# The line-of-sight game

Andrew Hamilton
Posers and Puzzles 25 Oct '08 19:48
1. 25 Oct '08 19:483 edits
This is a game I invented which I used to play with my brother:

The line-of-sight game (word count: 880)

This is a game with simple rules that typically only lasts 5 to about 15 minuets at most.

The game can be played on an ordinary chess board although it can also be played on a 10 by 10 board.
Each player has just four pieces (either checker pieces or chess pawn pieces can be used as pieces).
On an ordinary 8 by 8 chess board, the starting position for white’s pieces are a1, a7, g1 and g7 while for black it is b2, b8, h2 and h8. On a 10 by 10 board, the starting position for white’s pieces are a1, a9, i1 and i9 while for black it is b2, b10, j2 and j10

White goes first. There is no catching pieces in this game and no pieces are ever taken off the board.
No two pieces are ever allowed to be on the same square.

The object of the game is simple;
you must try and avoid being the first player that cannot do a legal move because the first player that cannot do any legal move looses the game.

In each go, with constraints, you can only move one of your own pieces and to a square that is next to it (either in front or behind or left or right or diagonally next to it). But you can only move one of your own pieces by moving that piece directly toward one of your other pieces and only if that other piece is either on the same row of squares or the same column of squares or the same diagonal line of squares as the piece you move and only if non of your opponent’s pieces is on any of the squares on that line of squares between the piece you want to move towards the other piece and that other piece. If there is an opponent’s pieces on one of the squares on that line of squares between the piece you want to move towards and the other piece of yours then that opponent’s piece is said to block the “line-of-sight” between the piece you want to move and that other piece of yours and this means you are not allowed to move it in that direction. In other words, to be allowed to move one of your pieces X in direction Y, if you imagine keep going in exactly direction Y from piece X and if the first other piece you meet is one of your own pieces, then that other piece is said to be in the “line-of-sight” of piece X and you are allowed to move piece X in direction Y by one square. But if do not meet any other piece or if you meet one of your opponent’s pieces first when going from your piece X in exactly direction Y then non of your pieces is said to be in the “line-of-sight” of piece X in that direction Y and you are NOT allowed to move piece X in direction Y.

For example, if white has two pieces on the same row on a4 and f4 and it is white’s go, then providing black has no pieces on the line of squares from b4 to e4 inclusive to block the “line-of-sight” then white either can move a4 to b4 or move f4 to e4.

That is all the rules -it is as simple as that! But there are various consequences of these rules:

1, Typically the game ends with all the pieces bunched up together around the centre of the board with one or the other player not having any room between the pieces to be able to make a legal move and thus looses the game.

2, Because no two pieces are ever allowed to be on the same square, if you have two pieces next to each other then obviously you are not allowed to move either one towards the other even if they are both your own pieces.

3, a highly desirable position to strive for would be to have one of your pieces X positioned so that it is in the line-of-sight of two other of your pieces but in opposite directions so that you can just keep moving your piece X back and forth between the two other pieces until your opponent pieces have their position exhausted. For example. If you position 3 pieces on a5, c5 and f5 then you can keep moving the one on c5 to d5 and then move it back again to c5 next go so just keep moving that same piece back and forth.

However, there is nearly always a way your opponent can block this by finding a way to move one of his pieces in the way of one of your line-of-sights.

4, draw is possible but rare -the only way the game can end in draw is in the unlikely outcome of BOTH players getting that desirable position where they can just keep moving the same piece back and forth but with NIETHER of the two played being able to place one of their pieces in the way and block a line-of-sight of the other.

5, there is no obvious “correct” strategy (-at least non that I can see).
2. 25 Oct '08 20:22
You are a very nice game creator. This is a very good game. Unfortunately, I do spend too much time solving games like this, and I fear I may be about to make this a lot less fun to play...

Second player can win by just doing rotational symmetry of the first players move each time. If the first player builds the perfect position, it's a draw.
3. 26 Oct '08 11:092 edits
Originally posted by doodinthemood
You are a very nice game creator. This is a very good game. Unfortunately, I do spend too much time solving games like this, and I fear I may be about to make this a lot less fun to play...

Second player can win by just doing rotational symmetry of the first players move each time. If the first player builds the perfect position, it's a draw.
…Second player can win by just doing rotational symmetry of the first players move each time. If the first player builds the perfect position, it's a draw....…

I hope you are wrong about that -I have to check it. If you are right then I must experiment with variations to these rules to prevent that while, at the same time, keeping the rules simple and, also, keeping the game likeable.

Can you give me an example of a series of moves that result in both players achieving the perfect position without either one being able to block the other’s perfect position? -I would like to analyse this. Non of my line-of-sight games that I have played have ever ended that way! -although, of course, I see no reason why one couldn’t end that way.
4. 26 Oct '08 11:50
sorry, I was wrong with "win"

I should have put "never lose"
5. 26 Oct '08 13:21
Sorry about double, last post was too distant to edit.

I think it may well be a win for the second player.
On a 4x4 board (the simplest possible) The rotational symmetry tactic clearly wins for the second player, as the first has only a 3x3 grid to work within, and cannot build the utopia position.
If we extend the board to a 5x5, then rotational can draw if the first player has his wits about him, so instead it becomes a question of whether or not the second player can drive the first towards a position which is basically the 4x4 grid. Playing a couple of games against myself, I see that this is actually very easy to do, but there doesn't seem to be set moves, which leads me to believe that the game is solvable, but only in the sense that checkers was - there is no reactionary win-algorithm, more a series of "what you should do if..."

Will carry on looking, but if this is the case, well done. Your game is brilliant.
6. 26 Oct '08 14:122 edits
Originally posted by doodinthemood
Sorry about double, last post was too distant to edit.

I think it may well be a win for the second player.
On a 4x4 board (the simplest possible) The rotational symmetry tactic clearly wins for the second player, as the first has only a 3x3 grid to work within, and cannot build the utopia position.
If we extend the board to a 5x5, then rotationa if..."

Will carry on looking, but if this is the case, well done. Your game is brilliant.
Thanks ðŸ™‚

I have experimented with hundreds of ideas for board games and the vast majority are “failures” but it is always interesting to analyse why each one doesn‘t “work” because that gives subtle clues to what might work.

I have invented another game (not one of my failures but one of the few “successful“ ones) called “acrids” that has a complexity somewhere between that for checkers and chess. The games tends to last a bit longer than those for checkers.
In this game, pieces can reproduce or “multiply” and the object of the game is to simply illuminate all your “live” reproducing opponent’s pieces and this is usually done by “bowing them up” by triggering a “chain reaction”.

With my dyslexia, it would take quite a few days on and off to tediously type all the rules out (I am very slow at this!) for “acrids” but I will try and find the time to do this and then I will post it in this forum when I have finished.