The sister game to Quarto!, Pyraos is perhaps even more elegant in its simplicity.
Where Quarto! uses wood pieces, Pyraos' equipment is all plastic. Thirty jawbreaker-size balls come in two colors: cream and a light grey. The black board includes a perimeter troth just a tad shy of being able to hold all 30 balls comfortably— it can be done, but you have to position things just so. The center of the board features a 4x4 grid of ball-sized depressions.
Players take turns placing one of their balls onto the board. Once four balls form a 2x2 square, it becomes possible to place a ball on top of them in the center of the square. When this is possible, instead of playing a marble from off the board a player may elevate an already-placed ball to a higher level— provided no balls are already on top of the one being moved.
If a player forms a 2x2 square of marbles all of his color, he may immediately remove up to two of his marbles from the board. The removed marbles can't have any other marbles on top of them, but can include the marble just placed. The advanced rules also allow this removal for forming a line of 4-in-a-row (on the bottom level) or 3-in-a-row (on the next higher level) all of your color. We've found that this rule makes the game much more interesting and highly recommend it.
The winner is the player who places the last marble at the top of the pyramid. Said another way, the first player to run out of marbles is the loser.
Pyraos is straightforward and, unlike Quarto!, it's absolutely impossible to draw. We haven't yet determined whether or not one player has an advantage. The first player seems to win more often than not, but that could be chalked up to many factors. I'm sure someone more fascinated by the mathematics could do a detailed analysis.
Obviously, winning depends on having more marbles than your opponent. As a result, once you establish a lead it is to your advantage to assume as defensive a posture as possible, blocking all possible configurations which would allow your opponent to reserve their marbles. This isn't necessarily easy, which makes the game engaging.
Pyraos plays quickly and is simple to learn and teach, making it a great game to leave on the coffee table to trap visitors with. Which makes Pyraos and Quarto! unusual among abstract strategy games.