Updated SEP4,01

*Star

This page is devoted to *Star, the latest game in the series (Mudcrack) Y, Poly-Y and Star, games by Ea Ea (that's me, previously known as Craige Schensted). *Star is what those other games wanted to be.

Kadon is planning to produce a beautiful *Star set this year. Mark Thompson is planning to host an Internet *Star tournament. If you would like to play *Star on the Web, go to the online page. The present page is a trial run for the booklet to go with the Kadon *Star set. Any suggestions are very welcome.

Rules for *Star

*Star is an abstract strategy connection board game for two players, the end product of the evolution from Hex to Y to Poly-Y to Star to *Star. It is played on the board shown here. The players take turns, each player on their turn filling in one cell (not previously colored) with their color. Of course, if the players continued to play until the board was entirely filled in, then the game would end at that point. But almost certainly the game will end with the players agreeing on what the score is long before the board is completely filled in.

Scoring

The 50 cells on the perimeter of the board (pericells) each contain one "peri". The 5 peries in the 5 corner pericells each have one "quark" associated with them. A player has two goals: to capture peries and quarks, and to connect "stars" together.

If a player has a connected region in their color which "owns" two or more peries, then that region is a "star". Both players can use the special star-shaped "bridge" at the center of the board to make a connection, but neither player may play in it. A star "owns" all of the peries which it contains and all of the peries which it encloses which are not owned by another star. In addition the player who has 3 or more of the 5 quarks gets an additional peri.

Each pericell on the perimeter of the board contains a peri, indicated on this figure by a little star. Here Blue has two groups. One of these groups is a star owning 3 peries, containing two and enclosing a third. The other blue group is not a star. It is a mere "spark" containing one peri. A group cannot "own" just one single peri. The peri which this blue group contains is owned by the red star which encloses it. The Red group is a star owning 5 peries and a quark (the player who owns the peri in a corner cell also owns the quark in that cell) --- containing 4 peries (and a quark) and enclosing the peri which Blue's spark contains.

There are several very different looking ways of scoring *Star which lead to exactly the same results as to who wins and by what margin.

I will discuss the latter two in more detail now.

Standard Score

You get one point for each peri you own (including the peri you might get for owning three or more quarks). In addition you get a "reward" for connecting your stars together equal to twice the difference between the number of stars the other player has and the number of stars you have.
Note that a "reward" is not always something you desire, as in "He got the reward due him for all of his evil deeds." Also note that the difference between Poly-Y, Star and *Star is that in Poly-y there is no reward for connecting stars together, in Star the reward is equal to the difference in the number of stars which the two players have, while in *Star the reward is equal to twice that difference.
Your "reward" is positive if the other player has more stars, and negative if you have more stars. In short your score is

the number of peries you own

plus (or minus) your reward.

The sum of the two player's scores is equal to the number of peries on the board (including one "quark peri") --- 51 on the "tournament" board, 31 on the "junior" board (the board heavily outlined with 7 cells along each edge in the middle of the tournament board). So the winning scores are 26 and 16 on the two boards.

Alternative Score

There is an alternative way of counting which the editor of Games magazine, R. Wayne Schmittberger, likes to use. His approach is to subtract his coplayer's score from his score. If you use this approach your score is

the number of peries you own

minus the number of peries your coplayer owns

plus (or minus) your REWARD.

Remember to count a "quark peri" for the player with more quarks.Your REWARD is your reward minus your coplayer's reward (which is the negative of your reward). So your REWARD for connecting stars together is four times the difference between the number of stars your coplayer has and the number of stars you have, positive if the other player has more stars, and negative if you have more stars. If you choose to use this method of keeping score then you win if your score is greater than zero, lose if it is less than zero.

Scoring Examples

In this example Blue has one star which uses the 5-pointed bridge in the center to connect two parts. This star contains and thus owns 7 peries and two quarks. Red has three stars. The large one using the bridge owns 8 peries (containing 5 and enclosing 3) and two quarks. Another Red star owns 3 peries (containing two and enclosing the third) and a quark. Red's third star contains and thus owns 2 peries.

All told Red owns 14 peries (including one "quark peri" because Red has 3 quarks). But Blue has been much more effective at joining stars together --- Blue has only one star whereas Red has three. Thus Red gets a "reward" of minus four. Red's score is 14-4=10. Blue gets a reward of plus four, so Blue's score is 7+4=11. Blue wins. As always on this small "beginner's board", the sum of the two player's scores is 21.

Note that the Red star which owns only two peries does not benefit Red at all. The negative "reward" Red gets for having another star exactly cancels out the two peries. The score would be exactly the same if Blue 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.


In the next example both players have 3 stars. Blue has a 2-peri star. But, unlike Red's 2-peri star in the previous example, this 2-peri star is not worthless because it also owns a quark --- which in this case is crucial because it gives Blue a third quark and hence one more point for the quark peri. Red also has a 2-peri star here which is not worthless because it separates two of Blue's stars. If this Red star were colored Blue then Red's loss of two peries would not be compensated by an increase in Red's reward as it was in the previous example because here, unlike the previous example, both players would have one less star. There is a Red "group" (of one cell) which contains just one peri. This is just a spark, not a star --- and the peri which it contains is owned by the Blue star which encloses it, which thus owns 5 peries. Red owns 10 peries. Blue owns 11 peries (including the quark peri). They have the same number of stars, so the rewards are zero and Blue wins, 11 to 10.


In the above two examples any of the unoccupied cells could be filled in by either player with absolutely no effect on the score, so obviously the game is over. However the players usually stop when both players can see what the score will be if both players play correctly. In the first example the game might have stopped at the point shown in this figure. Here if Red plays on any cell marked A, B, C or D then Blue can defend by playing in the other cell with the same label. And if Blue plays in any of the cells marked E, F, G or H then Red can play in the other cell with that label. The score will be the same as in the first example. These are examples of the "two-way stretch", one of the most elementary tactics.


On the left is a QuickTime movie of an example game due to R. Wayne Schmittberger. You will need the QuickTime plugin to play this QuickTime movie.With the button on the left you can see the game being played in about 10 seconds. With the buttons on the right you can step through the game move by move.

On the right is the final position in this game, and a second figure where additional regions have been filled in so as to make it easy to see what the score is. Red has 6 stars owning 27 peries and 3 quarks. Blue has 5 stars owning 23 peries and 2 quarks. Thus Red gets 27 plus one quark point minus a two point "reward" for a score of 26, while Blue gets 23 plus a two point reward for 25.

You will have a good grasp of basic tactics when you understand that, as far as scoring is concerned, these two figures are equivalent provided that the players are sufficiently competent. Of course strategy is something else.


The Pie Rule

It can be proven that, with correct play, the first player can always win --- but the proof does not give any hint as to what correct play is. Thus there is certainly a winning first play. Almost certainly there are losing first plays against which the second player could win with correct play --- in fact a continuum from the very strongest winning first play to the very weakest losing first play. By having the first play be right on the boundary between winning and losing we can balance the game almost perfectly between the two players. For even games we do this by using the pie rule --- I cut the pie and you choose which piece you want. "Cut" decides what the first move will be, "Choose" chooses whether to be the first or the second player. Choose can win with correct play, but the advantage is extremely small. In fact Cut has the opportunity to try to choose a losing first play that Choose will think is a winning play or a winning first play that Choose will think is a losing play.

No Matter What Level Your Skill

The Pie Rule is perfect when players are evenly matched. But *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. The game should be balanced so that the two players have nearly an equal chance of winning. This will make the game exciting for both players. Perhaps more importantly, this will allow both players to learn from the game (yes, even the stronger player). You can learn from the game if some of your moves "work" and some don't work. If the game is not balanced then all of the stronger player's moves "work" and none of the weaker player's moves work. So how is the game balanced?

N Points, N Stones

There are two main ways of balancing the game. The *Star version of what Go players call "komi" is the first and simplest. Add one or more points (depending on the difference in skill) to the weaker player's score and subtract the same number of points from the stronger player's score (to keep the sum of their scores 51 points).

The second way of balancing is for the weaker player to start the game with extra "stones" on the board (the game is commonly played by placing stones of two colors in the cells of a board). The best position for these stones is not well established, but a reasonsble choice would be S60, A60, *60, T60, R60, S30, A30, *30, T30, R30 in that order depending on how many stones are necessary (see Notation below).

When there is a very large difference between ths players, the stronger player should give advice in addition to balancing as above.

Notation

Here is a notation for the cells of the board which makes it easier to talk about board positions and to record games. The cells are given labels consisting of a letter (or an asterisk) and two numerical digits. The "letter" is *, S, T, A or R depending on which of the 5 sectors the cell is in. The first digit tells which ring the cell is in counting from the center 1, 2 ... up to 10, except that 10 is replaced by the single digit 0. The second digit goes from zero up to one less than the ring number, telling how far the cell is from one edge of the sector. If the second digit is zero then the cell is on a ray from the center to one of the 5 corners. If the second digit is half the first digit (remembering that 0 stands for 10) then the cell is on the line of symmetry halfway between two rays. The S corner is the cell S00, the S edge consists of the cells S00, S01, S02 ... S09 (and maybe also the cell T00).

*Star Tactics & Strategy

The Official Apocryphal History of *Star

Double *Star

KadonBooklet