# Solid

Genres Board game Abstract strategy game 2 3+ 3-9 minutes YU Young-jun March 1, 2016 solidwar.com facebook

Solid(쏠리드) is an abstract strategy board game for two players. A game of Solid starts with an empty board. The main object of the game is to fill your territories with your color by surrounding the vacant areas of the board. It is also possible to change your opponent's color on the board by surrounding it. You can win the game by filling the whole area of the board with your color. Solid is made by two Go lovers.

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## Definition

The board is a plain grid of tiles(small squares). A player can point one empty tile on the board, then the color of the tile becomes the player's one.

Rule1. Two players(Blue and Red) take turns, pointing one tile on the board at a time, with Blue playing first.
Rule2. The surrounded tiles by a player is filled with the surrounding player's color.
Rule3. The player who fills the whole tiles of the board wins the game.

## Mathematical definition

The board is a plain grid of tiles(small squares). A player can point one empty tile on the board, then the color of the tile becomes the player's one.

Rule1. Two players(Blue and Red) take turns, pointing one tile on the board at a time, with Blue playing first.

Let $T$ be the set of small squares that fill the Solid board, and among these, let $B, R, E$ be the set of blue,red,empty ones. Then $|T|=|B|+|R|+|E|.$

definition1. for $a∈T, b∈T\$ if $a, b$ are neighboring and sharing one side then we denote $a|b.\ \ \forall a∈T$ we can denote $a|a$ for convenience.

definition2. for $A\subset T,a∈A, b∈A\$ if there exist a natural number $n$ and $a_0, a_1, a_2, ... ,a_n∈A$ such that $a=a_0,\ a_0|a_1,\ a_1|a_2,\ a_2|a_3,\ ...,a_{n-1}|a_n,\ a_n=b$ then we denote $a||b∈A.$

definition3. We say $a\ is\ surrounded\ by\ B\$if $|T| ≥ 2|\left\{x:a||x∈(R\cup E) \right\}|.$
We say $a\ is\ surrounded\ by\ R\$if $|T| ≥ 2|\left\{x:a||x∈(B\cup E) \right\}|.$

Rule2. When Blue plays,the color of $\left\{ a:\ a\ is\ surrounded\ by\ B\right\}$ becomes blue.
When Red plays,the color of $\left\{ a:\ a\ is\ surrounded\ by\ R\right\}$ becomes red.
Rule3. The player who fills the whole tiles of the board wins the game.

## Atari, Double atari

### Atari

Atari is a state where a tile or a group of tiles may be captured on the next move.

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### Double atari

Double atari is a state where both are in atari at once.

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## Continuous atari, Pin

Continuous atari and pin are the capturing techniques which are also used in Go.

### Continuous atari

Continuous atari is a capturing technique making series of atari.

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### Pin

Pin is a capturing technique that makes tiles may be captured on the next move, even if the owner plays first.

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Net and ladder are the capturing techniques which are also used in Go.

### Net

Net is a technique that can snare the opponent.

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Ladder is a sort of continuous atari, that remains fatal result.

## Pros and Cons

### Pros

#### easy to learn

You must practice for a very long time to learn Go, but it takes only 30 minutes to learn to play Solid.

#### delightful to capture

In human DNA, there has been a strong desire to capture the enemy since he has hunted animals since ancient times. Even nowadays, that desire is alive, and has been formed for hundreds of thousands years. It reveals itself in many games. It reveals itself in Go, and more powerfully in Solid. In Solid, capturing easier than in Go, and more delightful since the prisoner's nearby area as well as the captured prisoner are yours at once.

### Cons

#### may be a trivial game

The first player Blue has an advantage over the second player Red. In case of Go, they give komi to the second player White. Komi is a piece of territory added to the territory of second player at the end of a game as compensation for playing the latter. But in Solid, they can't do that. Because the winner always takes all the territory, komi is meaningless. They need another measure to balance Blue and Red. On the other hand, how much advantage does the Blue have by playing first? Would Blue always win easily? No one knows yet. But we can easily know that if Blue always wins, then the method must be making a crosswalk.

Crosswalk means a fence which divides the board into two about the same sized areas, from an edge to the opposite edge. Obviously, if a player makes a crosswalk then he wins the game. It is also obvious that the first player Blue has the higher possibility of making a crosswalk than Red. How much is the possibility of Blue making a crosswalk? No one knows yet. If someone proves that the possibility is 100% and finds out the method of making a crosswalk, then Solid unluckily becomes a trivial game.

#### less diversity

Solid has much less diversity than Go. There is no variety which arises in narrow and enclosed area, on the contrary to Go. To complete one game, there needs to be about 200 plays in Go vs. 100 plays in Solid.

### Alternatives

To prevent Blue from making a crosswalk, you may 1.set the forbidden area. 2.limit the number of playing. 3. modify the rule of capturing.

#### set the forbidden area

If the first player can always win, then you may consider setting a forbidden area on the board at which the first player can't play, to reduce the value of the first play. It must be around the center, intuitively. How many tiles around the center are to be in the forbidden area? No one knows yet. You need more research on the size of the forbidden area.

#### limit the number of playing

If Blue can always win then you may consider limiting the number of Blue playing. That is, if Blue cannot win within the number-limit, then Red wins. How large is the number-limit? No one knows yet. It may be the average of the play numbers out of many games of Solid. You need more research on the size of the number-limit.

#### modify the rule of capturing

You may consider the capturing rule to be more strict, like this. You can not change the color of the surrounded tiles whose number exceeds the number of your tiles. In that case, even if Blue has succeeded in making crosswalk, the game is not over immediately, and will go on for a while. Red can try to break the Blue's fence down during that time. To do that, you must modify above definition3 like following:
definition3. We say $a\ is\ surrounded\ by\ B\$if $|B| ≥ 2|\left\{x:a||x∈(R\cup E) \right\}|.$
We say $a\ is\ surrounded\ by\ R\$if $|R| ≥ 2|\left\{x:a||x∈(B\cup E) \right\}|.$

#### winning rate of Blue without any alternatives

(At the board of 19x19)

Blue wins 52.03%

Blue wins 56.68% if both rank > 1300

Blue wins 61.43% if both rank > 1400

Blue wins 77.78% if both rank > 1500

## Size of the board

• The size of the game board was 19x19. We had to make it as large as possible to prevent the first player always winning, also, 19x19 was the maximum size that can be displayed on a smartphone. The size of the game of the Go board is 19x19.
• But the winning rate of the first player is too high at the size 19x19. It reaches about 80% in the game of high-rankers.
• Hence, we set a limit on the first-playing to reduce its value. It seems to be suitable that the first-playing must be on the line 5 or 6.
• If we have a limit on the first-playing, we don't need 19x19. It's too large. It is inconvenient on the smartphone, and boring.
• If we limit the first-playing to the edge, then we can reduce the size to 15x15.
• If we limit the first-playing to the corner, then we can reduce the size to 11x11.
• It seems to be 15x15 that is the funnest size. Now, 15x15 is in the test.

## Version history

0.2.3 - MARCH 18, 2016

Changed: 1 -> S

0.2.2 - MARCH 16, 2016

Changed: nickname -> Enter new name

0.2.1 - MARCH 14, 2016

Added : The handicap of the Blue

0.2.0 - MARCH 10, 2016

0.1.4 - MARCH 7, 2016

Changed: records -> records_replay

Minor bug fixed

0.1.3 - MARCH 6, 2016

0.1.2 - MARCH 4, 2016

Minor bug fixes

0.1.1 - MARCH 2, 2016