# Dice Game

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

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.

ROUNDTHROWSROUND

THROWS1122126212224123242338441124245132526626261371327128112

8259372913102530381126311112514322513383338144113439152535121611

364141712371318133861819253951420124013

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 ...