Laska
Rules,
Background,
Equipment,
Notation,
Openings,
Endings,
Advice,
Play, and
See Also
Rules
Laska is played on a seven-by-seven board,
using the corner squares and the other squares of that colour
(so on 25 squares of the available 49).
It uses eleven White counters and eleven Black counters.
The counters should
be ornamented on one side;
they start the game with the ornamented side downward,
and are turned over when promoted.
Taking : A taken counter is not removed from the board but placed
under the taking counter to form a column. If a column is taken, only
its top counter is added to the the bottom of the taking column. The
colour of the top counter determines the ownership of its column.
( So if the second-to-top counter in a column is a different colour
to the top counter, that column will change owner if taken;
I call this a weak column. )
As in draughts, multiple takes can be made per turn.
Taking is compulsory; there is no huffing.
A multiple take ends on promotion.
If there is a choice of takes, it is a free choice.
Promotion : When the opposite side is reached, the counter (or the
top counter of a column) is promoted by being turned over; it then becomes
an officer and can move diagonally in any direction. The rank of the top
counter determines the rank of its column. Officers remain as officers,
even while buried inside a column.
The Result :
The game ends when one side cannot move, or has no pieces left.
Probably there should be some rule for a draw by repetition of moves,
or after a certain number of moves without a take.
Drawn positions do exist (see the Endings)
but seem to occur more rarely than in chess.
Background
World chess-champion Emanuel Lasker published the rules in 1911;
you can read them in PDF format
or transcribed into HTML.
The game achieved popularity in the 1920s
and has enjoyed some revival in the internet era.
See:
en.wikipedia.org/wiki/Laska
A variant also exists in which only single takes are allowed;
it has been called Bignor Ludus.
It also is an interesting game,
with a more strategic character then Laska.
Equipment
Counters can be made from Poker chips,
if the poker chip is ornamented with painted signs
like dots or the card suits.
If you take eleven white chips and eleven black (or red) chips
and can scratch off the ornamentation on one side using a sharp edge,
then you have an excellent set of Laska counters.
The white chips shouldn't show the scratching,
but the black chips may benefit from e.g. light brush of black ink.
A counter-diameter of 40mm looks good on a 50mm square.
Lasker suggested using different colours for promoted counters
(green for white counters, red for black counters).
This has the advantage that both players can see
the promotion-status of every counter in a column.
But it involves exchanging a promoted counter rather than just turning it over,
which can lead to mistakes
in which one player is left with more than eleven counters on the board.
So if Lasker's colours are being used,
I suggest keeping the unused white and green counters
and the unused black and red counters
in two neat columns side-by-side close to the board;
these columns should always have the same height.
If the usual turn-over promotion is being used,
then the player on move should have the right to look through a column
to check the promotion-status of its buried counters.
The board is 7x7 (a chess-board is 8x8).
The colour of the corner-squares should be chosen
to present the two counters with as equal a contrast as possible.
One option is to cut one row and one file off an 8x8 chessboard,
especially one of those flexible vinyl roll-up boards.
For symmetry you could also cut off any border around the other two sides.
Or, you can leave the chess-board unharmed
and hide the extra row and column during play;
most simply with a couple of strips
e.g. of leather, cardboard or plastic,
or, if the chess-board has a wide border,
through a 7x7-hole cut in a 9x9 sheet.
You can play laska at the command-line using
this Perl script,
which in turn uses the
Term::Clui
CPAN module.
To install, just save it to somewhere in your $PATH, call it
laska,
make it executable, and if necessary edit the first line
to reflect where perl is on your system.
Or, you can play laska right here in the JavaScript of your web-browser,
using play_laska.html.
Notation
-
I name the squares, in chess style, a1 c1 e1 g1 b2 d2 f2 a3
and so on up to f6 a7 c7 e7 g7.
Others,
including Lasker himself,
have used a 1-25 notation in draughts style.
-
I use the word piece to mean something that occupies a square:
either a single counter, or a column of counters.
-
The unpromoted counters are called w and b,
and the promoted counters (officers) are W and B,
-
A column is listed from the top down, e.g. WbbwB
belongs to White, but if it is taken there will remain bbwB
which belongs to Black.
-
A piece on a square is written in one word, with the square first
followed by the piece: e.g. a1w or g7b or d4WbbwB
-
A move is written in chess style, e.g. c3-d4
-
A take is written by mentioning all three squares, and again,
the piece or pieces indicate the state of the board after the take.
For example, starting with b2w and c3b
White will take as follows: b2-c3-d4wb.
Or, starting with d2wBw and c3WbbwB
White will take as follows: d2-c3bbwB-b4wBwW.
-
Annotations are mostly borrowed from chess:
a final ! means a good move,
? means a bad move,
!! means an excellent move,
?? means a blunder,
!? means an interesting move,
?! means a dubious move.
Freestanding comments include:
+- means White has a winning advantage,
-+ means Black has a winning advantage,
= means the position is equal,
1-0 means White wins,
0-1 means Black wins.
1/2 means the game is drawn.
Other comments should be inside parentheses.
-
The four squares e5, e3, c3 and c5
I call the inner ring.
The eight squares d6, f6, f4,
f2, d2, b2, b4 and b6
I call the outer ring,
-
In general, a Forsythe-Edwards-style notation should be used
to describe positions, e.g. the starting position is
b,b,b,b/b,b,b/b,b,b,b//w,w,w,w/w,w,w/w,w,w,w w
where the commas are necessary to avoid confusion caused by columns.
When there are few pieces on the board, a position can also be specified
by listing all the pieces on their squares, followed by who is to move;
see the Endings section for examples.
Openings
The starting position is symmetric,
so there are only three distinct first moves:
1. a3-b4 (or g3-f4),
1. c3-b4 (or e3-f4) and
1. c3-d4 (or e3-d4).
In the opening, the board is crowded,
and there are no officers able to move to and fro,
so waiting-moves are scarce.
Since waiting-moves often make the difference between
survival and immediate defeat, they should not be squandered;
attacking a bare counter is better, and attacking a weak column better still.
-
1. a3-b4 c5-b4-a3bw (Wing-Gambit)
2. e3-d4
-
2... a5-b4 3. c3-b4-a5 e5-d4-c3
-
2... b6-c5 3. d4-c5-b6 a7-b6-c5
-
2... d6-c5 3. f2-e3 c5-b4 4. e3-f4 g5-f4-e3 5. d2-e3-f4 b4-c3-d2
6. e1-d2-d3 b6-c5 7. f4-e5-d6 c7-d6-e5 8. d4-c5-b6 a7-b6-c5
9. e3-d4 c5-d4-e3 10. d2-e3-f4 f6-g5
-
2... e5-f4 3. g3-f4-e5 d6-d5-f4
-
2... g5-f4 3. f2-e3
-
1. c3-b4 a5-b4-c3bw 2. d2-c3w-b4wb (Out-Out)
-
1. c3-b4 a5-b4-c3bw 2. b2-c3w-d4wb
(Out-In; in Brettspiele der Völker
Lakser calls this "The Hague Opening")
b6-a5
(or e5-f4)
3. d4-c5-b6wbb a7-b6bb-c5bw
4. e3-d4 c5-d4-e3bww
5. f2-e3ww-d4wb
(and now Black can choose between d6-c5b and e5-f4b)
-
1. c3-d4 e5-d4-c3bw 2. d2-c3w-b4wb (In-Out) d6-e5
3. b4-c5-d6wbb e7-d6bb-c5bw
4. e3-d4 c5-d4-e3bww
5. f2-e3ww-d4wb b6-c5
6. d4-c5-b6wbb a7-b6bb-c5bw
(and now White can choose between c3-b4 and c3-d4 or a waiting-move)
-
1. c3-d4 e5-d4-c3bw 2. b2-c3w-d4wb (In-In)
-
2 . . . f6-e5
3. d4-e5-f6wbb g7-f6bb-e5bw
4. c3-d4 e5-d4-c3bww
5. d2-c3ww-b4wb d6-e5
6. b4-c5-d6wbb e7-d6bb-c5bw
7. e3-d4 c5-d4-e3bww
8. f2-e3ww-d4wb b6-c5
9. d4-c5-b6wbb a7-b6bb-c5bw
(and now White might choose between e3-f4 or a waiting move like g1-f2)
-
2 . . . c5-b4
(in Brettspiele der Völker
Lakser calls this "The Berlin Defence")
-
2 . . . d6-e5
3. c3-b4 !?
-
3... a5-b4-c3 4. d2-c3-b4-c5-d6 e7-d6-c5 5. c1-d2!
-
3... e5-d4-c3 4. b4-c5-d6 e7-d6-c5 5. d2-c3-b4 d4-c3-b2
6. a1-b2-c3
Endings
In the endgame, the play tends to be dominated by officers;
the following study-examples use only officers.
The oppostion is very important, as with King-endings in chess.
In these examples, White has the advantage.
-
a1WWW b2BBB, White to move wins
in a leap-frog:
1. a1-b2BB-c3WWWB b2-c3WWB-d4BBW
2. c3-d4BW-e5WWBB d4-e5WBB-f6BWW
3. e5-f6WW-g7WBBB 1-0
-
If White has the oppostion,
the same process takes place, albeit three times slower:
a1WWW d4BBB, White to move wins:
1. a1-b2 d4-e5
2. b2-c3 e5-d6
3. c3-d4 d6-e7
4. d4-e5 e7-d6
5. e5-d6BB-c7WWWB d6-e5
6. c7-d6 e5-d6WWB-c7BBW
7. d6-c5 c7-d6
8. c5-d6BW-e7WWBB d6-e5
9. e7-d6 e5-d6WBB-c7BWW
10. d6-c5 c7-b6
11. c5-b6WW-a7WBBB 1-0
-
If your column is weakend by counters of the other colour
(or more so than that of your opponent),
then even the opposition is insufficient for survival.
c3WWWBB c5BBW, White to move wins:
1. c3-d4! c5-d4WWBB-e3BBWW
2. d4-e3BWW-f2WWBBB e3-f2WBBB-g1BWWW
3. f2-e1 g1-f2
4. d1-e2WWW-g3WBBBB 1-0
-
Often, one strong column can beat two weak ones, e.g.
c3BW c5BW e3WWBB, White to move wins:
1. e3-d4!
(not 1.e3-d2? c3-d2WBB-e1BWW and White doesn't have enough space to recapture
2.d2-c3 e1-f2 3.c3-d2 c5-b4 4.d2-e1 f2-e3 0-1)
1... c3-d4WBB-e5BWW
2. d4-e5WW-f6WBBB c5-b4
3. e5-d4 b4-a5
4. d4-c5 1-0
-
More complicated positions can often be decomposed into simpler parts, e.g.
a3W e5W a1B b6B, White to move
consists of two (more-or-less) separate oppositions:
1. e5-d6 b6-a5 2. d6-c7! a5-b4 3. a3-b4-c5WB a1-b2 4. c5-b4 1-0.
But often the parts are close together, and interact...
-
c3W e5W c5B e3B, Black to move loses.
1... e3-d4
(if Black just retreats he gets split into two separate oppositions,
so he tries the fork)
2. c3-b4! d4-e5-f6BW 3. b4-c5-d6WB f6-e7 4. d6-e5 1-0
-
c3W c5W e3B e5B, Black to move can draw.
1... e3-f4 (White has the oppostion, so Black must give way;
he must avoid becoming separated)
2. c3-d2 (not 2.c5-d4? f4-g5 0-1,
which shows why the inner-ring squares c3,c5,e3 and c5 are so useful;
this tactic is the main hope for the player without the opposition)
2... f4-g3 3. d2-e1 (White would like to play d2-e3, but 3.d2-e3? e5-d4 0-1)
3... g3-f4 4. e1-f2 f4-g3 5. f2-e1 g3-f4
and White can make no progress.
-
d2W d4W f2B f4B, Black to move can draw.
1... f2-g3 (White has the oppostion, so Black must give way;
not 1...f2-e1? 2.d4-e3 e1-d2-c3BW 3.e3-f4-g5WB 1-0
because opposition is conserved in this kind of exchange)
-
2. d2-e1 f4-g5 3. d4-e3 g3-f4 4. e1-d2
(not 4.e3-d4? f4-e5 0-1 nor 4. e3-d2? f4-e3 0-1)
4... f4-e5
and White can make no progress.
-
2. d4-e3 f4-g5!
(not 2...f4-e5? 3.e3-f4 e5-d4 4.f4-g5 d4-e5
[4...d4-e3? 5.d2-e3-f4WB g3-f4B-e5BW 6.g5-f4-e3WB 1-0]
5.d2-e3 e5-f4 6.e3-f2! 1-0 or 5...g3-f4 6. e3-d4! 1-0)
3. d2-c3 g3-f4 4. e3-f2
(not 4.e3-d4? f4-e5 0-1 nor 4.e3-d2? f4-e3 0-1)
4... f4-g3 and White can make no progress.
-
d2W d4W d6W f2B f4B f6B, Black to move can draw.
With three counters each, there are plenty of traps:
1... f2-g3 (not f2-e1? 2.d4-e3 1-0, so Black must give way)
2. d4-e3 (not 2.d2-e1? f4-e5 0-1)
2... f4-g5 (not 2...f6-g5? 3.d2-e1 1-0,
nor 2...f4-e5? 3.d6-e5-f4BW g3-f4B-e5BW 4. e3-f4-g5-f6-e7WBB 1-0)
3. d6-e7 (not 3.e3-d4? f6-e5 0-1, nor 3. d2-e1? f6-e5 0-1)
3... f6-e5 (not 3...g3-f4? 4.d2-e1 1-0)
4. d2-c3 g3-f4 5. e3-d4 (5.e3-d2 f4-g3 6.d2-e3 g3-f4 gets nowhere)
5... e5-f6 6. c3-b4 (not 6.e7-d6? f6-e5 0-1)
6... f4-e5 7. d4-c5 e5-f4
(or e5-d6 8.c5-b6 d6-e5 9.b6-c7 e5-f4 10.c7-d6 reaches the same position)
8.c5-d6 f6-e5
and White has made no progress.
-
a1Bw c1WwbBb f2B b4BB f4B b6b d6b a7B, White to move wins.
This amazing example comes from Lasker himself.
1. c1-b2! a1-b2wbBb-c3BwW
2. b2-c3wW-d4wbBbB b4-c3W-d2BBw
3. c3-d2Bw-e1WB-f2-g3WBB-f4-e5WBBB-d6-c7WBBBb-b6-a5WBBBbb d2-e3
4. d4-e5 e3-f4
5. e5-d6 f4-e5
6. d6-e7WbBbB e5-d4
7. e7-d6 d4-e3
8. d6-e5 e3-d2
9. e5-d4 d2-e1
10. d4-e3 1-0
Advice
A 7x7 board (since 7 is odd)
has a centre-file, a middle-rank, and a centre-square (d4).
-
Avoid wasting free moves;
in a fight over opposition one extra free move will win.
-
Wherever possible, divide the board into up to four Quadrants,
based on minimising direct tactical Quadrant-to-Quadrant interaction.
Quadrants will often be square,
because pieces sharing a diagonal can still interact.
Evaluate each Quadrant, more or less as a separate position, by:
-
Material, including officers, columns, weak columns, number of captives,
-
En-Prise especially multiple en-prise, and any forced Take-Backs,
-
Possible Moves, including opposition, mutual opposition, and free moves,
-
In the case of a blockade,
what balance of material is being kept out of play ?
-
An Attack-Take-Take against a single counter
brings a net material gain of one piece;
against a weak column it brings a material gain of two pieces;
but against a strong column it brings a loss of one piece.
The attaking piece must be a single counter,
unless you can safely re-take along the cross-diagonal.
-
There are two main Diagonals (seven squares long)
and four neighbouring Diagonals (five squares long).
Each of these diagonals can be the scene of an Attack-Take-Take battle,
with the winner being promoted.
The battles on these diagonals are to some extent independant,
but they cross on the five central squares.
-
Three pieces on a diagonal
are enough to attack the 5th, 6th or 7th rank.
-
Two pieces are enough to attack the 4th rank,
because the 1st rank is invulnerable.
Keep your 1st-rank counters in place as long as possible
(consider the start-position but with both 1st-ranks empty;
the player to move loses horribly).
-
Recognise different types of Quadrant-position,
and different types of Diagonal-position,
just as you recognise different words when reading.
-
The various Quadrants have effects that interact with each other,
and with the Diagonals,
just like the meanings of different words interact in a sentence.
-
If you can get control of a 4x4 Quadrant
then this guarantees you more space.
-
Often, a Quadrant becomes locked up,
but usually, one side holds the key;
then they can undo the lock whenever they choose.
If the keyholder has fewer counters locked up
then that gives them a material advantage elsewhere;
but even if locked-up-material is equal, holding the key is an advantage.
-
Lasker recommends
moving pieces towards the centre of the board,
and keeping the centre triangle c1d2e1 or c7d6e7 in their
starting-squares for as long as possible.
-
As long as a piece is on the edge of the board, it can't be taken.
-
In the endgame, if you have a weak column with several opposing captives
under one of your officers,
keep it in a corner and as out of play as possible.
-
In the endgame, with officers, space protects you against Zugszwang.
Conquer space using two pieces next to each other,
and if possible another coming in on the flank.
-
In the extreme endgame, number of pieces wins,
then column strength, then opposition.
See Also
-
The Rules of Lasca, the Great Military Game,
Emanuel Lasker, 1911; also
available in PDF
-
en.wikipedia.org/wiki/Laska
-
This
Lasca booklet by Ralf Gering
is the 21st volume of the 12-problem series,
published in the Facebook group "Popular Mindsports".
Other booklets are about Bashni, Stapeldammen and Focus.
-
The Perl script
http://www.pjb.com.au/laska/laska
-
www.lasca.org/
is a website about Laska by David Johnson-Davies,
developed from his previous site
research.interface.co.uk/lasca/about.htm
which originated from an article in Games & Puzzles.
-
Angerstein, Wolfgang :
Das Säulenspiel Laska: Renaissance einer
fast vergessenen Dame-Variante mit Verbindungen zum Schach.
In: Board Game Studies 2003 (Issue 5).
-
ascal.sourceforge.net
Ascal, a Gnome Lasca program, was programmed by Patrick Haase, Nils Kanning,
and Steffen Klemer while students at the University of Goettingen, Germany,
for an AI contest in the university course of C++ programming in Summer 2006.
-
An on-line version of Lasca is available at ig Game Center:
www.iggamecenter.com/
-
Laskers Manual of Chess, Dover Publications.
-
Brettspiele der Völker (1925).
-
Laska at boardgamegeek.com
-
en.wikipedia.org/wiki/Latrunculi
-
De Laude Pisonis (or Laus Pisonis)
probably by Gaius Calpurnius Piso
-
Les Jeux des Anciens by Becq de Fouquires
-
Steven Lomas, Postgraduate project, 1986 : Operating system design.
Steven wrote a programme to play Laska. It used a straightforward minimax
algorithm with lookahead, and performed quite well.
S. Lomas :
An intelligent Lasca game playing programme
(1986).
-
Graham Hood, Graduate Project, 1992 :
Artificial intelligence in playing board games.
Graham wrote a programme to play Laska. It could be used at various
levels of look-ahead, and its performance varied from blindingly fast
but stupid to excruciatingly slow but really rather clever. He had hoped
to experiment with different strategies, but unfortunately there wasn't
enough time. He did achieve a very smooth interface.
G. Hood : An intelligent Laska-playing programme (1992).
-
While a 2nd year student at UCL, Bruce Wilford wrote a Unix-based
Laska-playing program.
The program uses a quite standard mini-max technique, it grows the game
tree as it goes, so that moves are searched in the order that previous
moves suggested would yield the best results. It varies the lookahead
level based on available memory and time, so it plays fairly quickly.
The program should run easily under Linux.