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What is a Centipawn Advantage?

Introduction Current computer chess engines include a neat feature: the analysis bar. For example here is the analysis bar from chess.com. White to move, FEN: rnb2rk1/ppp2ppp/3p1q1n/4p3/7P/b1PPP3/PP1BBPP1/R2QK1NR w KQ – 0 1 The analysis bar is on the left, and the white portion is 74 “centipawn units” below the midpoint (matching […]

Exploring Chess Positions and Counts

Introduction In our earlier article “How Many Chess Games are Possible?” we derived that the number of typical short chess games is around 10151. This turned out to be much larger than the “Shannon number” 10120 side-note from Shanon’s remarkable 1950 paper “Programming a Computer for Playing Chess” Philosophical Magazine, […]

How Many Chess Games are Possible?

How Many Chess Games are Possible? Here is a fun question: how many different games of chess are possible? Counting the number of possible chess games is quite hard, as the numbers are large and chess board positions can be quite complicated. In this note we will try to estimate […]

Uncovering Hidden Price Elasticity

Mixed populations make correctly measuring price elasticity (the response of sales to price changes) difficult. In fact, standard methods often mis-price. In our latest screencast we show Bayesian methods and Stan can actually “un-mix” such populations and correctly infer price elasticity. This allows for much better price experiment outcomes.

I am Tired of Praise of Byproduct

I’ve been worrying a bit over the philosophy of creation and dissemination in the era of LLMs (large language models). I feel we are overly impressed with the byproduct or even the bycatch. LLMs do complete some tasks, write code, and produce superficially convincing texts. In my opinion, this is […]

How Logistic Regression Changes with Prevalence

Our group has written many times on how classification training prevalence affects model fitting. Tailored Models are Not The Same as Simple Corrections The Shift and Balance Fallacies Does Balancing Classes Improve Classifier Performance? The Intercept Fallacy Don’t Use Classification Rules for Classification Problems The upshot is: we feel re-balancing […]