Hacker News with Generative AI: Probability

Dice, (De)Convolution and Generating Functions (demofox.org)
I stumbled across a very cool YouTube video today that talks about how to look for alternate ways of labeling sides of two dice to give you the same random number distribution as if you added two standard dice together.

Mathematics, Probability, Dice, Games, YouTube

4 points by zdw 12 days ago | 0 comments

Formally Modeling Dreidel, the Sequel (buttondown.com)
Channukah's next week and that means my favorite pastime, complaining about how Dreidel is a bad game. Last year I formally modeled it in PRISM to prove the game's not fun. But because I limited the model to only a small case, I couldn't prove the game was truly bad.

Games, Probability, Hanukkah, Mathematics

100 points by todsacerdoti 31 days ago | 26 comments

Why probability probably doesn't exist (but it is useful to act like it does) (nature.com)
All of statistics and much of science depends on probability — an astonishing achievement, considering no one’s really sure what it is.

Philosophy, Science, Probability, Statistics

12 points by orcul 31 days ago | 2 comments

The Birthday Paradox Experiment (2018) (pudding.cool)
The chance that two people in the same room have the same birthday — that is the Birthday Paradox 🎉. And according to fancy math, there is a 50.7% chance when there are just 23 people+This is in a hypothetical world. In reality, people aren’t born evenly throughout the year, and leap years are excluded. However, the numbers should still be pretty close. More on this in the appendix. in a room.

Mathematics, Probability, Statistics, Experiments

75 points by thunderbong 57 days ago | 70 comments

Coincidences that make our existence possible (bigthink.com)
There are a few small cosmic details that, if things were just a little different, wouldn’t have allowed our existence to be possible.

Cosmology, Existence, Science, Probability

33 points by Brajeshwar 61 days ago | 47 comments

A boy girl paradox – or maybe not? (shankwiler.com)
The most liked comment answers 1/2, but the user got worn down by others until he recanted and agreed that the answer is 1/3. Many other comments give lengthy explanations as to why the answer is 1/3.

Probability, Math, Puzzles, Logic

12 points by iuvcaw 62 days ago | 0 comments

An alternative construction of Shannon entropy (rkp.science)
TL;DR: Shannon’s entropy formula is usually justified by showing it satisfies key mathematical criteria, or by computing how much space is needed to encode a variable. But one can also construct Shannon’s formula starting purely from the simpler notion of entropy as a (logarithm of a) count—of how many different ways a distribution could have emerged from a sequence of samples.

Information Theory, Mathematics, Statistics, Probability

126 points by rkp8000 66 days ago | 11 comments

Adventures in Probability (buttondown.com)
I hope everyone had a good weekend. I went on a hike. It was great.

Probability, Personal Experiences

164 points by kiyanwang 75 days ago | 39 comments

Universe would die before monkey with keyboard writes Shakespeare, study finds (theguardian.com)
Mathematicians have called into question the old adage that a monkey typing randomly at a keyboard for long enough would eventually produce the complete works of Shakespeare.

Mathematics, Probability, Language Models, Literature

83 points by hackernj 78 days ago | 158 comments

Monkeys Will Never Type Shakespeare (bbc.co.uk)
Two Australian mathematicians have called into question an old adage, that if given an infinite amount of time, a monkey pressing keys on a typewriter would eventually write the complete works of William Shakespeare.

Mathematics, Probability, Literature, Shakespeare

8 points by zabzonk 78 days ago | 2 comments

Probability-generating functions (entropicthoughts.com)
I have long struggled with understanding what probability-generating functions are and how to intuit them. There were two pieces of the puzzle missing for me, and we’ll go through both in this article.

Probability, Math, Statistics, Data Science

207 points by todsacerdoti 79 days ago | 48 comments

Understanding Gaussians (gestalt.ink)
The Gaussian distribution, or normal distribution is a key subject in statistics, machine learning, physics, and pretty much any other field that deals with data and probability. It’s one of those subjects, like $\pi$ or Bayes’ rule, that is so fundamental that people treat it like an icon.

Statistics, Machine Learning, Data Science, Probability

152 points by lapnect 88 days ago | 34 comments

Deriving the Kelly Criterion to Maximise Profits (obrhubr.org)
In a fictional casino which offers even odds on a fair coin toss game, how much of your money should you invest? If you said anything other than 0, you’re leaving broke at the end of the night.

Finance, Gambling, Probability, Mathematics

50 points by obrhubr 97 days ago | 34 comments

Jane Street Probability Guide [pdf] (janestreet.com)

Probability, Finance, Employment, PDFs, Jane Street

41 points by paulpauper 100 days ago | 6 comments

Mega Millions tickets will climb to $5, but officials promise better odds (apnews.com)
The cost of buying a Mega Millions jackpot dream will soon more than double, but lottery officials said they’re confident players won’t mind paying more after changes that will lead to larger prizes and more frequent winners.

Lottery, Gambling, Finance, Probability

5 points by geox 102 days ago | 3 comments

St. Petersburg Paradox (wikipedia.org)
The St. Petersburg paradox or St. Petersburg lottery[1] is a paradox involving the game of flipping a coin where the expected payoff of the lottery game is infinite but nevertheless seems to be worth only a very small amount to the participants.

Probability, Game Theory, Economics, Paradoxes

3 points by tazu 123 days ago | 0 comments

Randomness extractors: making fair coins out of biased coins (bytepawn.com)
In a previous post titled Fair coin from biased coin, I looked at the problem of creating a uniform random coin given access to a biased coin. I looked at multiple approaches, and determined that they're actually all the same in some sense.

Cryptography, Probability, Randomness, Algorithms

105 points by Maro 125 days ago | 52 comments

Lottery Simulator (2023) (perthirtysix.com)
Every so often, a lottery jackpot will get so high that I'll hear about it on the news or from a friend.

Lottery, Simulation, Probability, Entertainment

205 points by airstrike 129 days ago | 94 comments

Perplexing the Web, One Probability Puzzle at a Time (quantamagazine.org)

Probability, Puzzles, Quantum Computing

38 points by isaacfrond 138 days ago | 16 comments

Three crew investigated over Bayesian yacht sinking (bbc.com)

Probability, Statistics, Accidents, Marine Safety, Investigations

6 points by grugagag 142 days ago | 2 comments

The Law of Large Numbers or Why It Is a Bad Idea to Go to the Casino (easylang.online)