The Noble and Most Ancient Game of NIM | Game Theory 3 - Problem Solving

Описание: NIM is a very old game, with simple rules but complex strategy. Analysing any particular game of NIM using position analysis is possible, but can get quite time consuming, and it's easy to make mistakes. Finding a general strategy for NIM from scratch on the other hand is a very challenging problem.

In this video David runs through position analysis for the game of NIM starting with piles of 3, 5, and 7, and then indicates how you might set about discovering for yourself the general winning strategy, using all the general techniques, and a good dollop of luck and imagination.

You can read Charles Bouton's original paper analysing NIM here: http://www.jstor.org/stable/1967631. Note that while Bouton provides a strategy and a proof that it works, the paper give no indication of how one comes up with the strategy in the first place.

UCL Maths Dept Twitter: @MathematicsUCL.
UCL Maths Dept webpage: http://www.ucl.ac.uk/maths/.

Music:
-Variation 3 Canone all'Unisono (intro),
-Variation 10 fughetta (position analysis sequence), and
-Aria da Capo (outro)
from the Goldberg Variations by JS Bach, performed by Kimiko Ishizaka (CC0 no copyright).
Images:
Marble: http://pixabay.com/vectors/marble-bal... (public domain).

Video made by David Sheard with assistance from UCL.