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 :

ROLLABCROLLABC1WIN21WIN2WIN22WIN3WIN23WIN4WIN24WI

N5WIN25WIN6WIN26WIN7WIN27WIN8WIN28WIN9WIN29WIN10WIN

30WIN11WIN31WIN12WIN32WIN13WIN33WIN14WIN34WIN15WIN35

WIN16WIN36WIN17WIN37WIN18WIN38WIN19WIN39WIN20WIN40WI

N4115398

ABC72013

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

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 :

ROLLABCROLLABC1WIN21WIN2WIN22WIN3WIN23WIN4WIN24WI

N5WIN25WIN6WIN26WIN7WIN27WIN8WIN28WIN9WIN29WIN10WIN

30WIN11WIN31WIN12WIN32WIN13WIN33WIN14WIN34WIN15WIN35

WIN16WIN36WIN17WIN37WIN18WIN38WIN19WIN39WIN20WIN40WI

N4115398

ABC72013

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