The Mathematics of Sprouts - Survivors, Guards, Pharisees, a Moribundity Equation and some Strategy

2 years ago
25

Some interesting analysis of John Conway's paper-and-pencil Sprouts game: minimum and maximum bounds for number of moves; an explanation of the terms lives of a dot, live and dead dots, survivors, guards and pharisees; the strategy tree for the 2-dot game; an explanation of the Sprouts Conjecture with a current update on winning strategy results.
Many of the ideas are illustrated by a particular 4-dot Sprouts game.
Names of people mentioned: John Conway, Mike Paterson, Denis Mollison, Josh Jordon, Julien Lemoine and Simon Viennot.
Winning Ways for Your Mathematical Plays - Berlekamp, Conway & Guy
If you enjoyed watching this video please "like" it and "subscribe" to my channel @mistercorzi.
Chapters
0:00 Intro
0:40 A Typical 4-Dot Sprout Game
1:30 Establishing the 3n-1 Upper Bound for m
8:20 The variables s, d, g and φ
9:55 Discussion about Guards
12:27 Derivation of the Moribundity Equation
15:30 Establishing the 2n Lower Bound for m
17:11 Corollaries of the Bounds
19:05 Strategy Tree for 2-Dot Sprouts
24:33 Which Player has a Winning Strategy?
27:32 The Sprouts Conjecture
29:10 Current Position re Conjecture
29:38 End Links

Loading comments...