*STAR 

Copyright (c) 1980s/90s? Craige Schensted, Kadon

*Star is played on the following board:
 
  • DEFINITIONS
    • PERI - A cell from the board edge. There are 50.
    • QUARK - Each one of the five corner peries.
    • STAR - A connected group of stones of the same color that owns two or more peries. A group owns all the peries that it occupies plus the peries it surrounds that do not belong to another (inner) star.
  • TURN - At each turn, each player drops a friendly stone on an empty cell.
    • It is invalid to drop a stone on the middle cell (shaped as a star). This special cell establishes a virtual connection among all adjacent cells. 
  • GOAL - Wins the player with the highest scoring. The scoring is equal to A + B, where:
    • A = the number of peries the player owns
      • If the player owns at least 3 quarks, he gets an extra peri point.
    • B = 2 * (the number of enemy stars minus the number of friendly stars).

Notice that parcel B means the less stars a player has, the better. So, one goal is to connect the friendly stars together. The other goal is, of course, to maximize the number of owned peri.

 Peri Ownership [diagram from here]

In the diagram, there are two black groups but just one star. The upper group only owns one peri, so it is not a star. The only black star owns 3 peri.

White has only one group which is a star since it owns 5 peri (including the peri occupied with a black stone). The white star does not own the peries owned by black's inner star. This white group also owns a quark (since it owns a corner peri).

Score Example [diagram from here]

White has just one star, with 7 peries and 2 quarks. Black has three stars: (i) one with 8 peries and 2 quarks, (ii) one in the left with 3 peries and 1 quark, and (iii) another on the top with 2 peries. So, White owns 7 peries and Black 14 (including the extra peri for owning 3 quarks).

White has one star while Black has three, so parcel B is +4 for White and -4 for Black.

White gains 7+4=11 points, Black gains 14-4=10 points. White won the game.

The author says about this example: Note that the Black star which owns only two peries does not benefit Black at all. The negative "reward" Black gets for having another star exactly cancels out the two peries. The score would be exactly the same if White occupied one or both of these cells, or if neither player did. This is a positive feature which sets *Star apart from Star. Such a "trivial", easy-to-make star is worthless in *Star, whereas it is worth one point in Star.
 

Words from the author: *Star evolved from other connection strategy games. It is the end product of the evolution from Hex to Y to Poly-Y to Star to *Star. [...] *Star is a deep game with many levels of skill. A game between players at very different levels would not have the same tension and excitement as a game between equals, unless ... Fortunately *Star can easily be balanced between players of different ability without distorting the game. [...] There are two main ways of balancing the game. The *Star version of what Go players call "komi" is the first and simplest. Give a komi to the weaker player by adding one or more points (depending on the difference in skill) to their score and subtracting the same number of points from the stronger player's score (to keep the sum of their scores 51 points).

Check Kadon's website for much more information about the game, including tactical and strategic advises.