strategy
https://plus.maths.org/content/taxonomy/term/266
enPlaying with numbers
https://plus.maths.org/content/playing-number
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<p>Here's a game: pick a positive natural number and if yours is the smallest number no one else has picked, you win. What's the best strategy?</p>
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<p>We recently challenged our Twitter followers to a game: pick a positive natural number and if yours is the smallest number no one else has picked, you win. We are now pleased to announce that we've found a winner (who has been informed) and that the winning number is 6. Below is a histogram counting how many times the numbers up to 200 have been picked. There were a total of 127 responses, but for clarity the histogram misses out the 17 responses that were over 200 (142857 was the largest).</p><p><a href="https://plus.maths.org/content/playing-number" target="_blank">read more</a></p>https://plus.maths.org/content/playing-number#commentsFP-top-storystrategyTue, 24 Nov 2015 09:51:52 +0000mf3446470 at https://plus.maths.org/contentHow to win at Mornington Crescent
https://plus.maths.org/content/how-win-mornington-crescent
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Chris Budd and Jeremy Budd </div>
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This article casts a mathematical eye over a famous <em>non-game</em> enjoyed by thousands of people up and down the UK every week. </div>
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<p><em>If you enjoy that witty sense of humour commonly described as "English" then you'll love the idea of a non-game. This article casts a mathematical eye over a famous non-game enjoyed by thousands of people up and down the UK every week.</em></p><p><a href="https://plus.maths.org/content/how-win-mornington-crescent" target="_blank">read more</a></p>https://plus.maths.org/content/how-win-mornington-crescent#commentsFP-belowgame theorymathematical modellingnash equilibriumstrategyTue, 10 Nov 2015 09:02:47 +0000mf3446446 at https://plus.maths.org/contentTic-tac-toe!
https://plus.maths.org/content/tic-tac-toe
<p>We have just learnt a really nice fact about the game of tic-tac-toe. As you may know, tic-tac-toe always results in a draw if both players make the best moves possible at every step of the game. To force a draw you need to follow a particular strategy, which isn't too hard, but tedious to write down (see <a href="http://en.wikipedia.org/wiki/Tic-tac-toe#Strategy">here</a>).</p>
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<p style="width: 289px;"></p><p><a href="https://plus.maths.org/content/tic-tac-toe" target="_blank">read more</a></p>https://plus.maths.org/content/tic-tac-toe#commentscreativitygame theorystrategyThu, 02 Oct 2014 09:21:47 +0000mf3446154 at https://plus.maths.org/contentPlay to win with Nim
https://plus.maths.org/content/play-win-nim
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Marianne Freiberger </div>
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<p>In the game of Nim one player always has a winning strategy — it depends on an unusual way of adding numbers.</p>
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<p>Some games are all about luck. Your winning chance depends on the
roll of a die or the cards you've been dealt. But there are
other games that are only about strategy: if you play cleverly, you're
guaranteed to win. </p>
<p>A great example of this is the ancient game of Nim. Whatever the
state of the game, there is a winning strategy for one of the two
players. And a very cute form of addition tells you which of the two
players it is.</p><p><a href="https://plus.maths.org/content/play-win-nim" target="_blank">read more</a></p>https://plus.maths.org/content/play-win-nim#commentsbinary numbercreativitygame theorynimstrategyMon, 21 Jul 2014 10:18:30 +0000mf3446134 at https://plus.maths.org/contentOuter space: A question of tactics
https://plus.maths.org/content/outer-space-question-tactics
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John D. Barrow </div>
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<p>In many sports a particular tactical conundrum arises. The team captain has to choose the best order in which to use a group of players or set-plays in the face of unknown counter choices by the opposition. Do you want to field the strongest players first to raise morale or play them last to produce a late run for victory? John D. Barrow shows that randomness holds the answer.</p>
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<p>Left, right or centre?</p><p><a href="https://plus.maths.org/content/outer-space-question-tactics" target="_blank">read more</a></p>https://plus.maths.org/content/outer-space-question-tactics#commentsmathematics in sportouterspacerandomnessstrategyFri, 03 Sep 2010 15:41:16 +0000mf3445301 at https://plus.maths.org/contentGames people play
https://plus.maths.org/content/games-people-play
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Lewis Dartnell </div>
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<b>Combinatorial Game Theory</b> is a powerful tool for analysing mathematical games. Lewis Dartnell explains how the technique can be used to analyse games such as Twentyone and Nim, and even some chess endgames. </div>
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<div class="pub_date">November 2003</div>
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<p><a href="https://plus.maths.org/content/games-people-play" target="_blank">read more</a></p>https://plus.maths.org/content/games-people-play#comments27chesscoin gamescombinatorial game theorygame theorynimnon-partisan gamepartisan gamestrategytwenty-oneSat, 01 Nov 2003 00:00:00 +0000plusadmin2232 at https://plus.maths.org/contentBackgammon, doubling the stakes, and Brownian motion
https://plus.maths.org/content/backgammon-doubling-stakes-and-brownian-motion
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Jochen Blath and Peter Mörters </div>
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Backgammon is said to be one of the oldest games in the world. In this article, <b>Jochen Blath</b> and <b>Peter Mörters</b> discuss one particularly interesting aspect of the game - the doubling cube. They show how a model using Brownian motion can help a player to decide when to double or accept a double. </div>
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<div class="pub_date">May 2001</div>
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<h2>Backgammon: the game</h2>
<p>Backgammon is said to be one of the oldest games in the world. Its roots may well reach back 5,000 years, into the former Mesopotamia. From there, it spread out in variants to Greece and Rome as well as to India and China. It was played in England in 1743 when Edmond Hoyle fixed the rules for backgammon in Europe. After a revision in 1931 in the US, these rules are still in use today.</p><p><a href="https://plus.maths.org/content/backgammon-doubling-stakes-and-brownian-motion" target="_blank">read more</a></p>https://plus.maths.org/content/backgammon-doubling-stakes-and-brownian-motion#comments15BackgammonBrownian motiondoubling cubedoubling strategyindependencerandom walkstochastic processstopping timestrategyMon, 30 Apr 2001 23:00:00 +0000plusadmin2183 at https://plus.maths.org/contentMathematical mysteries: Chomp
https://plus.maths.org/content/mathematical-mysteries-chomp
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Helen Joyce </div>
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<p>Chomp is a simple two-dimensional game, played as follows.<br />
Cookies are set out on a rectangular grid. The bottom left cookie is poisoned.<br />
Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.</p>
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<div class="pub_date">March 2001</div>
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<p>Chomp is a simple two-dimensional game, played as follows.</p>
<p>Cookies are set out on a rectangular grid. The bottom left cookie is poisoned.</p>
<p align="center"><img src="/issue14/xfile/chomp.gif" /></p>
<p>Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.</p>
<p align="center"><img src="/issue14/xfile/cookiechomp.gif" /></p>
<p>The loser is the player who has to eat the poisoned cookie.</p><p><a href="https://plus.maths.org/content/mathematical-mysteries-chomp" target="_blank">read more</a></p>https://plus.maths.org/content/mathematical-mysteries-chomp#comments14Mathematical mysteriesstrategyThu, 01 Mar 2001 00:00:00 +0000plusadmin4748 at https://plus.maths.org/contentGame theory and the Cuban missile crisis
https://plus.maths.org/content/game-theory-and-cuban-missile-crisis
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Steven J. Brams </div>
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<b>Steven J. Brams</b> uses the Cuban missile crisis to illustrate the Theory of Moves, which is not just an abstract mathematical model but one that mirrors the real-life choices, and underlying thinking, of flesh-and-blood decision makers. </div>
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<div class="pub_date">January 2001</div>
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<p><a href="https://plus.maths.org/content/game-theory-and-cuban-missile-crisis" target="_blank">read more</a></p>https://plus.maths.org/content/game-theory-and-cuban-missile-crisis#comments13chickengame theorymixed strategynash equilibriumstable strategystrategytheory of movesMon, 01 Jan 2001 00:00:00 +0000plusadmin2174 at https://plus.maths.org/contentMathematical mysteries: What colour is my hat?
https://plus.maths.org/content/mathematical-mysteries-what-colour-my-hat
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Mark Wainwright </div>
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<p>This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.</p>
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<p>This is a game played between a team of 3 people (Ann, Bob and Chris, say), and a TV game show host. The team enters the room, and the host places a hat on each of their heads. Each hat is either red or blue at random (the host tosses a coin for each team-member to decide which colour of hat to give them). The players can see each others' hats, but no-one can see their own hat.</p><p><a href="https://plus.maths.org/content/mathematical-mysteries-what-colour-my-hat" target="_blank">read more</a></p>https://plus.maths.org/content/mathematical-mysteries-what-colour-my-hat#comments16error-correcting codegame theoryHamming codeMathematical mysteriesstrategyFri, 01 Dec 2000 00:00:00 +0000plusadmin4752 at https://plus.maths.org/contentMonte Carlo Monopoly
https://plus.maths.org/content/monte-carlo-monopoly
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<p>Dr. John Haigh, a mathematics lecturer from the University of Sussex, has found the ultimate strategy for winning at Monopoly: use the help of a computer!</p>
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<div class="pub_date">May 1999</div>
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<p>Dr. John Haigh, a mathematics lecturer from the University of Sussex, has found the ultimate strategy for winning at Monopoly: use the help of a computer!</p><p><a href="https://plus.maths.org/content/monte-carlo-monopoly" target="_blank">read more</a></p>https://plus.maths.org/content/monte-carlo-monopoly#commentscomputer simulationMonopoly board gameMonte Carlo methodstrategyFri, 30 Apr 1999 23:00:00 +0000plusadmin2682 at https://plus.maths.org/contentMathematics, marriage and finding somewhere to eat
https://plus.maths.org/content/mathematics-marriage-and-finding-somewhere-eat
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David K. Smith </div>
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How do you choose a partner? Is it an irrational choice or is it made rationally, based on a mathematical model which analyses the best potential partner you are likely to meet? </div>
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<div class="pub_date">September 1997</div>
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<p>There are a lot of everyday situations where people make decisions one after the other, and what is decided earlier affects the choices later on. One of the more serious of these is finding a partner. Most people want to find the best possible partner. <!-- FILE: include/centrefig.html --></p><p><a href="https://plus.maths.org/content/mathematics-marriage-and-finding-somewhere-eat" target="_blank">read more</a></p>https://plus.maths.org/content/mathematics-marriage-and-finding-somewhere-eat#comments3decision theoryGoogoloptimal stoppingsimulationstrategySun, 31 Aug 1997 23:00:00 +0000plusadmin2147 at https://plus.maths.org/content