Download a copy (pdf) - University of Salford

More documents

Recommendations

Info

PerspectivesMathematicsTheOptimalDartboardTo many people, darts is already a fiendishly difficult game, but now DavidPercy, Professor of Mathematics at the University of Salford, has made it evenharder.He has created the ‘Optimal Dartboard’ by re-arranging the numbers in such away that they minimise the chances of a high-scoring random throw. As wellas alternating odd and even numbers, Percy’s board also groups the numbers insimilar scoring clusters.(1+2+1)/4 Dartboard Comparison13Normal dartboardRunning averages1211109OptimalNormalAverage80 5 10 15 20Position on dartboardOptimal dartboard40 | May 2013
“ People have been lookingat this problem for thelast 30 years, but only asa bit of fun,” ProfessorPercy explains.“ But theywere using the wrongoptimality measureand also ignored the importance of havingalternating odd and even numbers. The idea isto make the dartboard as hard as possible.It is easier for a lucky throw to scorehighly in the left-hand side of the board,where there is a section containing12-9-14, with an average of 11.7, as wellas 16-7-19, with an average score of 14.“What they were looking at was tryingto make the difference between adjacentnumbers as large as possible, so that if youmiss a big number, you get a small number.But what you actually need to do is look atthe total score of two adjacent numbers andtry and make that as similar as possible all theway around the board.”Percy analysed the traditional board by tottingup the average scores for different sectionsof the board and laid out the plans for thenew board in a paper published in the journalMathematics Today.“The average of all the numbers on adartboard is 10.5, so put simply, you can gainby targeting those sections where the averageis higher than that,” he explains. He showedthat it was easier for a lucky throw to scorehighly in the left-hand side of the board,where there is a section containing 12-9-14,with an average of 11.7, as well as 16-7-19,with an average score of 14.With players traditionally trying to get from301 or 501 down to zero, the layout of theoptimal board also makes a big difference atthe end of the game, when players have to goout on a double. If they’re on an odd number,they’ll need to hit another odd number beforebeing able to go for a double. On the oldboard, even the worst player had a goodchance of hitting one close to the bottom ofthe board, with its cluster of four adjacentodd numbers 7, 19, 3 and 17.Percy’s new alternating arrangements hasput pay to this, along with another favourite,double 16. On the traditional board 16 and 8are next to each other, so if you miss double16 and hit single 16 instead, you then requiredouble 8, theoretically making it easier to hitas you already have your sights set on thatpart of the board. Similarly, the 10 and 6 areno longer adjacent, which makes finishingharder when players are on an even number.The dartboard was trialled at the BDO WorldProfessional Darts Championships in Januaryby darts legend Bobby George, and severalprototypes have been developed by leadingdartboard manufacturer Winmau. However,there are no plans to replace the traditionalboard, the numbering of which is thought todate back to the 19th century.Modestly, Percy adds: “Maths is often aboutfinding the optimal solution to a problem andthis is the optimal solution to that particularproblem. I lay no further claims – it was justan interesting piece of work!”May 2013 | 41
Page 1 and 2: PerspectivesResearch and Enterprise
Page 3 and 4: ContentsVol. 1: Issue. 1 | May 2013
Page 5 and 6: Design Against Crimewas established
Page 7 and 8: against ten design development proj
Page 9 and 10: ArtsWith experimental poetry becomi
Page 11 and 12: "The highest ranked player doesn’
Page 13 and 14: The National LotteryAnalytics can a
Page 15 and 16: The Salford MBAOne of the most flex
Page 17 and 18: “… the isle is full of noises,s
Page 19 and 20: Apple operates a closed system for
Page 21 and 22: thereby raising awareness. Research
Page 23 and 24: Wellness WorksOur “Total Wellbein
Page 25 and 26: Chief Fire Officer Steve McGuirk wi
Page 27 and 28: The University has a strong track r
Page 29 and 30: Along with Deb Hobz-Wyatt, James al
Page 31 and 32: Do you dig it?Dig Greater Mancheste
Page 33 and 34: Great excavationsAt the time of wri
Page 35 and 36: Social Care newsStudy investigates
Page 37 and 38: media monitoring to survey comments
Page 39: The mislabelling of fish is now ama
Page 43 and 44: Study proves classroomdesign really
Page 45 and 46: Conference ServicesA flexible plann
Page 47 and 48: Science newsFor up-to-the minute sc
Page 49 and 50: Peter Kay launchesnew comedy course
Page 51 and 52: Energy newsStay up to date with the
Page 53 and 54: International news & awardsSalford
Page 55 and 56: Campaigns in rude healththanks to s
Page 57 and 58: Admission: Free. Full Festival prog
Page 59 and 60: SalfordProfessionalDevelopmentBuild

Download a copy (pdf) - University of Salford

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?