Adam Boddison

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• Adam Boddison

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Objectives

• To understand what a strategy is.
• To learn how to play (and win!) some new games.
• To write down some strategies for the games we
  will play today.

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Os and Xs

• Take turns to put down O or X anywhere on a 6x6
  grid.
• If you get a winning line (3 in a row), then draw
  a line through them.
• The game ends when the whole grid is full.
• Winning lines cannot over lap.
• The person with the most winning lines is the
  winner!

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What is a strategy?

• A strategy is a set of instructions explaining
  what decisions to make.

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Os and Xs

• Is it better to go first or second?
• Should you try to get winning lines or stop your
  opponent from getting winning lines?
• Do you have any good tips for winning?
• Extension work Does your strategy still work
  with grids of different sizes?

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Nim 3-4-5

• Take turns to remove as many sticks as you want,
  but only from one row at a time.
• The person who picks up the last stick wins the
  game.

http//nrich.maths.org/public/viewer.php?obj_id12
74partindexre
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Nim 3-4-5

• Is it better to go first or second?
• Are there any winning positions?
• Can you guarantee a win?
• Extension work How does your strategy change if
  the person who picks up the last stick loses?

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Make 15

• Take turns to pick whole numbers between one and
  nine.
• Once a number is picked, it cannot be picked
  again.
• The first player to get exactly 3 numbers that
  sum to make 15 is the winner.

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Make 15
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2
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9
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Player 1
Player 2
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Make 15

• Is it better to go first or second?
• Are there any good or bad numbers?
• Is it better to try to win to try and stop your
  opponent from winning?
• Extension work Does your strategy still work if
  you change the target number?

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Traffic Lights

• On your turn you can either place a red counter
  in an empty space, or
• Swap a red counter for an orange counter, or
• Swap an orange counter for a green counter.
• The winner is the first player to get a row,
  column or diagonal of three counters all of the
  same colour.
• Remember, it is the person who completes the row
  that wins

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Traffic Lights
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Traffic Lights
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Traffic Lights
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Traffic Lights
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Traffic Lights
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Traffic Lights
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Traffic Lights
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Traffic Lights

• Is it best to go first or second?
• Which is easiest to get 3 red, 3 orange or 3
  green?
• Are there any winning positions?
• Extension work What happens if we introduce a
  fourth colour?

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Last Biscuit

• Begin the game with 2 piles of biscuits. One
  pile of 8 and another pile of 4.
• On your turn you can take as many biscuits as you
  want from one pile OR the same number of biscuits
  from both piles.
• The player who picks up the last biscuit wins the
  game.

http//nrich.maths.org/content/id/2656/LastBiscuit
.swf
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Squayles
Each player takes turns at removing any stick
along with all the others that touch it. For
example, if you chose the blue stick below, then
the six red sticks must be taken too.
Whoever takes the last stick wins the game. Try
to find winning strategies.
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Attack or Defend

• Take turns to move 1 counter of your own colour.
• You can move 1 square up, down, left or right,
  but NOT diagonal.
• You can only move into an empty space.
• To capture a counter, you can jump over it and
  land in an empty space.
• If a player cannot move, then the game is over
  and the player with the most counters left wins.

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Attack or Defend?
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Questions?