Adam Cottam

1
Adam Cottam

• The Mathematics of Darts

2
Introduction

• Brief History
• Rules Scoring
• Dart Board Layout Board Setup
• Probability
• Mechanics
• Arithmetic Finishes
• Darts in teaching

3
A Brief History

• Middle Ages
• Henry VII
• Soldiers in battle
• Tree Slices
• 20th Century game evolves as we know it today

4
Rules of Darts

• Round the Board, Shanghai
• 301, 501
• Three darts each
• First to zero
• Finish on double
• Going Bust

5
Scoring

• Bulls eye 50
• Outer Bull 25
• Inner band Treble
• Outer band Double
• Other areas Single

6
Board Setup
7
Dartboard Layout

• 20! 2432902008176640000 arrangements
• Optimal Arrangement
• How do we find this arrangement?
• Brian Gamlin
• How did he do it???

8
Basic Probability

• Random Dart-Throw Model
• Use measurements to calculate areas
• Use these to calculate probabilities

• P(Bull Score) 0.00143
• P(Treble Score) 0.00337
• P(Double Score) 0.00549

9
Mechanics

• Set up model of dart after release
• Assumptions

• Dart is particle and air resistance neglected
• Acceleration due to gravity 9.8 ms-2

• Also need following information

• Length of arm at point of release
• Distance player learns over oche
• Height of player

• Possible uses include prediction of optimum
  throw angle

10
Arithmetic

• Crucial in darts for two reasons-

• No arithmetic no game
• Can improve chances of winning in finishing
  stage

11
Finishing

• Part of game where you win (or lose!)
• On a finish
• Eg. 170 T20 T20 Bull
• Eg. 45 5 D20 or 13 D16 or etc
• Sometimes more than one route to zero
• Which route is best???

12
Arithmetic Advantage

• 45 5 D20 13 D16 etc
• What if we miss going first route?
• What if we miss going second route
• Clearly second route better
• 32 is best double

13
Bobby George

• Bobby George's Checkout Calculator

14
Darts and Teaching

• Fewer numbers of children taking maths
• Lack of application?
• Darts can help!

15
Numeracy skills for Adults

• 15 million adults lack skills to pass a Maths
  GCSE (dfes website)
• How to improve skills?
• Get On campaign

16
Bibliography

• www.planetdarts.tv (6th Feb)
• www.bdodarts.com (7th Feb)
• www.dartboards.com (6th Feb)
• www.bbc.co.uk/sport (7th Feb)
• http//www.dfes.gov.uk/readwriteplus/Darts_and_num
  eracy (6th Feb)