Friday, February 19, 2010

Results of Unofficial "Mini Tournament"

1-2. andrewP-   3 points
----- Zandor-     3 points

3.captncavern- 2 points

4-5. pim-           1 point
-----randrews-   1 point

[andrewP:  x/1/0/1/1]   [Zandor: 0/x/1/1/1]   [captncavern: 1/0/x/1/0]   [pim: 0/0/0/x/1]
[randrews  0/0/1/0/x]

Wednesday, February 10, 2010

Prohibition!

Don't bend the rules. You might find yourself inventing a new game!

Sunday, February 7, 2010

Games once evolved through what is now called gamesmanship. No course is now left for the "games designer" other than to be a charlatan- and to exercise his or her gamesmanship in the least offensive way.
Shipley 1979

Thursday, January 14, 2010

NOTE
When I submitted Mirador to Games I thought that the strongest opening moves were near the centre. This is clearly not the case. Opening moves are stronger near to a corner. The opening move in Fig.1, for example is good enough for the second player to have better chances by invoking the swap option.

A TWO PLAYER PENCIL AND PAPER GAME

Mirador is a connection game played on a 27 x 27 grid of small squares. It can be played on graph paper (by marking off a 27 x 27 area) using coloured pencils to indicate the placement of watchtowers, or miradors, each of which will occupy a 2 x 2 square.

Several factors combine to make this a very fast and unusual game: line-of-sight connection (which is a feature of Sid Sackson's game Network); graded placement (incorporating the use of micro squares); and equivalent goals- that is, either player can win by connecting the board edges either from north to south or from east to west.

A significant feature of the game is that players can use their opponent's placements to facilitate their own connections (see "Peeps" and "Leapfrogging" in the "Common Plays" section below). So, in trying to win the race to connect, you must check that the next move you plan to make doesn't inadvertently improve your opponent's chances more that yours.

RULES
Equipment
The grid begins empty. The 729 squares of the grid are called "micro squares".

Play
Players take turns, drawing one mirador per turn on the grid. Each mirador occupies a 2 x 2 array of micro squares. One player uses a red pencil, the other player uses a blue pencil. Four such placements, from the start of a game, are shown in Fig.1.

Swap Option
Red plays first, whereupon Blue may either reply as Blue, or decide to play as Red. Allowing this opportunity is necessary to prevent Red getting too favourable a game by opening with a central play. After the choice to swap or not has been made, the game takes its course with turns alternating until a player "declares" (see below).

Move Restrictions
A mirador may not be placed in which any portion of its sides touches the side of another mirador (regardless of colour). Diagonally adjacent placements are permitted, but only if the miradors involved are of the same colour.

Connection and Winning Connection
Diagonal adjacency is one for of connection. Another is simple adjacency to the side of the board. However, the main form of connection in Mirador is line-of-sight connection. This occurs when a mirador has an empty row or column of micro squares either between itself and a side of the board or between itself and a friendly mirador.

The mirador placed on red's first move has a tenuous line-of-sight connection with all four sides of the board. A connection of this find is broken, of course, if enemy miradors are placed so as to break the row(s) or column(s) of the line-of-sight.

If a situation arises in which the opponent has no legal move available to block the connection, then the connection is secure.

A winning chain is one that connects either pair of opposite sides of the board (north to south or west to east) and in which the connection is unstoppable. This will often- but not always- be composed of secure connections, as explained below.

Declaring a Win
After playing a move, a player may declare a win if he believes that , even after the challenge precess described belo, he will be left with either a north-south or an east-west connection. (A combination of both connections- a kind of "double win" is theoretically possible, but should be rare except in composed problem positions.)
Fig. 2


The Challenge Process
After his opponent has declared a win, a player may challenge. In many games this would be pointless. Fig.2 shows a win for Blue made up entirely of secure connections, making the win for Blue very clear. Fig.3 shows a rather different situation. Here there are a number of insecure connections to the north. Red, having just played the marked move, nevertheless declares, believing that breaking all the connections is not possible.

When a player wishes to challenge (as Blue does here) he is allowed to take as many succesive turns of play as he needs to try to break the connection. Fig.4 shows how, in this instance, Red's declaration was faulty. Blue has cut the winning chain, and has achieved this with just two accurate placements. Fig.5 shows the same position, but with Red's last play moved a micro square further north. Declaring would now be sound.

A declaring player is not obliged to indicate a particular orientation of connection that he regards as unstoppable, and, if he did so, this would not invalidate his winning with a different connection. In Fig.6, Blue has just played to the marked placement and declared. He has potential north-south and east-west connections. Red can challenge, and then stop, either of these (playing at A or B to stop the
north-south or the east-west connections respectively) but cannot stop both. A correct challenge wins.

Common Plays
Some types of plays are shown in the additional diagrams. As with all connection games , efficient moves achieve several objectives simultaneously, such as restricting the range of future placements.

Note on Graded Placement
Another angle on this is to place the game in the context of Golomb's work on "polyominoes". From this perspective each mirador is a square tetromino. Much finer graded placements would be possible, and would perhaps even benefit certain classes of game- as yet unexplored, in which square polyominoes could also be used. There are 676 possible placements for the first Mirador in this game. A game played on a 54 x 54 sized grid ,with 4x4 sized placements, would enable , at the outset 2,601 initial placements.