So it goes.
Amazons is a modern game (1992) that feels like a game that could've been invented hundreds of years ago. To me, this is a very valuable attribute of any modern abstract (though not strictly required). I came across this game a few year ago after I bought a 10x10 Checkers board and searched for games to play on it. The rules were clear and concise and I was soon on my way.
Designer: Walter Zamkauskas
Category - combinatorial
Mechanic(s) - blocking, grid movement, territory control
The game is very simple. On a 10x10 board two players place their "amazons" in a pre-arranged configuration on the board (standard and variant configurations abound). On alternating turns each player moves one of their amazons any number of spaces in any direction in a straight-line. After the amazon has stopped moving, the same player "shoots an arrow" from the stopping location any number of spaces in any direction in a straight-line. The only constraints are that neither amazons nor arrows can pass through a location containing an amazon or arrow.
The goal of Amazons is technically to be the last player able to make a move, but in reality most players stop long before that point and tally the number of spaces that they uniquely control. What that means is that eventually a condition will arise where each player will have all of their amazons located in discrete zones blocked off by arrows and containing no enemy amazons. When this occurs the players can tally up the total number of squares in their control zones and the player with the highest total wins.
The goal and gameplay of Amazons is incredibly lucid and obvious. That said, playing the game at a high level is very hard. The game is the epitome of the "seconds to learn, lifetime to master" ethos that drives designers of combinatorial abstracts into fits of insomnia. Amazons is a game that is worthy of, and indeed supportive of intense and prolonged study. I mentioned above that the game typically ends before it ends by identifying isolated regions and counting territory. However, beginners and amateurs (myself included) are encouraged to continue play until indeed one is truly unable to make a move. The reason for this recommendation is that territory scoring assumes perfect play-outs of isolated pieces, and in my experience this is hard to come by without performing those play-outs many times. Indeed, I saw a situation where an opponent had a slightly larger territory than me, but misplayed the endgame and lost by 2 points. Your mileage may vary.
Indeed a modern classic, and one of the very few luck-free 2-player strategy games I would rate even a tad higher than the wonderful Gipf- series (together with Lines of Action and Gyges).