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Havannah
Havannah, of all my games, has the simplest rules. It has been played very extensively, not only at
the games club "Fanatic" at the University Twente, the Netherlands, but throughout the mathematics
department, at the Go club and in fact all over the place. It has also been marketed by the german
company Ravensburger
in 1981 and even became 'game of the year'. But its commercial success remained moderate and it disappeared
from the market a few years later.
I never disputed Ravensburger's marketing strategy: they're doing a great job for well over a hundred years.
But I didn't agree either: the board was definitely too small and so were the stones. The point is that
manufacturers, if at all, prefer tactical games with simple rules and a one-dimensional strategy.
Take the countless five-in-a-row variants, or even
Havannah's tactical support act. There may be tactical problems in such games and they may not lack depth.
But there's no strategical dilemma. Havannah's image, taken from the box, was just that: a nice fifteen
minutes game & don't make a meal of it. I should have offered them Hexade, but I hadn't invented it yet.
Havannah is very much a strategical game. You can learn the rules in less than a minute, but it may take
you more than a year to develop comfortable strategical concepts. Its tactics, though not as manifold and
profound as those of Go, are beautiful and can be mastered up to perfection, but only in the context of its
double-edged strategy.
The basic strategical dilemma
The game had already been played for over a year on a daily basis in the mathematics department's
canteen by more than a dozen regular players, all
using what would later be coined snake strategy, with the emphasis on speed. That is:
players were inclinded towards moves that
would threaten to connect fast rather than sure. Then Roelof Moll, a local Chess player who had played only for
a few weeks, came and started winning consistently by following his Chess instinct and taking the center.
He didn't care for speed, he cared for safety. His reasoning was this: Havannah, of all games
that can end in a draw, has the smallest margin (which is true). Therefore a consistently good defense
must at some time turn into an attack.
It doesn't matter how 'fast' a group threatens to connect, if it's dead.
Cutting the opponent's groups from above (that is: from the center) limiting their options to at
most two sides and a corner, apparently without attacking, he eventually dictated the game towards
the center, where he had already established dominance. He proved that all our previous strategies
were in dire need of reconsideration. His contribution to Havannah, spider strategy
was a breakthrough that finally showed us the strategical dilemma:
Havannah is featured in R. Wayne Schmittberger's
"New Rules for Classic Games" (John Wiley & Sons, Inc. New York
- ISBN 0-471-53621-0).
Rules
- The game starts on an empty board. Players move in turn to place one stone on an empty cell.
White moves first
- The game is won by the first player to complete a ring or a bridge
or a fork. All of these are 'chains': closed connections of one color
- A ring is a chain around at least one cell
- A bridge is a chain linking two corners
- A fork is a chain linking three sides. Corners do not belong to sides
That's it. In "New Rules for Classic Games", Wayne states that a ring should
surround at least one vacant cell. This is not the case: the cell may be occupied by either
player.
Strategy & Tactics
The Safety versus Speed dilemma can be illustrated in a nutshell. Consider the diagram.
White 1 brings the intended connection one step closer, but isn't save: black can cut with 2.
White 3 is safe: without a simultaneous threat of a higher priority, black cannot cut. But white has not gained any tempo: he still needs two moves to connect.
From this example an inductive understanding may already emerge that
safety and speed tend to follow different routes!
This principle pervades
Havannah from the very basic tactics shown, to the intuitive realms of opening strategy.
One of the first strategic goals in Havannah is is the establishment of a frame,
a connection aiming at a ring, bridge or fork, that, though still incomplete, cannot be broken by
the opponent. Consider the next diagram.
Top left the five black stones are hovering above the top sides and the right side and white cannot prevent
black from reaching these sides. There seems to be a cutting point however, and indeed, white can
prevent a connection between the two stones on the left and the three on the right.
But in doing so he pushes black straight into victory, as can be seen top right!
Black 2 on white 1 is called a 'cup'. The stones 2, 4 and 6 not only threathen to connect up with the
existing stones but worse: if black insists on preventing this, they threaten a fast fork on their own!
Black's 'cut' has made his situation worse than it was. Therefore the initial five stones do in this
situation constitute a frame.
But not in any situation: at the bottom one white stone is added and now a cut is possible: white 7
is a ring threat that requires an answer, allowing white to jump with 9, effectively cutting and denying
black access to the left side and bottom left corner.
- Generally, whether a particular incomplete connecion is a frame, depends on tactics.
You've just seen an example
- If it is a frame, attacking it makes things worse.
The best defense is having a faster frame. If that's not the case you're in trouble
- The number of moves needed to turn a particular frame into a chain, also depends on a variety of
tactics, usually involving ring & bridge threats
There's much more to tell about Havannah, and some of it has found its way into
 .
You can also play online in there.
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