Winning Ways for Your Mathematical Plays
by Elwyn R. Berlekamp, John Horton Conway, Richard K. Guy · first published 2001
84% recommend16% neutral
Why HN recommends it
Playful, fun guide to combinatorial game theory and surreal numbers, gentler and more accessible than On Numbers and Games; good for browsing and for readers curious about the math behind games and puzzles.
Summarised by Claude from recommending comments
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2008–2026On numbers and games
John Horton Conway
Recommended by 15 · mentioned by 1915 recommend · 19 mention15 recommend · 1915 recommend
2009–2026Surreal numbers
Donald Knuth
Recommended by 27 · mentioned by 4127 recommend · 41 mention27 recommend · 4127 recommend
2010–2025Mathematics and its history
John C. Stillwell
Recommended by 15 · mentioned by 1715 recommend · 17 mention15 recommend · 1715 recommend
2008–2026Visual complex analysis
Tristan Needham
Recommended by 38 · mentioned by 5038 recommend · 50 mention38 recommend · 5038 recommend
2012–2026The Joy of X
Steven H. Strogatz
Recommended by 15 · mentioned by 2015 recommend · 20 mention15 recommend · 2015 recommend
2010–2026Understanding Analysis
Stephen Abbott
Recommended by 31 · mentioned by 3831 recommend · 38 mention31 recommend · 3831 recommend
2009–2026Elements of Information Theory
T. M. Cover, Joy A. Thomas
Recommended by 20 · mentioned by 2820 recommend · 28 mention20 recommend · 2820 recommend
2009–2025Naive Set Theory
Paul R. Halmos
Recommended by 29 · mentioned by 3529 recommend · 35 mention29 recommend · 3529 recommend
…Dasgupta, Papadimitriou, and Vazirani) - Algorithm Design (by Kleinberg and Tardos) - Feynman Lectures on Physics - Landau & Lifschitz's series - Vladimir Arnold's books on ODEs and Classical Mechanics - Winning Ways for your Mathematical Plays (by Berlekamp et al.) - Elements of Information Theory (by Cover & Thomas) - Information Theory, Inference, and Learning Algorithms (by MacKay) - Network Optimization (by Bertsekas) - Convex Optimization…
on “Reading list for those who love to learn” ↗…puzzle would be harder to solve efficiently with backtracking, because it's not obvious until the end that you're on the wrong path. If you're interested in the mathematics of peg-jumping puzzles, see "Winning Ways for your mathematical plays, Vol 2", by Berlekamp, Conway, and Guy, which discusses the mathematics of the plus-shaped peg-jumping puzzle in detail.
on “Solving edge-match puzzles with Arc and backtracking” ↗The book Winning Ways for Your Mathematical Plays[1] has three main algorithms that are in the vein of this basic idea. They were actually optimized for ease of remembering and executing on. With full documented solutions for moving specific cubes…
on “Two-part Rubik's algorithms” ↗I believe this is Richard Guy of "Winning ways for your mathematical plays". It's definitely worth browsing if you're interested in game theory or recreational math.
on “Richard Guy has died” ↗…1 False *Game> half + half == 1 True *Game> half * 1 == half True *Game> half * (one + one) > 1 False The best resources for learning are both by Conway: "Winning Ways for your Mathematical Plays" (WW) and "On Numbers and Games" (ONAG). WW is more accessible and introduces you to numbers via games, whereas ONAG is more of a hard-core math book that explains games via numbers. WW is probably…
on “Infinity Is Not a Number - It's a Free Man” ↗"On Numbers and Games" is a great book but it can be tough. "Winning Ways for your Mathematical Plays" by Berlekamp, Conway & Guy is a gentler introduction to surreal number. It's also very fun.
on “A Software Engineer’s Adventures in Learning Mathematics” ↗>>> Study game theory And you start seeing mini prisoners dilemmas in all interactions. Maybe dated, but still loads of fun: Game of Life John Conway's Winning Ways For Your Mathematical Plays https://annarchive.com/files/Winning%20Ways%20for%20Your%20M... I'd add probability theory to the mix. Computer Age Statistical Inference is a modern classic https://web.stanford.edu/~hastie/CASI/
on “How to get rich without getting lucky” ↗See John Conway's classic on Combinatorial Game Theory Winning Ways For Your Mathematical Plays https://en.wikipedia.org/wiki/Winning_Ways_for_your_Mathemat... As far as programming agents to play board games you can check out this Python implementation of Monte Carlo Tree Search http://mcts.ai/code/python.html
on “Ask HN: Are there board games like Go, Hex etc but a bit simpler?” ↗While I had no name recognition of this brilliant theorist, turns out he is the same guy that wrote Winning Ways for Your Mathematical Plays (recommended). Also found this sad news: https://news.berkeley.edu/2019/04/18/elwyn-berlekamp-game-th...
on “How to Always Win at Dots and Boxes (2015) [video]” ↗…from Conway, which makes it a very easy read that still touches on the important concepts in his work, in his own words; also highly recommend all the Numberphile videos featuring him for that)- then: Winning Ways for your Mathematical Plays is really fun to thumb through. The Book of Numbers is fantastic and something I would gift to any mathematically curious, somewhat independent, child. Knuth's Surreal Numbers is also a great read.…
on “Ask HN: What kind of math do you study in your free time?” ↗Winning Ways For Your Mathematical Plays by Berlekamp, Conway and Guy
on “Ask HN: Math books you recommend just for the way they are written?” ↗…triangle centers[0] with the late Steve Sigur, who was not a research mathematician but a high school teacher. Of course the Game of Life is an enduring classic, but I’ll also always have fond memories of Winning Ways for Your Mathematical Plays and Sphere Packings, Lattices and Groups (affectionately known as SPLAG). The mathematical world has truly lost a living legend. [0] https://books.google.com/books/about/The_Triangle_Book.html?...
on “John Conway has died” ↗For a more playful and, some would say, practical view, read "Winning Ways for Your Mathematical Plays" (http://en.wikipedia.org/wiki/Winning_Ways_for_your_Mathemati...)
on “What are imaginary numbers?” ↗A few immediately come to mind: 1. Winning Ways for Your Mathematical Plays 2. A Singular Mathematical Promenade, available for free online: https://perso.ens-lyon.fr/ghys/promenade/ There are many other math books I really like - over the years I've collected a long list of…
on “Ask HN: Math books you recommend just for the way they are written?” ↗If this interests you, the series "Winning Ways for Your Mathematical Plays" is something to add to your bookshelf. And if you ever see "On Numbers and Games" in a used book store (the $200 price tag on Amazon is a bit hard to swallow), its another one to get.
on “Hackenbush (2021) [video]” ↗