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.
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7/6/2020
This is the final video in the sub-series on problem solving in
game theory. David finishes looking at the technique of pairing,
where you try and pair up your moves with your opponents so that you
can avoid losing, and maybe even win. David uses this to find
strategies to force a draw in two variants of Noughts and Crosses,
and to find a winning strategy in the game Jumping Coin.
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7/5/2020
Sticking with combinatorial games, David moves on from position
analysis to talk about a new technique to study games. It can be
applied to Misère Noughts and Crosses (Misère Tic-Tac-Toe), the game
mentioned at the end of the previous video, to prove that both
player can force a draw.
To explore this technique further there are three new games to think
about: 1D Noughts and Crosses, 5-in-a-row Noughts and Crosses (play
here: tic.netlify.app/), and Jumping Coins.
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7/5/2020
A short presentation from Dr Nick Ovenden and Dr Alex Diaz on CHIMERA - a collaboration between various different groups that looks at using Mathematics to solve medical issues.
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7/1/2020
A short discussion with Professor Christina Pagel and Professor
Rebecca Shipley, as they discuss their very different career paths
after completing an undergraduate degree in Mathematics.
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7/1/2020
David continues exploring the technique of position analysis as a way to find winning strategies for mathematical games. He analyses two games: Picking Up Sticks, and Wythoff's Game.
He also introduces the game of NIM, an apparently simple game which turns out to have very complex and interesting game play. We will try and find a winning strategy for NIM in the next video. In the meantime, you can have a go at playing it yourself here: www.transum.org/Software/Nim/.
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6/20/2020
In this, the first video in the series on problem solving in Game Theory, David introduces a class of combinatorial games for two players which lend themselves to being studied mathematically. We then look at a technique for finding winning strategies for these games called position analysis, which is basically a special version of the general technique to work backwards.
This technique can be used to find a winning strategy for the game of 21 Dares. David describes two more games where you can try to find winning strategies. These are Picking Up Sticks, and Wythoff's Game.
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6/20/2020
David explains how you can apply the five general problem solving techniques introduced in the previous video to solve the three problems he set last time: Cutting Up Chocolate, A Busy Bee, and Hilbert's Hotel Hunt.
For the next video, you are tasked to think about the game of 21 dares, and see if you can come up with a winning strategy.
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6/20/2020