ƧƿѦςɛ♏ѦਹѤʞ<p><span class="h-card" translate="no"><a href="https://mathstodon.xyz/@gregeganSF" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>gregeganSF</span></a></span> <br>Right, so this isn't like Bertrand's paradox where the result depends upon the specific method of 'choosing random points' - right?<br>:-) <br><a href="https://mastodon.social/tags/JustChecking" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>JustChecking</span></a> <a href="https://mastodon.social/tags/maths" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>maths</span></a> <a href="https://mastodon.social/tags/probability" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>probability</span></a></p>
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When designing games, the basic maths of probability systems can be useful, but also lead to a bit of head-scratching, especially for those of us for whom high school maths lessons have receded somewhat into the fog of ages past. Our archive article for this week, Axes and Arithmetic part one, gives some basic things you might need to know:
https://exilian.co.uk/forum/index.php?topic=5593.msg119417#msg119417
ExilianAxes and Arithmetic 1: Percentages and ProbabilityAxes and Arithmetic 1: Percentages and Probability
What?! No, the author, Dr. Marcus Du Sautoy, is a math PhD and should know better! Dominoes have only one representative of unequal values, but with dice there are two ways of getting that result.
For example, scoring a 9 on 2D6 has probability 4/36. But the 6-3 and 5-4 are just 2/21 of the (non-blank) dominoes! This is a terrible way to simulate a d5!
From "Around the World in Eighty Games" which wasn't great on its history but now I gotta question its math too?
This 33-minute documentary video from Veritasium on Markov chains and their wide applicability is excellent.
youtu.be- YouTubeEnjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
Vincenzo Crupi has revised his SEP-entry on Confirmation, https://plato.stanford.edu/entries/confirmation/
plato.stanford.eduConfirmation (Stanford Encyclopedia of Philosophy)
#statstab #388 The odds are it's wrong: Correcting a common mistake in statistics
Thoughts: Report probabilities instead, which in R (not SPSS) can be easily computed for your models.
#odds #oddsratios #riskratios #probability #r #logisticregression
omg mein guter Freund zombiecalypse hat mal wieder abgeliefert: "Wieso gehen Pläne schief, erster Grund: Optimismus".
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@androcat
It applies to all branches of science. For example statistics: there's no such thing as "letting the data speak for themselves"; they're always interpreted against a background of assumptions and prior knowledge.
I spent two weeks trying to numerically demonstrate convergence of the generalized central limit theorem for the critical case where the variance just becomes infinite. I failed! I suspect my choice of norm was a poor one.
Modeling the sum of 10^30 random variables is challenging.
https://www.skewray.com/articles/the-generalized-central-limit-theorem-for-a2-pareto-and-student-s-t
www.skewray.comThe Generalized Central Limit Theorem for α=2: Pareto and Student's-t | Skewray ResearchWhat happens when the central limit theorem convergence at the exact parameter where the variance becomes infinite? Poor choice of norm!
ICYMI: 
How do mathematicians find patterns in unpredictable events? This #video explains randomness through Michel Talagrand's groundbreaking work on mathematical inequalities.
Random events follow patterns called "normal distributions". After 1,000 coin flips, getting only heads is almost impossible—randomness becomes predictable within limits.
Learn more: https://zurl.co/fHXT4
How do mathematicians find patterns in unpredictable events? This #video explains randomness through Michel Talagrand's groundbreaking work on mathematical inequalities.
Random events follow patterns called "normal distributions". After 1,000 coin flips, getting only heads is almost impossible—randomness becomes predictable within limits.
Learn more: https://thekidshouldseethis.com/post/randomness-probability-math-talagrand
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@alsutton Everytime I go down that rabbit hole, I take a step back and add some context about the #MagicSkyDaddies, #ZombieJews, and other #ImaginaryFriends BILLIONS of people #Whisper their #SelfishWhispers to to bend the laws of #Physics, #Chemistry, #Biology, and #Probability to grant their #SelfishDesires and #beLIEve and will pay 10% of their earnings to. Here is some context:
(29 May) Your next gaming dice could be shaped like a dragon or armadillo
Statistically, “the real behavior of a rolling object is largely a function of its geometry.”…
https://s.faithcollapsing.com/g6yqw
Archive: ais: https://archive.md/wip/HYNoa ia: https://s.faithcollapsing.com/oeaqj
#3d-printing #computational-science #computer-simulations #geometry #probability #science #shape-analysis
Your next gaming dice could be shaped like a dragon or armadillo https://arstechni.ca/5RvQ #computationalscience #Computersimulations #shapeanalysis #probability #3Dprinting #geometry #Science
Ars Technica · Your next gaming dice could be shaped like a dragon or armadillo
Just yesterday, I was musing to a (younger) research visitor, "I hope that within my lifetime we will still see another breakthrough on the bounds for R(3,k)"...
https://arxiv.org/abs/2505.13371
I am excited to see what developments follow on from here!
(Also that old adage: just as soon as you publish a survey (https://arxiv.org/abs/2501.03379) it is out of date.)
arXiv.orgA new lower bound for the Ramsey numbers $R(3,k)$We prove a new lower bound for the off-diagonal Ramsey numbers, \[ R(3,k) \geq \bigg( \frac{1}{3}+ o(1) \bigg) \frac{k^2}{\log k }\, , \] thereby narrowing the gap between the upper and lower bounds to a factor of $3+o(1)$. This improves the best known lower bound of $(1/4+o(1))k^2/\log k$ due, independently, to Bohman and Keevash, and Fiz Pontiveros, Griffiths and Morris, resulting from their celebrated analysis of the triangle-free process. As a consequence, we disprove a conjecture of Fiz Pontiveros, Griffiths and Morris that the constant $1/4$ is sharp.