--- title: "#probability articles | Hashnode" description: "Explore 96 articles tagged #probability on Hashnode. Tutorials, guides, and how-tos from the community." url: "https://hashnode.com/tag/probability" --- Tag # #probability 96 posts · 12 followers [Kea Mmakola](https://hashnode.com/@keammakola) · [Oct 6](https://hashnode.com/posts/house-always-wins/6ac51b94b2865e9c10b2400f) ### [I Built a Prediction Bot Just to Prove Your Betslip Will Lose](https://keammakola.hashnode.dev/house-always-wins?utm_source=hashnode&utm_medium=feed) I built a football prediction bot. Nearly 70% of strong predictions were right, but its betting back-test lost money. Explore the data and code. 7 min read · [keammakola.hashnode.dev](https://keammakola.hashnode.dev/house-always-wins?utm_source=hashnode&utm_medium=feed) [José Nunes](https://hashnode.com/@josenunes) · [Sep 1](https://hashnode.com/posts/product-of-experts/6a9714744ab676b1a442eba0) ### [Product of Experts](https://ml-classroom.hashnode.dev/product-of-experts?utm_source=hashnode&utm_medium=feed) Behind the Scenes 22 min read · [ml-classroom.hashnode.dev](https://ml-classroom.hashnode.dev/product-of-experts?utm_source=hashnode&utm_medium=feed) [CalculatorQueen](https://hashnode.com/@calculatorqueen) · [Aug 28](https://hashnode.com/posts/expected-value-is-not-a-forecast-engineering-a-transparent-crafting-calculator/6a918f675009b9858e4656e3) ### [Expected Value Is Not a Forecast: Engineering a Transparent Crafting Calculator](https://calculatorqueen.hashnode.dev/expected-value-is-not-a-forecast-engineering-a-transparent-crafting-calculator?utm_source=hashnode&utm_medium=feed) Build a transparent crafting expected-value model with visible costs, success probability, break-even chance, validation, and tests. 7 min read · [calculatorqueen.hashnode.dev](https://calculatorqueen.hashnode.dev/expected-value-is-not-a-forecast-engineering-a-transparent-crafting-calculator?utm_source=hashnode&utm_medium=feed) [Uche Ozoemena](https://hashnode.com/@codewithoz) · [Jul 16](https://hashnode.com/posts/the-sigmoid-function-a-layman-s-intuition/6a58d62db8eee100f4ad4f93) ### [The Sigmoid Function: A Layman's Intuition](https://incodethismeans.com/the-sigmoid-function-a-layman-s-intuition?utm_source=hashnode&utm_medium=feed) Odds, logarithms, and a bit of algebra to make it click. 9 min read · [incodethismeans.com](https://incodethismeans.com/the-sigmoid-function-a-layman-s-intuition?utm_source=hashnode&utm_medium=feed) [Fundacja Dobre Państwo](https://hashnode.com/@dobrepanstwo) · [May 26](https://hashnode.com/posts/how-much-does-tomorrow-cost-the-mathematics-and-ethics-of-financial-markets/6a15285fc8f2fa5a2036a9a2) ### [How Much Does Tomorrow Cost? The Mathematics and Ethics of Financial Markets](https://fundacjadobrepasntwo.hashnode.dev/how-much-does-tomorrow-cost-the-mathematics-and-ethics-of-financial-markets?utm_source=hashnode&utm_medium=feed) This article provides a deep analysis of the mathematical framework of contemporary finance, treating quantitative tools as a grammar for describing an uncertain future. The author focuses on the tria 1 min read · [fundacjadobrepasntwo.hashnode.dev](https://fundacjadobrepasntwo.hashnode.dev/how-much-does-tomorrow-cost-the-mathematics-and-ethics-of-financial-markets?utm_source=hashnode&utm_medium=feed) [Macaulay001](https://hashnode.com/@oladimeji2025) · [May 11](https://hashnode.com/posts/berkeleys-1973-admit-rates-flip-sign-when-you-stop-pooling-the-departments/6a025d302d1b69abf22b8207) ### [Berkeley's 1973 admit rates flip sign when you stop pooling the departments](https://forgottentheorieshashnodedev.hashnode.dev/berkeleys-1973-admit-rates-flip-sign-when-you-stop-pooling-the-departments?utm_source=hashnode&utm_medium=feed) In 1903 Udny Yule wrote a short paper on the association between two 7 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/berkeleys-1973-admit-rates-flip-sign-when-you-stop-pooling-the-departments?utm_source=hashnode&utm_medium=feed) [Macaulay001](https://hashnode.com/@oladimeji2025) · [May 11](https://hashnode.com/posts/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq/6a025d702d1b69abf22b821f) ### [I tested Bertrand's 1887 ballot formula on 648 vote splits and the answer was always (p-q)/(p+q).](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq?utm_source=hashnode&utm_medium=feed) In 1887 Joseph Bertrand sent a four-page note to the \*Comptes Rendus\* of the French Academy. The question he asked is one you can pose to a child. Two candidates run for office. A wins with p votes, B loses with q < p. The ballots are pulled from the 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-bertrands-1887-ballot-formula-on-648-vote-splits-and-the-answer-was-always-p-qpq?utm_source=hashnode&utm_medium=feed) [Macaulay001](https://hashnode.com/@oladimeji2025) · [May 11](https://hashnode.com/posts/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough/6a025d6e859efcceac079c31) ### [I tested von Mises's 1939 birthday claim with exact arithmetic and 10^5 Monte Carlo trials per group size. 23 people really is enough.](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough?utm_source=hashnode&utm_medium=feed) In 1939 Richard von Mises published a short paper with the unwieldy title \*Über Aufteilungs- und Besetzungswahrscheinlichkeiten\*. Inside is the calculation that everyone now calls the birthday paradox. Pick 23 people at random. The probability that t 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-tested-von-misess-1939-birthday-claim-with-exact-arithmetic-and-105-monte-carlo-trials-per-group-size-23-people-really-is-enough?utm_source=hashnode&utm_medium=feed) [Macaulay001](https://hashnode.com/@oladimeji2025) · [May 11](https://hashnode.com/posts/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it/6a025d6b2d1b69abf22b821d) ### [Chebyshev's 1867 bound holds on every distribution I threw at it, and a two-point mix landed within 0.2% of saturating it.](https://forgottentheorieshashnodedev.hashnode.dev/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it?utm_source=hashnode&utm_medium=feed) In 1867 Pafnuty Chebyshev published a short proof of an inequality that any student of probability eventually meets: 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/chebyshevs-1867-bound-holds-on-every-distribution-i-threw-at-it-and-a-two-point-mix-landed-within-02-of-saturating-it?utm_source=hashnode&utm_medium=feed) [Macaulay001](https://hashnode.com/@oladimeji2025) · [May 11](https://hashnode.com/posts/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would/6a025d662d1b69abf22b8219) ### [I sampled a million coin flips with decaying probabilities. The 1909 dividing line showed up exactly where Borel said it would.](https://forgottentheorieshashnodedev.hashnode.dev/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would?utm_source=hashnode&utm_medium=feed) In 1909 Émile Borel was working through a problem about decimal expansions of real numbers, and he proved a small lemma to dispatch a side case. Eight years later, Francesco Paolo Cantelli sharpened it. Together the two halves became one of the clean 6 min read · [forgottentheorieshashnodedev.hashnode.dev](https://forgottentheorieshashnodedev.hashnode.dev/i-sampled-a-million-coin-flips-with-decaying-probabilities-the-1909-dividing-line-showed-up-exactly-where-borel-said-it-would?utm_source=hashnode&utm_medium=feed)