repeated rock-paper-scissors, students adopted what can be called “win-stay lose-shift” strategy (if they had won a round, they’d stick with the same action, whereas losers would switch to the option they just lost to). This is an example where the strategy is outcome-focused vs. process-driven.
- Great Wall of China was financed with profits from a lottery run by the Han dynasty, a 1753 lottery funded the British Museum, and many of the Ivy League universities were built from takings from lotteries arranged by colonial governments.