Games of Strategy
These are games requiring only a pencil and a piece of paper
Sprouts
Sprouts starts with three (or more) dots on a piece of paper. The rules are as follows:
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The players take turns moving.
A move has two parts: drawing a line and making a new dot.
The line must go from a dot to a dot so that it does not cross another line and so that once
the line is draw, no dot has more then three lines coming out of it. The animated game marks
these used-up dots with red X's. You might want to circle used-up dots.
The new dot goes on the line the player just drew (this means it starts with two lines coming
out of it).
The winner is the last player to move. Notice in the animated game that there are two dots
that are not used-up at the end. They get marked with light blue X's because, even though
they are not used-up, you can't use them as the ends of a line without crossing another line.
As the animated game shows a line can go from a dot to itself as long as you don't break the
"three lines" rule.
The strategy in sprouts lies in using your lines to divide the paper up into parts that trap dots. It is
very hard to think through all the ways this came can come out because of the many different ways
it can divide up the paper. If the three dot game gets too easy four you, start with more dots. This
game is a good tool for building your sense of spatial perception on flat surfaces.
Pipelayer
Pipelayer is a game played with two grids of dots that are
offset from one another, as shown. We will call them white
dots. This examples has 6x7 and 7x6 grids of dots, but you
more or less as long as they leave each player with one
dimension. The long dimension should be one longer than
dimension. The rules are as follows:
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slightly
and black
can use
longer
the short
The players take turns moving by connecting two
dots.
A player can only connect dots that are adjacent horizontally or vertically and also only dots
of his own color. In the example the blue player owns the white dots and the red player
owns the black dots.
No move may draw across another move.
To win a player must make a continuous connection from one side of the board to the other
in the long direction for his color of dots. For the blue player in the example this is from left
to right; the red player is trying to connect top to bottom. The blue player wins the example
game and then his connecting path from left to right lights up yellow.
Capture
Capture is a two player game played on a grid of dots like the one shown
to the right. The players take turns connecting dots that are horizontally
or vertically adjacent. If a player can complete a square by connecting
two dots then they capture that square. You must draw another line after
making a capture. A player may, thus, make a large number of captures
in a single turn. After the last capture he must still connect two dots.
Most of the strategy in this game amounts to forcing the other player to
complete the third side of a square. Beyond that, one capture may allow
others and so you should work to arrange that you get the big chain of
captures.
It may be easiest to put the player's initials in the squares they capture. Of course the person who
captures the most squares wins.
Battleship game
The game is played on two square grids, one for each player. The grids are typically square, and the
individual squares in the grid are identified by letter and number. On one grid the player arranges
his own ships and records the shots by the opponent. On the other grid, the player records his own
shots.
Before play begins, each player arranges a number of ships secretly on the grid for that player. Each
ship occupies a number of contiguous squares on the grid, arranged either horizontally or vertically.
The number of squares for each ship are determined by the type of the ship. The ships cannot
overlap (i.e., at most one ship can occupy any given square in the grid). The types and numbers of
ships allowed are the same for each player. These may vary depending on the rules. A typical
arrangement would be:
1 aircraft carrier (5 squares)
1 battleship (4 squares)
1 destroyer (3 squares)
2 cruisers (2 squares each)
1 submarine (1 square)
Another arrangement would be:
1 aircraft carrier (5 squares)
1 battleship (4 squares)
1 destroyer (3 squares)
1 submarine (3 squares)
1 cruiser (2 squares)
After the ships have been positioned, the game proceeds in a series of rounds. In each round, each
player has a turn. During a turn, the player announces a list of target squares in the opponents' grid
which are to be shot at. If a ship occupies one of the squares, then it takes a hit. When all of the
squares of a ship have been hit, the ship is sunk. After the target list has been given, the opponent
then announces which of his ships have been hit. If at the end of a round all of one player's ships
have been sunk, the game ends and the other player wins. If all of both players ships are sunk, the
game ends in a tie.
The number of target squares that a player may shoot at in a given turn is determined by the
condition of the players' own ships at the beginning of the round. The player is allowed to target one
square for each square in his own ships which are not sunk. Thus with the ships described above,
the players would have 17 shots in the first round. As each ship is sunk, the player losing that ship
loses the corresponding number of shots. Thus with the ships described above, if the battleship is
sunk, the player loses 4 shots.
Variations
Many variations in the basic rules are possible, including the sizes of the grids, the numbers and
sizes of this ships, the numbers of shots allowed, and when hits are announced. Most of the variants
simplify the game, which is useful for younger players.
In one variant, the opponent announces a hit after each target square is given. This reduces the
challenge of guessing the locations of the ships.
In another variant, the number of shots allowed is reduced by each individual hit, rather than by
ships sunk. This reduces the benefit for locating ships precisely.
Mu Torere
Mu Torere is a blockade game played by the Ngati Maori people from the east cost of New
Zealand’s North Island. It is the only board game that the Maori people played before their country
was colonised.
Mu Torere Rules
· Each player always has four counters.
· They are placed on the board at the kewai – the end
points of the star.
· The middle – the putahi is left empty at the start.
· Decide which player goes first. A player may move one
counter to an empty space.
· You can only move to an adjacent kewai
· You can only move to the putahi if your counter is next
to one of your opponents.
The winner is the player who blocks all of their opponents
pieces preventing them from moving.
Try and think what configuration of counters would
prevent your opponent from moving.
Other similar games can be found at http://atschool.eduweb.co.uk/ufa10/games.htm
Jam
This is a Dutch game for two players. You need the game board shown below. It is easy to
draw if you want to play this on paper. You will need two different colour pencils
(highlighters are good to use).
The dots are towns. The 9 straight lines are roads going to and through the towns.
Each player takes a turn to colour over a
straight road (even though it may pass
several towns).
player to colour three roads going to or
the same town wins.
whole
through
The first
through
Does it matter which player goes first?
road is it best to colour first?
Which
What happens to the game if you add another
two?
road or
The following games all have a similar
and can be played using similar strategies.
structure
These are 2-player games requiring only a pile of counters or some other conveniently
sized objects (buttons, coins, matchsticks, stones, paper-clips, sweets etc.)
NIM
This is the best known of this type of game and has many variations. The form in which it
most often appears is as follows.
Arrange 15 counters into 3 groups of 3, 5 and 7.
Players take turns at taking out counters from these groups.
A players may take as many counters (but at least one) as he or she chooses, but all the
counters taken must be from the same group.
The winner is the player who takes the last counter (or counters).
Investigate the winning strategy using Binary - Click here
Bachet's Game
Put several counters down to make a single group.
Though almost any size of group can be used, between 15 and 25 counters make for a
reasonable game.
In their turns, players take 1, 2 or 3 counters from the group.
The winner is the player who takes the last counter (or counters).
Tsyanshidzi
Put several counters down to form two groups of different sizes (say a 13 and a 17).
Each player in turn may make one of the following moves - Take any number of counters
from one group or Take the same number of counters from both groups.
The winner is the player who takes the last counter (or counters).
Skittles
Arrange several counters in a straight line with each one touching (or assumed to be
touching) those either side.
In their turns, players may take out 1 or 2 counters from anywhere in the line, but 2 may
only be taken provided they are 'touching' each other.
The winner is the player who takes the last counter (or counters).
Lasker's Nim
Arrange 15 counters into 3 groups of 3, 5 and 7.
Each player in turn may make one of the following moves - Take any number of counters
from one group or Divide any one group into two groups.
The winner is the player who takes the last counter (or counters).
Grundy's Game
Arrange several counters into groups.
There can be any number of groups (from 1 upwards) and any number of counters
(greater than 3) in each group, but 3 groups with between 9 and 13 counters in each group
make a reasonable starting position.
Each player in turn has to divide any one group into 2 groups of different sizes (so a group
of 1 or 2 counters cannot be divided).
The winner is the last player who is able to make an allowed move.