Dice Game Maths Investigation

GCSE Maths

Dice Game

Introduction

My aim in this investigation is to investigate three questions:

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

2. 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.

Predictions

Before I actually do the game in the proper way I’m going to make

a few predictions. This will help me to understand possible results

better.

I predict that C will be the most likely winner as it has the highest probability

of winning the game when it’s his turn. I say this even though it takes its turn

last. I believe B will be the second most likely winner as it too has the second

highest probability; and the same goes for A- least likely for the same reason.

As for the most likely length of game in terms of the number of rolls of the

dice to produce a winner - I believe that the answer to this question could be 3

as it is the first opportunity for C to win and it has a 50% chance of winning

every throw it has (3/6). Obviously A and more so B will win before it even gets

to C sometimes but over the whole game the most likely winner will be C on

average.

Method

To do this investigation – first I played the game. We were told by

our teacher to play it 30 times and to take down the results with

ultimate care - which we did successfully.

Results

After carrying out the experiment in a careful and strategic way I found some

interesting results.

I found that A won just twice (2/30), B won thirteen time (13/30) and C won

a total of fifteen times (15/30). This shows that at this stage that C is the more

likely winner.

Another very important set of results in terms of finding a result for the last

question, most likely length of game. I found that B won eight times on the

second throw, C won thirteen times on the third throw, A won twice on the

fourth throw, B won three times on the fifth throw, C won twice on the sixth

throw, B won once on the eighth throw and once on the eleventh throw.

Below is a table displaying the results – it shows the number of throws it took

for someone to win and who actually won.

Information on table of results

On the table below along the top is the number of throws it took for someone

to win.

And, along the side is the game number (game number 1,2,3,4,5 etc.)

Where it has the letter X it means that whichever letter was throwing at the

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Dice Game Maths Investigation

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