# Tag: games

COL is a map-coloring game invented by Colin Vout.
Two players Left (bLack) and Right (white) take turns in coloring the
map subject to the rule that no two neighboring regions may be colored
the same. The last player to be able to move wins the game. For my talk
on combinatorial game theory in two weeks, I choose for a simplified
version of COL, namely COLgo which is played with go-stoned on a
(partial) go-board. Each spot has 4 neighbors (North, East, South and
West). For example, the picture on the left is a legal COLgo-position on
a 5×5 board. COL is a simple game to illustrate some of the key features
of game theory. In sharp contrast to other games, one has a general
result on the possible values of a COL-position : each position has
value $z$ or $z+\\bigstar$ where $z$ is a (Conway)-number (that is, a
dyadic integer) and where $\\bigstar$ is the fuzzy game {0|0}. In
the talk I will give a proof of this result (there are not so many
results in combinatorial game theory one can prove from scratch in 50
minutes but this is one of them). Of course, to illustrate the result I
had to find positions which have counter-intuitive values such as 1/2.
The picture on the left is an example of such a position on a 5×5 board
but surely one must be able to find 1/2-positions on a 4×4 board
(perhaps even on a 3×3?). If you have an example, please tell me.

On a slightly different matter : I used the psgo.sty package in LaTeX to print the (partial)
go-boards and positions. If I ever write out the notes I’ll post them
here but they will be in Dutch.

The
game of sprouts is a two-person game invented by John Conway and Michael Paterson in 1967 (for some
historical comments visit the encyclopedia). You just need pen and paper to
play it. Here are the rules : Two players, Left and Right, alternate
moves until no more moves are possible. In the normal game, the last
person to move is the winner. In misere play, the last person to move is
the loser. The starting position is some number of small circles called
“spots”. A move consists of drawing a new spot g and then drawing two
lines, in the loose sense, each terminating at one end at spot g and at
the other end at some other spot. (The two lines can go to different
spots or the same spot, subject to the following conditions.) The lines
drawn cannot touch or cross any line or spot along the way. Also, no
more than three lines can terminate at any spot. A spot with three lines
attached is said to be “dead”, since it cannot facilitate any further
action.

You can play sprouts online using this Java applet.
There is also an ongoing discussion about sprouts on the geometry math forum. Probably the most complete
information can be found at the world game
of sprouts association
. The analysis of the game involves some nice
topology (the Euler number) and as the options for Left and Right are
the same at each position it is an impartial game and the outcome
depends on counting arguments. There is also a (joke) variation on the
game called Brussels sprouts (although some people seem to miss the point
entirely).

Some years ago I invented some variations
on sprouts making it into a partizan game (that is, at a given
position, Left and Right have different legal moves). Here are the rules
:

dots. Left is allowed to connect two White dots or a White and bLue dot
or two bLue dots and must draw an additional Red dot on the connecting
line. Right is allowed to connect two White dots, a Red and a White dot
or two Red dots and must draw an additional bLue dot on the connecting
line.

White dots. Left is allowed to connect two White dots or a White and
bLue dot or two bLue dots and must draw an additional bLue dot on the
connecting line. Right is allowed to connect two White dots, a Red and a
White dot or two Red dots and must draw an additional Red dot on the
connecting line.

Although the rules look pretty
similar, the analysis of these two games in entirely different. On
february 11th I’ll give a talk on this as an example in
Combinatorial Game Theory. I will show that Cold Antwerp Sprouts
is very similar to the game of COL, whereas Hot Antwerp Sprouts resembles SNORT.

As I am going to give a talk on Combinatorial Game Theory early
next month I have to update my rusty knowledge of canonical forms of
two-person game positions, their temperature theory and the like. As
most of the concepts in this field are recursive they are hard to work
out by humans but easy for computers. So it is nice to have a good
program to use. I remember that David Wolfe wrote a couple of years ago the Gamesman Toolkit but it seems he has taken it off
his website. Still, you can get it from the Software released by Michael Ernst page. So,
Then do the following

cd Desktop/games sudo make sudo cp
games /usr/bin/ /usr/bin/games

to get it up and
running (for documentation of how to use it see the Gamesman
Toolkit-paper above. But, it seems that as of July 2003 there is a much
better alternative around : the Combinatorial Game Suite of Aaron Siegel. It is an open source Java-program so it
runs on many platforms (including Mac OSX). Here is the way to get it
cgsuite-0.4-folder on your desktop. Then type

cd
Desktop/cgsuite-0.4 java -jar cgsuite.jar

and after a few
questions (including whether you want to be on the mailing list of the
project) the program starts up. It is very well documented with an
on-line manual which I have to read over the coming
days…

What then is all this WarWalking, WarDriving,
WarChalking and so on? In particular, why the aggressive
War-word in them ? From what I learned, the historical origin of
these terms comes from the 1983 movie “War Games” in which a
kid sets up his modem to dial numbers until it finds a computer to hack
leading inevitably to the US-army in total panic. This hobby created the
phrase WarDialing. In analogy, a person driving around in a car
with a laptop in search for wireless networks is said to be
WarDriving, if (s)he is on foot it is clearly WarWalking.
Because of the aggressive nature of the War-subword some people have
re-engineered an explanation :

WAR = Wireless
Access Reconnaissance

so let us hope this acronym
will catch on. Now then, what is WarChalking ? It was invented by
Matt Jones and the idea is that a WarWalker should write a symbol in
chalk on the wall nearest to the discovered Access Point describing its
nature (see picture on the left) : the first sign depicts an open
node, the next a closed one and the last one is a node with
WEP-protection (btw. WEP=Wired Equivalent Privacy). A lot
of people seem to take this fairly serious, there is even a webpage warchalking.org devoted to it on which you can
there had to be also an American site containing among other things a not
that active forum. Further, the unofficial HOW-TO of WarDriving may be
interesting. To me it all sounds as an excuse to buy a
laptop

We
have two old Macintosh Classics in perfect condition : one is the
first Mac-computer I bought back then and the other is one i adopted
when the mathematics department moved from UIA to our present place and
the secretary wanted to throw it away. But what can we do with them???
Well there seems to be a lot of potential : for instance you can turn
them into a linux-box of sorts, or you can get them to access the internet, some even claim they can be
turned into a webserver. And I think I once saw a page telling
how one could run OS X on a MacClassic (in fact really using it as an
external terminal to a working iMac) but I can\’t find the URL right
now. To me all this seems to be a bit pathetic, why use these nice
little boxes for something they can hardly handle and for which we do
have better equipmet around? So, what shall we do with those two
boxes?

Why not just do the things we used to do with
them back then : playing games (who did not play lemmings on a Classic?
or gnuChess), HyperCard applications, I even wrote a fair number of
TeX-files on a Classic. But as they have a harddisk of only 80Mb we have
to make choices, or dont we? Well, not really as I still have an old
SCSI 2Gig harddrive laying around (at the time 2 gigabytes seemed to be
an enormous amount of space and admit it, compared to 80Mb it is
enormous). So here is the plan : connect these two Classics via a
SCSI-cable to the externed 2 GB harddisk and load the disk with all
interesting stuff one can still find for 68k Macs.

Luckily there is a marvelous place for all these programs on the
interesting via normal means (that is an ordinary iMac) and dump it onto
the external HD so we can use the two Classic-boxes mainly to play games
(and there is a huge number of them on the archive). If you have better
uses for them, please let me know…

Some interesting URLs for low-end Macs :
– The
pure-mac Olden section
– Jag\’s house where older macs still
rock

– The Kids domain Black and White Mac Shareware page
and