DGame Task

Task 1 Task 2 Task 3 Task 4

Task 5 Task 6 Task 7 Task 8

Task 9 Task 10 Task 11

NC Level 3 to 8

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DGame Task 1

American Football

You will need a die and a counter.The picture below represents a football pitch, with the ball in the centre.

 

Throw a die. If the score is 5 or 6, A 'kicks' the ball towards B, 5 or 6 spaces. If the score is 1, 2, 3 or 4, B 'kicks' the ball towards A, 1, 2, 3 or 4 spaces.

Is the game fair?

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DGame Task 2

Roll two dice and work out the difference.

Is the game fair?

WIN StartLOSE

O,1 or 2 move left

3,4 or 5 move right

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DGame Task 3

Toss two coins and look at what you get. You need two tails to win. A game costs 5p. How much money should be given for a win?

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DGame Task 4

Tim has invented a game for 2 players, which he thinks is fair.

Player A has 2 coins, the first coin is numbered 1and 3, the second coin is numbered 0 and 4. He/she flips both coins and adds the 2 numbers together to get a score.

Player B rolls an ordinary 6 sided die.

The player with the highest score wins.

Is the game fair?

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DGame Task 5

Place counters on the squares numbered 2 to 12. Roll two dice and add to decide which player moves forward one square. The game should be played several times and discussion about the

fairness of the game encouraged.

http://nrich.maths.org/2491

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DGame Task 6

You buy a four sided fair dice and paint two of the sides red, one blue and one green. You charge your friends 15 pence for two throws. If the player throws a ‘double’ (the same colour twice) then they win 50 pence. If the player throws a mix (different colours) then they win nothing.

Is the game fair?

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DGame Task 7

A player rolls two dice and receives from the bank a prize of as many pence as the difference between his score and 7. What would be his expected winnings? Is 2p a fair price to charge each player for a single roll of the two dice?

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DGame Task 8

A game consists of three successive tosses of a coin. A player receives 5p for the first head, 10p for the second and l5p for the third. Therefore, if he gets two heads he gets 5p + 10p = l5p. If the game is free and it has to be fair how much should a player have to pay to the banker for getting no heads? How would you change this game if you were running it during a charity fund raising event?

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DGame Task 9

You select a number between 1 and 6, and stake some money.  

Three dice are rolled and you win if your selected number appears on any of the dice.

If your number appears once then you win the amount you bet. (And get your money back) If the number appears on two of the dice, then you win twice the amount you bet. (And your money is returned) If all three dice show his number then you wins three times the amount you bet. (Plus his stake back)

If your number doesn’t appear then you lose your stake money. Is the game fair?

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DGame Task 10

You will need two coins. This game is based on tennis but uses coins. There are two players, A and B. Each has a coin.

A serves by tossing a coin. If the outcome is heads H, the service is good; if tails T, there is a fault.Two services are allowed. H or TH give a good service; TT gives a double fault, and B wins the point. If the service is good, B tosses a coin.If the outcome is heads, it is a good stroke; if tails, the point is lost. This continues until the point is lost.  

Is it a fair game?

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DGame Task 11

This is a game for 3 players – we’ll call them A B and C.The game is played by rolling a single dice 

Round 1Player A rolls first. If he rolls a 1 he wins and the game ends. If he does not roll a 1 he passes the dice to player B.Player B rolls the dice. If he rolls a 2 or 3 he wins and the game ends. If he does not roll a 2 or 3 he passes the dice to player C.Player C rolls the dice. If he rolls a 4, 5 or 6 he wins and the game ends. If he does not roll a 4, 5 or 6 he passes the dice to player A for round 2. 

Each round is played in exactly the same way as round 1. Is the game Fair?