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GAME TABLE :Team 1
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 2
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 3
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 4
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 5
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 6
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
Risk and Reward (Teacher’s notes)
These notes are intended to assist the teachers working with groups of students at a table, they give an overview of
the lesson and suggestions on how to get the most from the activity.
Each table will need:
A six sided die
One set of student sheets per student
Short introduction :
One of the aims of the new Core Maths qualifications is to show how mathematics is used almost every day, in work
and other aspects of our lives. This activity shows just one situation, there are many more which use exactly the
same mathematical ideas.
The theme of this activity is risk and reward. It is a game designed to make you think about how you make decisions
which involve an element of risk. Mathematicians often use games to investigate how people react in situations and
decide on winning strategies. Although it can mean other things, a winning strategy generally means the one which
we gain the most from, for example in business this could be the most profitable. The activity will provide
opportunities to discuss common misunderstandings such as Gambler’s Fallacy, and think about the model and the
assumptions, for example:
Is it fair to assume that the pots will always catch a lobster or be washed away in bad weather?
Will the probability of good weather increase in summer and decrease in winter?
Introducing the game
Although it is possible for everyone to play as individuals, playing as pairs makes the task of playing and recording
easier and tends to increase discussion when deciding on where to place the pots.
Run through the instructions getting the students to fill in the sheet ready for the first day. (See the students’
sheet(s) at the end of this document).
When everyone has made the decision of where to place their pots for the first day, roll the die and determine the
weather, it is probably better if you do this.
Play the game for a short time, aim to allow the students time to experience the process of decision making. (5-10
rounds)
Some things to look out for whilst playing the game:
Are they quite risk averse at the start but gradually take more risks as the game progresses?
How do students react after a good round/bad round?
Sometimes, after a bad round, students take more risks to try and gain a larger profit on the next round. Sometimes
students also take more risks after a good round because they feel they are playing with winnings rather than their
own cash. You could discuss the pitfalls of such approaches.
Comments like “It’s been good weather for the last three or four rounds, it’s more likely to be bad weather on the
next round”. Although over a long run the weather should balance out to the expected probabilities this does not
influence individual rounds. Just like when flipping a coin, we expect roughly equal amounts of heads and tails, but on
each flip the probability of heads remains ½.
Discussing the game
Aim to bring out the points mentioned above under “some things to look out for”.
At some point before introducing the weather simulation data the person leading the session will attempt to bring
things together.
It may be possible for the presenter to quickly collect data from each group and arrive at a figure for each of the
number of good days, bad days and hurricanes, in total. The presenter will then introduce the idea of using a
computer model to gather data for a year. The presenter will then suggest working with the simulated weather data
and work will resume at tables.
Then introduce the weather simulation data.
Use the first question and the prompt on the student sheet to encourage the students to consider how this data
could be used by the lobster pot businesses. Give them time to think and offer suggestions.
You are looking to prompt them towards working out the anticipated profits over the course of a year for an
offshore and inshore pot.
For example using the data in the first diagram on the “weather simulation data” sheet see below.
There are 69 bad days, 290 good days, and 5 hurricanes, on the 69 bad days an offshore pot will be lost making a loss
of £6, or profit of -£6, over the simulated year this would amount to 69 x -£6 which is -£414. On the 290 good days
an offshore pot makes £5 per day making a total of 290 x £5 which is £1450. Finally on the 5 days when there is a
hurricane a loss of £6, or profit of -£6, is incurred on each of the days making a total loss of £30.
If a pot was placed offshore every day for a year then the business would anticipate earning (69 x -£6) + (290 x £5) +
(5 x -£6) = £1006
69
290
5 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 1
The inshore pot makes £3 on a good day, £5 on a bad day and -£6 when there is a hurricane, so for an inshore pot,
the profit for year 1 would be (69 x£5) + (290 x £3) + (5x-£6) = £1188
In this year placing the pot inshore would have been more profitable.
Here are the values for all simulations
Year 1 Year 2 Year 3 Year 4
Bad Days 69 70 57 61
Good Days 290 293 304 300
Hurricane 5 1 3 4
Offshore Profit £1,006 £1,039 £1,160 £1,110
Inshore Profit £1,185 £1,223 £1,179 £1,181
Finish by considering the final question.
Would this strategy win every single round?
You are aiming to get them to see that although the earnings over a year tends to be better for the inshore pots, each
individual round is subject to random chance.
It is easy to check back and see how many times the offshore pots were better in the previous gameplay. Ask the
students to look back at their game and see.
The presenter will at an appropriate point gather the class together to round off the session. If your students have
reached this stage please consider the extension below.
Extending the task
On the ”Year 3” simulation (57 bad days, 304 good days, and 4 hurricanes) the anticipated earnings from inshore and
offshore pots were almost equal. Challenge the students to find a set of data that make the anticipated earnings
from inshore and offshore equal. Is this possible? Is it likely? Are there more than one set of values?
Thinking solution
As hurricanes affect the income from inshore and offshore pots in same way, the number of hurricanes can be
ignored.
For every good day the offshore pot gains an extra £2 over the inshore pot. (ie offshore £5, inshore £3)
For every bad day the offshore loses £11 to the inshore pot. (ie offshore -£6, inshore £5)
This means for every bad day the offshore pot needs 5.5 good days to stay on equal terms.
Providing that this condition is met the values of both pots should be the same. The number of hurricanes would be
365 – (good days + bad days).
For example, 56 good days 308 bad days and one hurricane.
Within the constraints of the problem this means the bad days must be an even number, and the combined total of
good days and bad days cannot exceed 365, one year.
Using algebra
a = good days b = bad days and c = hurricanes we need 5a -6b – 6c = 3a + 5b – 6c 5a -6b = 3a + 5b 2a = 11b a = 5.5b
Student sheet Lobster Pots
Lobster pots - is a game which can be used to think about risk and reward. Your business involves fishing for
lobsters; these can be sold for a good profit at the local fish market. Sometimes fishing in more risky areas can bring
greater rewards but there are also potential problems.
Each player starts with a boat and 6 lobster pots. The pots can be placed either inshore or offshore, and left
overnight to catch lobsters.
If the weather is good, you can expect to catch one lobster per pot, both inshore and offshore. As the offshore
lobsters are bigger and of better quality, they fetch more at the fish market, £5 each compared with £3 for the
inshore lobsters. However, if the weather is bad the offshore pots get washed away, they cost £6 each to replace. In
bad weather, only the inshore pots catch lobsters. As fewer lobsters are available, the price of an inshore lobster
increases from £3 to £5.
The weather is normally good (5 out of 6 days). If the weather is bad on one day then the probability of getting good
weather on the following day falls to 4 out of 6. Three bad days in a row result in a hurricane and all of the pots,
inshore and offshore, are destroyed.
Playing the game
1. Each Team starts with £40 and 6 lobster pots.
2. For the first round assume the weather on the previous day was good.
3. Decide how many lobster pots you wish to place inshore and how many you wish place offshore.
4. Fill in columns 1 and 2 in the game table below.
5. Roll the dice to decide the overnight weather conditions.
If the weather on the previous day was good, rolling (1,2,3,4, or 5) gives good weather, a 6 gives bad weather. If the previous day was bad weather, rolling (1,2,3, or 4) gives good weather, a (5 or 6) gives bad weather. Three consecutive days of bad weather produces a hurricane on the third day and all the pots, both inshore and offshore, are lost and must be replaced.
6. Calculate how much each team has earned/lost and complete the row.
7. Repeat instructions 3 to 6 until finish time is called.
GAME TABLE :Team 1
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 2
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 3
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 4
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 5
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
GAME TABLE :Team 6
Day Inshore
pots
Offshore
pots
Weather
Overnight
Income
(I)
Costs
(C)
Profit
(I-C)
Running
total
1
2
3
4
5
6
7
8
9
10
Weather simulation data
This weather data was produced by a spreadsheet which simulated playing for 365 days.
How could this data be used by the lobster pot players?
Use the data to suggest a strategy which could prove successful if the game were played for 365 rounds.
Would this strategy win every single round?
69
290
5 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 1
70
293
1 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 2
57
304
3 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 3
61
300
4 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 4
About MEI
• Registered charity committed to improving
mathematics education
• Independent UK curriculum development body
• We offer continuing professional development
courses, provide specialist tuition for students
and work with industry to enhance mathematical
skills in the workplace
• We also pioneer the development of innovative
teaching and learning resources
Statistical and
financial
modelling
Modelling cycle
problem
????
problem
????
solution
PPPP solution
good
enough?
Business Simulation
The rules
Your data Table Good days Bad days Hurricanes
1
2
3
4
5
6
7
8
9
10
Totals 0 0 0
How could this
data help you
to decide
where to place
your pots ?
Would the data
be exactly the
same if we
played the
game again?
Weather simulation for a year
Text
Exam question
Financial modelling
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Jun-11 Sep-11 Dec-11 Apr-12 Jul-12 Oct-12
CPI inflation (%)
130
135
140
145
Jun-11 Sep-11 Dec-11 Apr-12 Jul-12 Oct-12
Unleaded petrol, per litre (p)
Mr Green drove 6753
miles on business last
year.
His car does an average
of 42.3 miles per gallon.
1 gallon = 4.54 litres
Estimate how much Mr
Green will spend on
petrol for business
journeys next year.
Financial modelling - mortgage
Student sheet Lobster Pots
Lobster pots - is a game which can be used to think about risk and reward. Your business involves fishing for
lobsters; these can be sold for a good profit at the local fish market. Sometimes fishing in more risky areas can bring
greater rewards but there are also potential problems.
Each player starts with a boat and 6 lobster pots. The pots can be placed either inshore or offshore, and left
overnight to catch lobsters.
If the weather is good, you can expect to catch one lobster per pot, both inshore and offshore. As the offshore
lobsters are bigger and of better quality, they fetch more at the fish market, £5 each compared with £3 for the
inshore lobsters. However, if the weather is bad the offshore pots get washed away, they cost £6 each to replace. In
bad weather, only the inshore pots catch lobsters. As fewer lobsters are available, the price of an inshore lobster
increases from £3 to £5.
The weather is normally good (5 out of 6 days). If the weather is bad on one day then the probability of getting good
weather on the following day falls to 4 out of 6. Three bad days in a row result in a hurricane and all of the pots,
inshore and offshore, are destroyed.
Playing the game
1. Each Team starts with £40 and 6 lobster pots.
2. For the first round assume the weather on the previous day was good.
3. Decide how many lobster pots you wish to place inshore and how many you wish place offshore.
4. Fill in columns 1 and 2 in the game table below.
5. Roll the dice to decide the overnight weather conditions.
If the weather on the previous day was good, rolling (1,2,3,4, or 5) gives good weather, a 6 gives bad weather. If the previous day was bad weather, rolling (1,2,3, or 4) gives good weather, a (5 or 6) gives bad weather. Three consecutive days of bad weather produces a hurricane on the third day and all the pots, both inshore and offshore, are lost and must be replaced.
6. Calculate how much each team has earned/lost and complete the row.
7. Repeat instructions 3 to 6 until finish time is called.
Weather simulation data
This weather data was produced by a spreadsheet which simulated playing for 365 days.
How could this data be used by the lobster pot players?
Use the data to suggest a strategy which could prove successful if the game were played for 365 rounds.
Would this strategy win every single round?
69
290
5 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 1
70
293
1 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 2
57
304
3 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 3
61
300
4 0
50
100
150
200
250
300
350
Bad Days Good Days Hurricanes
Nu
mb
er
of
day
s
Weather
Simulated Weather For Year 4
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