Fruit Machines

 Introduction Fruit machines (or slot machines or one-armed bandits as they are sometimes known) are common place in most pubs and are also found in amusement arcades and casinos. Playing them is a form of gambling and as such it is illegal for anyone under the age of 18 to use them. Fruit machines work in a fairly simple way, although they have become much more complex over the past decade with the introduction of computer chips into their mechanism. Older style fruit machines would work purely on the basis of probability in terms of how much money they would pay out. Modern machines are usually set to pay out a certain percentage of any money that is put into them (usually between 75% and 80%). These machines are therefore much more likely to pay out if they have had a lot of money put into them but not payed out recently. For the questions that follow, we are only going to look at the older probability based fruit machines. More information about how fruit machines work can be found at money.howstuffworks.com/slot-machine.htm

 Exercises Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

A fruit machine with 3 dials and 20 symbols (not all different) on each dial is illustratred opposite. Each dial can stop on any one of its 20 symbols, and each of the 20 symbols on each dial is equally likely to occur. The machine costs 10p a go. The three symbols highlighted determine how much, if anything, is won.

Suppose the machine makes the payouts shown in the table.

 Combination Payout(in 10p's) 3  BARS 40 3  STRAWBERRIES 5 3  GRAPES 5 3  APPLES 5 2  BARS 20 2  CHERRIES 5

Question 1
Complete the frequency chart below for each dial.

 Symbol Dial 1 Dial 2 Dial 3 BAR 2 1 1 STRAWBERRY 1 8 GRAPE 7 APPLES CHERRY PEAR

Question 2
We want to find the probability of each of the combinations above to see if it is worth playing. We first consider the 3 BARS combination.

(a)  In how many ways can you obtain 3 BARS?
(b)  How many possible combinations (including repeats) can be made altogether from
the three dials?

(c)  What is the probability of obtaining 3 BARS?

Question 3
We can use the same method used above to find other winning combinations. Find the probabilities of obtaining each of the other winning combinations.

(a)  3 STRAWBERRIES (b)  3 GRAPES
(c)  2 APPLES (d)  2 BARS
(e)  2 CHERRIES

 Question 4 The amount you would expect to win is found by multiplying together the probabilty of each winning combination by the amount it pays out (from the table at the top) and adding all of the amounts together. What is the expected gain or loss for each play on the machine? (Don't forget to take off your initial 10p payment) Give your anser to 2 decimal places p    gainloss

Just for Fun
Use the fruit machine simulator below to see how much money you would win if you put £10 into the machine. Try using the hold buttons as well to see if this improves your chances of winning (these are available when they flash).

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