1. Probability – Experimental & Expectation – Activity A
This activity is designed to allow students to explore experimental &
expected probabilities by constructing biased ‘casino games’.
‘Pre-Made’ games and ‘To Make’ games are included. Students could create
their own from scratch. Other than unequal possible outcomes,
students could weight the dice/spinners.
The activity has flexible outcomes, but students should be able to discuss and
write about their game and other students’.

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3. A good mathematician would never gamble.
Disclaimer!
A good mathematician would never gamble.
There is no skill involved and you are
playing by someone else’s rules.
The odds are against you and
you are guaranteed to lose money over time!
Gambling can lead to addiction and
people lose lots of money,
and even relationships, because of gambling.

4. 1 2 1 2 John and Julie have £10 each at the start of a game.
John flips a coin and if it lands on tails he wins and gets £1 from Julie.
If it lands on heads he loses and gives £1 to Julie.
After 50 throws how much will John have?
1 2
We expect John to win 50% of the time.
During the game we expect John to win the
same amount of money that he loses.
P(Heads) =
1 2
P(Tails) =

5. In Roulette people bet on a ball landing on a number or a colour.
There are 38 numbers including 0 and 00.

6. W L If you bet on Red, and the ball lands on Red,
you double your money.
Jim starts with £5.
He has the idea to always put £1 on Red.
Bet £1
Win/Lose? W L
Running total £6 £7 £5 £4
His money stays around £5.
But over time he will lose all his money.
Why?

7. 18 38 18 38 2 38 P (RED) = P (BLACK) = P (GREEN) =
Jim’s money would stay the same if
There was only red and black.
But if he plays 38 times, two times
the ball will land on green.
The probability of winning isn’t 50%.
The odds are against him!

8. 18 38 18 38 2 38 P (RED) = P (BLACK) = It’s biased! P (GREEN) =
This is how casino’s take your money.
Sometimes you win but more times you lose.
Over time, you are guaranteed to lose all your money!

9. In roulette you will lose 53% of the time.
The expectation is that if you play 100 times,
you lose 53 times.
The game looks fair,
but in the long run you are guaranteed to lose!
In this activity you will design a game for someone else to play.
Your job is to design the game so
it looks fair but
the player would lose all their money eventually!

10. You can choose to make… …or something you invent yourself!
In this activity you will design a game for someone else to play.
Your job is to design the game so
it looks fair but
the player would lose all their money eventually!
You can choose to make…
Dicey Dice!
Lucky Landing!
…or something you
invent yourself!
Super Spinner!

11. INSTRUCTIONS
1) Choose a game to make.
2) Decide how many WIN/LOSE outcomes you will have for your game.
How else could you make your game biased?
3) Find someone to play the game 20, 25 or 50 times.
Record how many wins/loses they get.
Express the wins as a fraction and convert this to a percentage.
Remember roulette was a 53% lose percentage. How close were you?
Questions to Answer:
Does your game look fair?
Is it fair?
Why? Why not?
If someone played the game 100 times, how much money would they win/lose?
Would you want to play your game?
Next time, how would you change your game?
Can you make it look even fairer?

12. Find someone to interview about their game.
Do you like their game? Would you play it?
Record their answers to the questions.
You should be able to report back to the teacher about the student you interviewed and their game.
Questions to Answer:
Does your game look fair?
Is it fair?
Why? Why not?
If someone played the game 100 times, how much money would they win/lose?
Would you want to play your game?
Next time, how would you change your game?
Can you make it look even fairer?

13. Is the distribution of the squares fair?
There are 50 WIN! squares and 50 LOSE squares, so this game is not biased.
Is the distribution of the squares fair?
If the dice/coin hits any side it must be re-thrown, is this fair?

14. WIN! LOSE LOSE LOSE Dicey Dice! FOLD & STICK FOLD & STICK FOLD & STICK
In this game,
the player makes a bet and
rolls a tetrahedral dice
(an equilateral pyramid).
If the dice lands on WIN!
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
FOLD & STICK
WIN!
Construct the game and let someone play it
20, 25 or 50 times
and record the results.
LOSE
Is this game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
FOLD & STICK
INSTRUCTIONS
Attach to cardboard and
cut out the shape including the tabs.
Fold & stick the tabs to
make the tetrahedral dice.

15. Super Spinner! WIN! WIN! LOSE LOSE INSTRUCTIONS
Attach to cardboard, cut out and
carefully push a pencil through
the centre hole.
In this game,
the player makes a bet and
spins the octagonal spinner.
If the spinner lands on WIN!
the player gets double their bet.
If the spinner lands on LOSE
they lose their bet.
WIN!
LOSE
Construct the game and let someone play it
20, 25 or 50 times
and record the results.
Is this game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?

16. If the coin/dice hits any side then the
Lucky Landing!
FOLD &
STICK
FOLD &
STICK
FOLD UP
WIN!
LOSE
In this game,
the player makes a bet and
throws a coin or dice into the tray.
The ‘casino employee’ decides whether
the dice is on
a WIN! or a LOSE square.
If the dice lands on WIN!
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
If the coin/dice hits any side then the
player must re-throw!
FOLD UP
FOLD UP
Construct the game and let someone play it
20, 25 or 50 times
and record the results.
Is this game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
FOLD &
STICK
FOLD &
STICK
FOLD UP

17. If the coin/dice hits any side then the
Lucky Landing!
FOLD &
STICK
FOLD &
STICK
FOLD UP
WIN!
LOSE
In this game,
the player makes a bet and
throws a coin or dice into the tray.
The ‘casino employee’ decides whether
the dice is on
a WIN! or a LOSE square.
If the dice lands on WIN!
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
If the coin/dice hits any side then the
player must re-throw!
FOLD UP
FOLD UP
Construct the game and let someone play it
20, 25 or 50 times
and record the results.
Is this game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
FOLD &
STICK
FOLD &
STICK
FOLD UP

18. Dicey Dice! FOLD & STICK FOLD & STICK FOLD & STICK In this game,
the player makes a bet and
rolls a tetrahedral dice
(an equilateral pyramid).
If the dice lands on WIN
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
FOLD & STICK
Decide how many WIN and LOSE outcomes
your dice will have.
How else could you make the game unfair?
Complete the faces before constructing the dice.
Let someone play the game 20, 25 or 50 times
and record the results.
FOLD & STICK
Is your game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
INSTRUCTIONS
Attach to cardboard and
cut out the shape including the tabs.
Fold & stick the tabs to
make the tetrahedral dice.

19. Dicey Dice! VERY TRICKY! FOLD & STICK In this game,
the player makes a bet and
rolls the 10-sided dice.
If the dice shows WIN
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
Is your game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
Decide how many WIN and LOSE outcomes
your dice will have.
How else could you make the game unfair?
Complete the faces before constructing the dice.
Let someone play the game 20, 25 or 50 times
and record the results.
VERY
TRICKY!
INSTRUCTIONS
Attach to cardboard and
cut out the shape including the tabs.
Fold & stick the tabs to
make the dice.
FOLD & STICK

20. Super Spinner! INSTRUCTIONS Attach to cardboard, cut out and
carefully push a pencil through
the centre hole.
In this game,
the player makes a bet and
spins the spinner.
If the spinner lands on WIN
the player gets double their bet.
If the spinner lands on LOSE
they lose their bet.
Decide how many WIN and LOSE outcomes
your spinner will have.
How else could you make the game unfair?
Complete the spinner before constructing it.
Let someone play the game 20, 25 or 50 times
and record the results.
Is your game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?

21. If the coin/dice hits any side then the
Lucky Landing!
FOLD &
STICK
FOLD &
STICK
FOLD UP
In this game, the player makes a bet and
throws a coin or dice into the tray.
The ‘casino employee’ decides whether
the dice is on a WIN! or a LOSE square.
If the dice lands on WIN
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
If the coin/dice hits any side then the
player must re-throw!
FOLD UP
FOLD UP
Decide how many WIN and LOSE outcomes
your game will have.
Complete the board before constructing it.
Let someone play the game 20, 25 or 50 times
and record the results.
Is your game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
FOLD &
STICK
FOLD &
STICK
FOLD UP

22. If the coin/dice hits any side then the
Lucky Landing!
FOLD &
STICK
FOLD &
STICK
FOLD UP
In this game, the player makes a bet and
throws a coin or dice into the tray.
The ‘casino employee’ decides whether
the dice is on a WIN! or a LOSE square.
If the dice lands on WIN
the player gets double their bet.
If the dice lands on LOSE
they lose their bet.
If the coin/dice hits any side then the
player must re-throw!
FOLD UP
FOLD UP
Decide how many WIN and LOSE outcomes
your game will have.
Complete the board before constructing it.
Let someone play the game 20, 25 or 50 times
and record the results.
Is your game fair?
Why? Why not?
Can you calculate the % probability
of winning or losing?
If the player plays 100 times,
how many times would they win?
If the player bet £1 each time,
how much would they win/lose?
FOLD &
STICK
FOLD &
STICK
FOLD UP

23. tom@goteachmaths.co.uk Questions? Comments? Suggestions?
…or have you found a mistake!?
Any feedback would be appreciated .
Please feel free to