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The Glass Bead Game
A Modern Mancala
General
Mancala's are among the oldest boardgames known to man. They can be found in a huge variety of variants
and under many different names from South Africa to the Phillipines.
In his "New Rules for Classic Games" (John Wiley & Sons, Inc. New York - ISBN 0-471-53621-0),
Wayne Schmittberger remarks of the Glass Bead Game: "Christian Freeling has created a mancala-type game that
may make you want to forget all the previous ones you've seen". The reason for his enthusiasm lies in a
number new concepts I brought to the general principle and the way they interact.
- In traditional mancalas all beads are equal. Here they come as Gems & Stones.
- Gems have point value. They can be captured, but cannot capture
- Stones have no point value. They can capture, but cannot be captured
- Gems themselves range in value
- There are two mutually exclusive ways to make a capture, direct & indirect.
Both allow for single as well as multiple captures
These concepts, among other things, make the order in which the beads of a particlar pit are distributed,
totally irrelevant in usual mancala's, an important issue. The strategical and tactical implications allow
for a drastic reduction in the material needed. The Glass Bead Game is not only deeper and wider and more
strategically and tactically rewarding than any other mancala, but also considerably smaller.
Rules
The board consists of two rows of five 'pits' and two 'cups' for collecting captured beads.
There are two players, north and south. Each player controls the five pits on his side.
In the initial position each pit contains one stone and one gem, see diagram 1.
Diagram 1
Gems have the following pointvalue:
There are 30 points worth of gems in the game.
- Players move and must move in turn. On his turn a player selects a pit on his own side of the board,
picks up all the beads in it, and sows them, one at the time, into the other pits around the board,
moving in a counter-clockwise direction
- While sowing, a player is free to choose which bead to drop in which pit. No pit may receive more than
one bead unless there are enough beads to go around the board more than once. No pit may be skipped except
that if the pit whose contents are moved contains more than nine beads, the original pit is skipped.
Thus the tenth bead is sown into the same pit as the first, and any additional beads continue to be sown
counterclockwise, as usual
Capture
- If the last bead sown is a stone that falls into a pit on the opponent's side of the board, and
if that opponent's pit contained exactly one bead before the stone was placed there, the player making
the move makes a capture. It's irrelevant whether the single bead in the opponent's pit got there because
the opponent left it there, or whether it was placed there by the moving player as part of the same turn
(in a move that involved enough beads to go around the board and into the opponent's pits once again).
What is captured depends on the single bead in the final pit:
- If it is a gem, it is captured, which means that it is placed in the player's cup
- If it is a stone, the player may choose any gem from any of the opponent's pits and place
it in his cup. This is known as indirect capture. If there are no gems on the
opponent's side of the board, the player may choose any gem from his opponent's cup instead.
This makes that no gem is ever completely safe till the game is over. If the opponent's cup
is empty too, no capture is made
Multiple Capture
- If the last two or more beads sown are stones that fall into pits on the opponent's
side of the board, and if each of these pits (in an unbroken row counting backwards from the last)
contained exactly one gem before the stones were placed there, the player making the move
makes a direct multiple capture of all gems involved
- If the last two or more beads sown are stones that fall into pits on the opponent's
side of the board, and if each of these opponent's pits (in an unbroken row counting backwards from the last)
contained exactly one stone before the stones were placed there, the player making the move
makes an indirect multiple capture, which means that he may choose one gem for every pit involved,
from his opponent's pits. If there are no or an insufficient number of gems on the opponent's side of
the board, the player may proceed to choose any gems from his opponent's cup instead, till he reaches
the appointed number or till no more gems are available
To illustrate capture let's make a few moves from the initial position without asking strategical
questions as yet. As you see, pits are identified by the letters "A" to "E"
for south and "a" to "e" for north.
A move is noted down by the pit and the
sequence.
Stones have "0" for their mark. South begins.
Diagram 2
Diagram 2 shows the position after
It is south's turn and pit D is under attack from pit e.
The third move of south and the answer of north are both indicated. In this particular
opening south's third move, 3. D0,
is quite obvious, not only because of the threat of an indirect capture, but because it
simultaneously adds to pit E, which is of prime strategic importance! North answer is less obvious.
Consider the situation after the indicated moves:
Diagram 3
In diagram 3 it's again south's turn. If he moves
4. E1000 he captures a green gem in pit d. It's not a multiple capture, because pit c contains a stone, not a gem,
and direct & indirect capture don't mix. Nevertheless, why doesn't he? And why does he play
4. C304 instead, exposing the blue gem
in pit D to capture by north's pit e?
The answer is: strategy! You don't go for the small stuff. Sacrificing a gem or two is well worth
the investment if it allows you to sow a HOUSE. But before I come to that I'll return to
the rules with an obvious question: what happens if the player to move faces five empty pits?
- If a player empties his last pit while there are still gems in play, the opponent on his next turn
is obliged to 'feed' him at least one bead
Start of the Endgame
When all gems have been captured, the endgame starts. With only stones in play, indirect capture
from the opponent's cup is the only means to alter the score.
Players now are no longer under the obligation to feed an opponent who ran out of beads, but quite contrary
find it their prime target, provided they have enough points.
Object
A player can only win in the endgame. He does so when he has at least 15 points and his
opponent, to move, has no beads in any of his pits. 'Emptying' the opponent while having less than 15
points is not illegal, but loses the game. Draws cannot occur.
Strategy - the concept of a House
The most important strategical concept in the Glass Bead Game is a house.
A house is a pit with enough beads to go all around the board and enter the opponent's pits
a second time. For reasons yet to be explained, a house is always build in the rightmost cup.
Diagram 4
In diagram 4 it's north's turn. He has made some minor captures, but south has a house.
If north moves pit e south will move pit D, dropping the thirteenth bead
in the house and after north d, south C and north e,
south will be able to sow a house of 14, the maximum available. Let's assume north doesn't like this scenario
and moves pit d. South now moves C2 and north must empty his last pit.
He moves e00521 and we're in diagram 5.
Diagram 5
The house holds 13 beads, which means it is aimed at pit d. A direct capture might look
like this:
Diagram 6
South moved E5431100000000.
He makes a direct multiple capture of four gems worth 13 points and threathens a further indirect
capture with pit D, now aimed at north b. Could he have done better?
Consider the following indirect capture:
E0000511340000.
Diagram 7
This indirect multiple capture entitles south to choose four gems from north's pits and to proceed
choosing from his cup if these contain an insufficient number. In this case this means south must
satisfy himself with the three beads indicated. He now has 12 points, but north has none!
This obviously is better than the direct capture of diagram 6.
Of course there are other options to consider and other considerations to make.
The position resulting from the capture is one of them: does it hold immediate threats or possibilities
to recapture? Are the tempo conditions unfavourable? Things like that.
Defense against a House
In order to be effective, a house must be aimed at empty pits. Houses may fail against a good defense.
Consider diagram 8.
Diagram 8
With south to move, he has no other option than a single direct or indirect capture in pit e,
the one the house is aimed at. There's no possibility for a multiple capture because after the move pit
d will contain three beads, breaking the sequence necessary for a multiple capture.
With north to move the situation is even worse for south: north's only option,
d2, defends pit e
against the house, so south must either sow it without making a capture, or overfeed it to impotence.
Tempo
It will be clear that tempo plays an important role here, there and everywhere in the game.
An illustration of the main principle involved is shown below. It concerns a very legitimate question
that you'll find yourself asking time and again: how many moves can I make inside my own pits so that
I don't have to feed my opponent (which would provide him with more tempo).
Diagram 9
In diagram 9 you'll find the answer to be 14. To do so, start with pit D
and proceed by taking the rightmost pit of the set A to D each time.
If, on the other hand, you were to start with pit
A, this would simultaneously mark the end of it!
This admittedly blunt example nevertheless illustrates basics. All other considerations and refinements
of strategy and tactics revolve around it and interact with it. A player may speed up the game by moving
pits on the left, or slow down moving pits on the right, and the reasons may be strategical,
building a house, or tactical, like having to move a pit to avoid immediate capture.
The Endgame
Diagram 10
In diagram 10 north has just moved c000
and attacks pit A with both e and d.
A counter attack by moving pit D doesn't fix the problem because north would take 5
points from south's cup, while south would capture the last gem in play, see diagram 11.
Diagram 11
From south's point of view the problem is that he has 13 points and that he will lose if north succeeds
in leaving him without a move. This danger however is not immediate: tempo conditions are heavily in
south's favour. But he faces the task of feeding north in such a way that the latter cannot avoid a capture,
tipping the scale, and making sure north cannot recapture and making sure he can next leave north without
a move. This might prove problematic.
The alternative in diagram 10 is moving pit A, simultaneously
attacking pit e. From north's point of view this attack is no big deal: a one point
gem doesn't tip the scales, so he must make an indirect capture anyway. He might decide to allow it,
to prepare a little trap with d00.
If south now captures with B0000, we're in diagram 12.
Diagram 12
Tempoconditions now are in north's favour so eventually south will have to move pit
A and allow a capture that will tip the scales.
Endgames can be very complicated and a writing a good program, despite the obvious affinity
between mancala's and computers, may prove more difficult than one would anticipate.
There's much more to tell about the Glass Bead Game, and some of it has found its way into
 .
You can also play online there.
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