Dice Game

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Dice Game

Three players A, B and C play a game with a single dice.

The rules of the game are:

Player A ALWAYS goes first.

A rolls the dice. If the dice lands showing a 1 then A wins the game. If A

does not role a 1 then B takes a turn.

B rolls the dice. If the dice lands showing a 2 or 3 then B wins the game. If

B does not roll a 2 or 3 then C takes a turn.

C rolls the dice. If the dice lands showing a 4, 5 or a 6 then C wins the

game. If C does not roll a 4,5 or a 6 then A starts again.

This procedure continues until there is a winner.

Investigate any or all of:

The probabilities of each of A, B or C winning the game.

Who will be the most likely winner?

3. The most likely length of the game in terms of the number of rolls of the

dice to produce a winner.

Playing the game.

Before we started to work out all the probabilities for the questions we

played the game to give us an idea of what th outcome should roughly be.

Here are the results :







As you can see from this pie chart, in practice it suggests that B is the most

likely player yo win the game. From looking at this I would predict that when
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I have worked out all of the probabilities B will have the largest chance of

winning the game by far and A will have the smallest chance.





This frequency graph shows that in practice the game is most likely to be

won in the first round.

This frequency graph shows each round will normally take between 2 and 3

rolls of the dice to produce a winner. This also coincides with what I have

said about the being most ...

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