Insert one of the following prepositions that will best suit the context: because, because of, in spite of, despite

1. In both instances one cannot just continually play a pure strategy like heads or stone ____ the opponent will soon catch on and play the associated winning strategy.

2. For two-person zero-sum games, the 20th century’s most famous mathematician, John von Neumann, proved that just ____ all such games have optimal strategies for both players they can be called fair games.

3. For example, for stone-paper-scissors one can toss a six-sided die and ____ the numbers tossed select either stone, paper or scissors.

4. It can be shown that heads-tails is a fair game ____ the same optimal mix of strategies that both players have.

5. Practise questions and answers. Ask your neighbour:

1. How many pure strategies there are for the game of coin tossing; for the game stone-paper-scissors?

2. What ways there are to control how to randomize?

3. What the optimal strategy is, given that the game is being played many times?

4. What fair games he/ she knows.

Give the main ideas of text “Strategies”. Retell the abovementioned text briefly using the main ideas as a plan of rendering.

Text 6

Before you read:

Have you ever had a chance to play any mathematical game? What king of game was it?

Read the text and outline puzzles and games mentioned in it. Try to solve some problems if possible.