## New abstract game : winning strategy?

Decision and strategy, simulations and probability models, card and board games, ...
Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### New abstract game : winning strategy?

Hi everybody,

Here is my new game :

I want to know if there is a winning strategy or if the players play optimally the game will lead to draw.

Thank you for any comment.

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

Maybe it needs long time to answer to my question.
Anyway are the rules clear ?
Is the game interesting?
Thank you for any feedback

hk
Posts: 10488
Joined: Sun Mar 26, 2006 9:34 am
Location: Haren, Netherlands

### Re: New abstract game : winning strategy?

Or is that the game?

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

hk wrote:I can't view your image.
Or is that the game?
I do not understand but I can see the picture without any problem.
You can try an external site where I posted the game under another nickname

http://www.mymathforum.com/viewtopic.php?f=24&t=27315

thundre
Posts: 356
Joined: Sun Mar 27, 2011 9:01 am

### Re: New abstract game : winning strategy?

hk wrote:I can't view your image.
Or is that the game?
The PE server says "The selected attachment does not exist anymore."
This part of the URL keeps getting deleted when I add it: &sid=805a95f54249eb9c81f03e5cf74ae328
I think I understand the game. Maybe I can explain the rules better.

Two 4x4 boards. Each player has one "home" board. He starts out with 3 pieces in 3 corners of his home board and 1 piece in 1 corner of the other player's home board.

On each turn, each player must move one piece on each board. Pieces move one square horizontally or vertically, so 4 possible directions, and they cannot move onto other pieces.

If a player cannot move his visiting piece, he loses. So the objective is to surround your opponent's piece on your home board (and also prevent your opponent from doing it on the other one).

Can surrounding always be accomplished? I think so. Move your 3 pieces into the center and drive the visitor onto the edge, then pen him in.

Which player can accomplish it faster? Intuitively, the first player has a half-move advantage. But there could be a parity issue that costs him a move.

There are 7280 possible board states. It shouldn't be too difficult to analyze completely.

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

Thanx a lot for your explanation.
You did it better than me.
Trapping your opponent is always possible but what is the required number of moves to do it in the worst case?
I created 2 variants :
-one with 6 against 3.
-the other with numbered pawns (it is the complex one)

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

When connected I have no trouble seeing the picture.
What's the problem? I do not know.

rayfil
Posts: 1403
Joined: Sun Mar 26, 2006 4:30 am
Contact:

### Re: New abstract game : winning strategy?

I can see the pictures correctly. I'm using IE8 under WinXP.
When you assume something, you risk being wrong half the time.

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

It seems that the second player win if he moves smartly.

Alhazen
Posts: 94
Joined: Sun Feb 20, 2011 9:55 pm

### Re: New abstract game : winning strategy?

I will post another game soon.