The hottest Probability Substack posts right now

And their main takeaways
Category
Top Education Topics

Against Learning From Dramatic Events

Astral Codex Ten • 19340 implied HN points • 16 Jan 24
🚌 Education Probability
  1. Updating beliefs based on single dramatic events may not be very impactful in the long run.
  2. Predictions can be more valuable than reacting strongly to individual events.
  3. Coordination and response to dramatic events are important, but fundamental beliefs should not change drastically.

Domain Transformations: The Art of Finding Easier Spaces

Software Bits Newsletter • 103 implied HN points • 05 Jan 26
🕹 Technology Probability
  1. Transform hard problems into easier ones by moving to a different domain, doing the simpler computation there, and (if needed) transforming the result back; this is worth it when the transform cost plus the easier computation is less than solving the original problem.
  2. Use well-known transforms to fix numerical and computational issues: log-space turns tiny-product underflow into stable sums (use the log-sum-exp trick to add probabilities safely), Fourier turns convolution into cheap pointwise multiplication, and embeddings or kernels lift data so linear methods work.
  3. Always check that a transform preserves what you need and that the round-trip cost is justified; the best algorithms exploit problem structure by finding the space where the computation becomes simple.

All Bayes Everything

Holodoxa • 239 implied HN points • 14 Jun 24
🔬 Science Probability
  1. Bayes' Theorem is a powerful concept in probability theory that helps update beliefs based on new evidence, highlighting the importance of combining prior knowledge and new data.
  2. Bayesian methods can offer valuable improvements to scientific research practices by emphasizing uncertainty, effect magnitude, and probability distributions over traditional p-values and null hypothesis testing.
  3. The concept of the brain functioning as a prediction machine aligns with Bayesian principles, suggesting that the brain uses prior knowledge and new sensory inputs to make predictions and construct conscious experiences.

Going for Broke

The Better Letter • 275 implied HN points • 06 Oct 23
💰 Finance Probability
  1. In a coin-flipping experiment, even financially savvy individuals struggled with optimal betting strategies.
  2. The world is far more random than we realize, affecting markets and investments unpredictably.
  3. Probabilistic strategies can help in decision-making, especially when human biases lead to suboptimal choices.
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Law of Large Numbers and the Gamblers Fallacy[Math Mondays]

Technology Made Simple • 179 implied HN points • 11 Sep 23
🚌 Education Probability
  1. The Law of Large Numbers states that as the number of trials increase, the average of results will get closer to the expected value.
  2. This law is crucial in scientific fields, allowing predictions on chaotic events, leading to industries like gambling and insurance.
  3. Misunderstanding the Law of Large Numbers can lead to the Gambler's Fallacy, as it deals with the convergence of infinitely many experiments, not individual ones.

Math Problems

The Better Letter • 157 implied HN points • 17 Mar 23
🔬 Science Probability
  1. Unlikely events happen more often than we realize, influencing outcomes in sports, investments, and life.
  2. Probability plays a significant role in determining outcomes, such as in coin tosses, NCAA brackets, and market predictions.
  3. Randomness, noise, and unpredictability are intrinsic to life, affecting decision-making and the way we perceive events.

There are Complex-Number One-Norm Square-Root of Probability Amplitudes of 0.006 in Which Sam Bankman-Fried Is Happy

Brad DeLong's Grasping Reality • 676 implied HN points • 05 Oct 23
💰 Finance Probability
  1. Amplitudes in quantum-mechanical superposition relate to philosophy-of-probability vs. psychology.
  2. Understanding the Kelly Criterion for betting based on win-loss odds and maximizing returns.
  3. Traders use the Kelly Criterion for survival, making positive-value bets, and psychological factors.

Yet Another Ball and Urn Problem

Metarational • 59 implied HN points • 13 Feb 24
🔬 Science Probability
  1. The problem involves repeatedly selecting balls from an urn, inspecting their color, putting them back, and adding another of the same color. The goal is to find the probability that the majority of balls in the urn will be white after a large number of repetitions.
  2. To solve the problem, it was analyzed that there must be at least half white draws to achieve a white majority. Calculations led to a final result of 11/16 as the probability limit.
  3. The solution involved understanding the probabilities of different color sequences and using Riemann sums to simplify and find the answer, showcasing an intricate application of mathematics to a probability riddle.

Tanks for the memories

Logging the World • 179 implied HN points • 11 Dec 22
🔬 Science Probability
  1. In a raffle with a large number of tickets, the biggest number drawn out starts to show some structure as more tickets are selected.
  2. By looking at the maximum value drawn in a raffle, one can estimate the total number of tickets, a concept applied in statistics like the German tank problem.
  3. Sequential numbering schemes can reveal interesting insights, as seen in situations like the Skripal poisonings and Novak Djokovic's COVID test, highlighting the importance of careful numbering practices.

Log Odds or Probability

Mindful Modeler • 139 implied HN points • 25 Apr 23
🔬 Science Probability
  1. Log odds are additive, probabilities are multiplicative. Some interpretation methods like expressing predictions as a linear sum may benefit from log odds.
  2. Edge transitions, like from 0.001 to 0.01, may sometimes be more significant than middle transitions, like 0.5 to 0.6.
  3. Probabilities offer intuitive understanding for decision-making, cost calculations, and are more commonly familiar compared to log odds.

The Monty Hall problem: The golden goat variation

Simplicity is SOTA • 131 implied HN points • 03 Feb 25
🔬 Science Probability
  1. The Monty Hall problem has a new twist, focusing on a valuable goat instead of a car. In this version, knowing which goat is valuable affects your choice.
  2. Using Bayes' theorem can help calculate the probabilities in this variation. After a goat is revealed, you can reassess your chances to make a better decision.
  3. The essential lesson is to update your beliefs with new information. Recognizing how new clues impact your choices is key to making smarter decisions.

A model of models of probability

Bram’s Thoughts • 78 implied HN points • 23 Nov 23
🔬 Science Probability
  1. People generally have a simplified internal model of probability with five main categories.
  2. People tend to struggle with accurately gauging differences in expected values within the 40-60% range.
  3. Individuals often display overconfidence in their predictions for probable events and can become overly upset when these predictions fail.

Understanding Different Uncertainty Mindsets

Mindful Modeler • 179 implied HN points • 24 Jan 23
🔬 Science Probability
  1. Understanding the fundamental difference between Bayesian and frequentist interpretations of probability is crucial for grasping uncertainty quantification techniques.
  2. Conformal prediction offers prediction regions with a frequentist interpretation, similar to confidence intervals in linear regression models.
  3. Conformal prediction shares similarities with the evaluation requirements and mindset of supervised machine learning, emphasizing the importance of separate calibration and ground truth data.

What is Bayesian Statistics? The Beginner Math Guide (Part One)

The Software & Data Spectrum • 78 implied HN points • 13 Apr 23
🔬 Science Probability
  1. Bayesian Statistics is used in various fields like Machine Learning, Engineering, Data Science, and more.
  2. Bayesian Thinking involves observing data, holding prior beliefs, forming hypotheses, gathering evidence, and comparing hypotheses.
  3. Probability is a way to measure belief strength, and calculating probabilities involves counting outcomes and using ratios of beliefs.

If You Want to Hit Your Target, Take More Shots

The Palindrome • 6 implied HN points • 18 Dec 25
📖 Philosophy Probability
  1. If you want to hit your target, take more shots — more attempts raise your chance of success.
  2. Trying lots of ideas across different areas (projects, posts, dating, work) leads to more wins because each attempt gives feedback you can learn from and improve.
  3. Unlikely successes become likely with enough trials, so don’t be discouraged by early failures — persistence and volume pay off.

Chutes, ladders, and Markov chains

A Piece of the Pi: mathematics explained • 72 implied HN points • 04 Dec 24
🚌 Education Probability
  1. The game of Chutes and Ladders is a fun example of a Markov chain. It shows how the next move depends only on where you are now, not on how you got there.
  2. There are different types of game boards, some allow for winning while others can trap players forever. Ultimately winnable boards guarantee that a player can reach the end if they keep playing.
  3. On average, players need about 39 spins to win the game, and surprisingly, most random boards created will still offer a winning chance.

How I once won the lottery

inexactscience • 19 implied HN points • 06 Sep 23
🚌 Education Probability
  1. Sticking to one choice in a lottery doesn't change your odds, which stay at 1 in 24 no matter what. It seems like it should matter, but it really doesn't.
  2. If a lottery is unfair and avoids streaks, choosing the same number can actually be a better strategy because it decreases your risk of never winning.
  3. Many people fall for the gambler's fallacy, thinking just because a number hasn't won in a while, it should win soon. But in a fair lottery, each draw is independent and has the same odds.

The most important assumption in statistics- IID [Math Mondays]

Technology Made Simple • 39 implied HN points • 01 Aug 22
🔬 Science Probability
  1. The most important assumption in statistics is IID, which stands for Independently and Identically Distributed
  2. IID assumption is crucial for statistical analysis - it helps in making accurate deductions and avoiding mistakes, like the gambler's fallacy
  3. Understanding IID involves recognizing independent and identical distributions in data samples, which are essential for various statistical techniques

My Talk About the Sleeping Beauty Paradox

By Reason Alone • 16 implied HN points • 07 Nov 24
📖 Philosophy Probability
  1. The Sleeping Beauty paradox involves a coin flip that affects how often she wakes up, which raises questions about probability. People have different opinions on how she should assess the chance of heads when she wakes up.
  2. One group, called 'halfers', believes the chance of heads remains 50/50 since she doesn't gain new information about the coin when waking up.
  3. Another group, 'thirders', argues she should think there's a one in three chance it's heads because of how many times she might wake up, depending on the coin flip.

Probability Distributions 101

Olshansky's Newsletter • 68 implied HN points • 20 Feb 23
🔬 Science Probability
  1. Probability is about the likelihood of events happening.
  2. Probability distributions are functions describing random events over a sample space.
  3. Key concepts include random variables, probability mass function, probability density function, cumulative distribution function, Gaussian distribution, and Bernoulli distribution.

The Science of Science

The Palindrome • 3 implied HN points • 30 Jul 25
🔬 Science Probability
  1. Thinking in terms of probabilities helps us make better judgments when we are not certain. Unlike absolute truths, we can measure how likely something is to be true instead.
  2. Bayes' theorem allows us to update our beliefs based on new evidence. This means we can make smarter decisions by adjusting our understanding as we gather more information.
  3. To figure out causes from effects, we can use conditional probabilities. This helps us connect symptoms, like a headache and sore throat, to possible underlying issues, like the flu, in a more accurate way.

Your Brain is Wrong About Probability

The Palindrome • 2 implied HN points • 01 Jul 25
🔬 Science Probability
  1. Our brains often misunderstand probability, leading us to make poor decisions. We think past events can change future outcomes, but each event is independent.
  2. In games like poker, winning one hand might be luck, but winning consistently is about skill and understanding the odds.
  3. Chasing losses, like believing you're 'due' for a win after losing, can lead to financial problems. It's important to recognize that bad luck doesn't influence future chances.

Siêu trí tuệ: tìm số nguyên tố hay là tăng minh bạch cho ngành đánh đề

Thái | Hacker | Kỹ sư tin tặc • 39 implied HN points • 27 Dec 19
🔬 Science Probability
  1. When faced with challenges involving prime numbers, clever algorithms can help quickly eliminate composite numbers and pinpoint the secret numbers.
  2. The difficulty of a problem depends on the randomness of number selection within a matrix and the position of prime numbers.
  3. Designing a fair random number generation system is crucial for ensuring transparency, not only in intellectual competitions but also in traditional gambling industries.