Amazons

I think that Amazons is a great game.  Its rules are simple but it feels deep to play.  It has a great advantage of not needing specialist equipment to play.  The game was designed on a 10x10 checkerboard, but it plays well on an 8x8 chess board, or a 6x6 board for beginners, or even on an irregular shaped checkered board!  Depending on board size, each player has a number of Amazon queens (warriors from Greek mythology) - 4 each for the standard 10x10 board.  These do not need to be queens from chess sets, any sets of pieces will do.  You also need markers to denote squares that become out of bounds to both players - counters or coins would be fine.  A turn consists of (a) Moving a queen to an empty square like a chess queen, but not over another piece or a blocked squared. (b) Firing a flaming arrow from this new position, again to an empty square like a chess queen, but not over another piece or a blocked squared.  The square the arrow lands on must be marked and becomes blocked to both players.  So, as the game progresses, more and more squares become blocked, leaving less and less space for the queens to manoeuvre. The first player who cannot move loses!

Here is a link to an excellent Introductory video to Amazons by Elwyn Berlekamp (pioneer of Combinatorial Game Theory, co-author of Winning Ways for your Mathematical Plays, writer of error-correcting codes that allowed spacecraft from Voyager to the Hubble Space Telescope to send accurate, detailed and beautiful images back to Earth, and more . . .) as part of the stimulating Numberphile series of recreational mathematics videos.

A good strategy for Amazons at the start of a game seems unclear.  Later in a game, tactical manoeuvres to trap an opponents queen into a very small area is an obvious goal, but this can be hard to achieve without loosing control elsewhere on the board.  I know of little literature on the subject, but BoardGameGeek Member Errant Deeds shares his thoughts in a downloadable strategy guide pdf.  When this was written in 2014, he says this was the only guide around, and I can find nothing of significance written since!? 

However, because of its simple rules but deep play, Amazons is a good game for AI programming research.  For example, here is a link to a Master's thesis.  I wonder if the recent advances using neural networks for Go (AlphaGo) and Chess (Alpha Zero) will ever be applied to Amazons?

Several of the game playing websites include Amazons to play PvP, but strangely not Boardspace.  There are also several options to play a computer program.  I like Invader v2.1 which is very flexible.  I used to be able to beat it on low levels, but at the time of writing, I can't beat it at its lowest setting of 3 seconds per move!  I need to practise . . .