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        riddles >> hard >> I invented a new board game :-)
        
(Message started by: Yossarian on Jan 8^th, 2003, 10:48am)

Title: I invented a new board game :-)
Post by Yossarian on Jan 8^th, 2003, 10:48am

The new board game.

This game has very simple rules, but playing could be made as
complicated as needed. Using different boards and altering rules
it could be also made as easy as needed.This game could be used
for teaching math at school, just playing, training your favourite
AI engine or for a competition of ultra-intellectual players.
I'll give two descriptions of the game - the basic one, the way we
played it, and the formal one - for creating game variations etc.

1. The basic game
The board. The game board is a 7 by 9 grid of points, where checkers
will be placed. All points are connected with lines, and every line
has its numeric value, from 1 to 5, written on it.
The leftmost 7 and rightmost 7 points are called
home locations. So each player has its own set of home points, marked
as H and h. Here is an ASCII drawing of the board. Other points are represented by *

H-1-*-1-*-1-*-1-*-1-*-1-*-1-*-1-h | | | | | | | 1 3 2 1 2 3 1 | | | | | | | H-1-*-2-*-4-*-1-*-1-*-4-*-2-*-1-h |\ | /| | |\ | /| 1 5 5 5 2 1 2 5 5 5 1 | \|/ | | | \|/ | H-1-*- -*- -*-1-*-1-*- -*- -*-1-h | /|\ |\ | /| /|\ | 1 5 5 5 2 2 1 2 2 5 5 5 1 |/ | \| \|/ |/ | \| H-1-*-2-*-4-*-2-*-2-*-4-*-2-*-1-h |\ | /| /|\ |\ | /| 1 5 5 5 2 2 1 2 2 5 5 5 1 | \|/ |/ | \| \|/ | H-1-*- -*- -*-1-*-1-*- -*- -*-1-h | /|\ | | | /|\ | 1 5 5 5 2 1 2 5 5 5 1 |/ | \| | |/ | \| H-1-*-2-*-4-*-1-*-1-*-4-*-2-*-1-h | | | | | | | 1 3 2 1 2 3 1 | | | | | | | H-1-*-1-*-1-*-1-*-1-*-1-*-1-*-1-h

Checkers.
Checkers can be placed in all points, marked with *
and to home points. Each player has checkers of his color.
Every checker has a direction marker and its numeric value
(also from 1 to 5) drawn on it.
For this sample game, each set of checkers is :
1 checker marked '5'.
2 checkers marked '4'
3 -"- '3'
4 -"- '2'
5 -"- '1'

In the beginning of the game the board is empty. So the first
move should be placing one checker to any of the player's
empty home positions. It is not allowed to put checker on the
home position that is occupied with the checker of any color.
There are two rules about placing new
checkers : 1) if the player has no checkers of his color on
the board, he cannot pass and must place one. 2) if there are
only two checkers of the same value, but different color on
the board, the player may not move, but must place a new one.

Moving checkers.
Checkers can be moved from one point to the next point along the line,
connecting them. Also checkers can be rotated so that
its marker will point to another line. Each player in turn
can either move one checker to the next point or rotate it
in place or pass. Checkers can be moved in any direction, regardless
of its orientation, but only along lines on the board.

Taking checkers.
Each checker already on the board has its strength. The strength
depends on direction. In the direction of the marker on the checker
its strength = summ of its own value and the value of the line
in this direction. In all other directions the strength = maximum
of these values. Here is an example :

5
|
-2-(4)-4-[1]
|
3

(4) and [1] are the checkers and their values. If (4) points to
the west, it will have the following strength :
6 to the west, 5 to the north, 4 to the south, 4 to the east.
While moving, the checker can take other player's checker, standing
on its place, if its strength in the direction of the move is greater
than the strength of the other checker in opposite direction, i.e.
along the same line. In our example, if [1] points to the west, its
strength along the line, connecting two checkers is 1+4 = 5, so it
can take (4) in its move.
There is one note on moving checkers. If after moving the checker to
the new place you find that its direction has no line in its new place,
you should NOT reorient the checker. It must still point to the same
direction, and its strength in ALL directions will be max(ch.value,line.value)
Moreover, you can intentionally rotate the checker so that it will
not point to any line, but after next move(s) it will align with one.

The goal
There are two ways to end the game and to win - by taking all opponent's
checkers or occupying all his home points. When all home points are
occupied with other player's force, the game ends immediately.
In the case when there are two checkers of the same value left on the
board and no player has more checkers to place, the game also ends,
but nobody wins.

The complete description.
The game board is a graph with at least one special 'home' point
for each of N players. Each arc of the graph has a value of any
kind (natural number, complex number, matrix, whatever) associated
wit it. Arcs of every node of the graph has natural numbers associated
with them. Checkers are objects, having two properties : its strength
and direction. The direction is a natural number. There are also
two game functions : one for calculating strength in the direction
of the checker, another for any other direction. These functions should
take parameters of the same type as the corresponding strength and
produce the result of the same type.
There is one predicate, with two parameters of the type, which is
returned by the game functions. This predicate is used to decide,
whether the checker could be taken.

That's all, folks. I invite you all to play this game, to design
new boards, new game functions and predicates, and to analyse the game.
I still have no name for this game. One can think of
for example, checkers are tanks of different strength and lines are
landscape; but I do not like military thematic.

Is there a winning strategy ? Could the game come to stalemate ?
(one obvious case of stalemate is reduced by rules)

//Table changed to proportional font, and "New" removed from title by Icarus

Title: Re: NEW: I invented a new board game :-)
Post by Garzahd on Jan 8^th, 2003, 11:47am

You seem to be missing some edge strengths on the 3rd and 5th lines.

Seems that the game would very easily reduce to stalemate. Putting your 5er on a 5 edge makes it completely indestructible; it'd also be pretty hard to nail on a 4 edge. The 3/3 points are extremely well defended; drop a 3+ strength guy on one, pointing diagonally home towards row 4, and you're pretty cleanly barricaded against most assaults.

The game also seems very slow moving, since rotating a piece counts as a move. And of course, this would be the primary stalemate mechanism.

Are you permitted to rotate a checker to a direction where no edge exists? If so, that would present a slighly better argument against the game being a stalemate, I think.

Perhaps the game needs something analogous to the spy in Stratego; a unit with 0 strength who has the special ability of killing the 5er (on offense only).

Title: Re: NEW: I invented a new board game :-)
Post by James Fingas on Jan 8^th, 2003, 1:38pm

Garzahd,

I'm not sure about a 5-strength piece being so indestructible. You could gang up on it by having two smaller pieces pointing at it along two different edges. In order to keep from being taken, the 5-strength piece has to take one of the smaller pieces (because it can't point at both of them at once).

However, taking one of the smaller pieces means it has to move out of its position of strength, and in fact it's possible to guard the smaller pieces so that the 5-strength piece can't safely take them.

I think it's safer to keep your 5-strength piece off of the (3,3), (7,3), (3,5), and (7,5) locations. If the only edges pointing at a 5-strength piece have strength 1, then that piece can only be taken by your opponent's 5-strength piece.

Title: Re: NEW: I invented a new board game :-)
Post by Garzahd on Jan 8^th, 2003, 5:04pm

Oh, I misread the rules. It took me about 3 reads to figure out that the defensive strength of a piece isn't symmetric from all sides. That does make things somewhat more interesting.

So then the sea of 5-edges around home isn't terrible defensible; an enemy 1 prowling through the area (pointed properly) could wipe the proverbial floor unless the opponent kept each defender pointed at the 1.

It seems that one can still trivially force a stalemate by dropping their 5 on a home space. (Personally, I wouldn't have my 5 barging around the board until I got a better handle of how useful they were on attack.)

Title: Re: NEW: I invented a new board game :-)
Post by redPEPPER on Jan 9^th, 2003, 3:20am

For clarity purposes, the board in a proportional font:

Code:

H-1-*-1-*-1-*-1-*-1-*-1-*-1-*-1-h
| | | | | | |
1 3 2 1 2 3 1
| | | | | | |
H-1-*-2-*-4-*-1-*-1-*-4-*-2-*-1-h
|\ | /| | |\ | /|
1 5 5 5 2 1 2 5 5 5 1
| \|/ | | | \|/ |
H-1-*- -*- -*-1-*-1-*- -*- -*-1-h
| /|\ |\ | /| /|\ |
1 5 5 5 2 2 1 2 2 5 5 5 1
|/ | \| \|/ |/ | \|
H-1-*-2-*-4-*-2-*-2-*-4-*-2-*-1-h
|\ | /| /|\ |\ | /|
1 5 5 5 2 2 1 2 2 5 5 5 1
| \|/ |/ | \| \|/ |
H-1-*- -*- -*-1-*-1-*- -*- -*-1-h
| /|\ | | | /|\ |
1 5 5 5 2 1 2 5 5 5 1
|/ | \| | |/ | \|
H-1-*-2-*-4-*-1-*-1-*-4-*-2-*-1-h
| | | | | | |
1 3 2 1 2 3 1
| | | | | | |
H-1-*-1-*-1-*-1-*-1-*-1-*-1-*-1-h

Title: Re: NEW: I invented a new board game :-)
Post by Yossarian on Jan 9^th, 2003, 3:38am

I'm sorry I had to write rules in such long and hard to
understand manner. English is not my native language.

Correct, leaving 5th in the home place and not moving them
leads to stalemate in this board.

To take out 5 there should be at least two paths to
the point where it stands.

Title: Re: NEW: I invented a new board game :-)
Post by william wu on Jan 9^th, 2003, 12:40pm

Interesting. Out of curiosity, what motivated you to make this game?