The Human Fruit Machine

Transcription

1 The Human Fruit Machine For Fetes or Just Fun! This game of chance is good on so many levels. It helps children with maths, such as probability, statistics & addition. As well as how to raise money at a fair for a good cause. It will also give them a sense of enterprise. Children not only love playing this game, but also enjoy setting up & running the stall with friends. Give these instructions to the children to see if they can work it out for themselves. TIPS FOR SUCCESS It s good to use a bell when a prize is won. This makes it fun & attracts attention to your stall. At Christmas, you can pull the fruit out of Christmas stockings & use a sleigh bell. Chocolate coins make good prizes. Fruit can also be used as prizes, especially if you want to teach children about nutritional values. Use the one with the greatest nutritional value as the best prize. You will need 3 cotton, draw-string bags 9 pieces of wooden fruit or vegetables 4 mini wooden boxes (3 for drawing fruit into & 1 prize box) Prizes, we suggest gold & silver chocolate coins, or fresh fruit A Coin Pot (a decorated baked bean tin makes a good noise when a coin is thrown in) A table & 3 chairs in a row Pens & Card for poster making A Bell or whistle The rules You will need 3 people to run the stall; the human part of the human fruit machine. The 3 people sit side by side behind a table. Each person places one of the small wooden drawers in front of them on the table. Each person has a cotton bag with 3 pieces of fruit inside, one of each type. They sit with the bag on their lap with one hand inside it. When a player wants to play, they are asked to put a coin in the coin pot & ring the bell. This begins the game. When each person running the stool hears the bell they place their hand on one of the pieces of fruit inside their bag. Together they count to 3 aloud & on 3 place whatever fruit they have in their hand in the wooden box on the table. The combination of fruit is checked to determine if a prize has been won. If it is a winning combination a prize is put in the prize drawer & the bell is rung.

2 Maths & Enterprise Before you can start playing, it is necessary to work out: a) What to charge players for a GO, b) What COMBINATIONS of fruit to give a prize for, & c) What value the prizes should be Remember, the goal is to a) Attract players to your stall b) Charge players enough to pay for the prizes c) Raise funds for your chosen cause d) Have Fun! Here are some tips on how you could go about this COST PER GO How much should you charge a player for a GO. If it is too high, they will save their money for other more reasonably priced activities. If it is too low, you won t collect enough money to cover the cost of buying alluring prizes to tempt people into playing. They will prefer to spend their money where they can get more for their money. The cost you can charge per GO will also depend on how much pocket money potential players get. CHANCE OF A WIN The chance of winning is also important to the players. If the chance of winning is too low, they simply won t play. If too high, you may give away more in prizes than you raise for your cause. A fruit machine generally gives prizes for drawing PAIRS of fruit or THREE OF A KIND. Before you can decide how often & what value of prizes to give you must calculate the likelihood of drawing particular COMBINATIONS. This will give you the likelihood (also called the probability) of a player winning. You can use the following exercises to help you work out a reasonable cost per GO how often to give prizes & the value of prizes. Alternatively, you can calculate them using your own method.

3 EXERCISES 1) Work out How many possible combinations of fruit there are You have 3 bags with 3 types of fruit in each. You will be randomly picking 1 fruit from each bag resulting in a set of 3. Because the fruit is picked randomly each Combination is equally likely to be drawn. Where a small number of items is concerned (9 in our case) it is possible to write down & count all the possible combinations. Write out all the Combinations using the grid below. Use L for Lemon, G for Grape & T for Tomato. It is important to work systematically to ensure no combinations are missed, for instance begin with all the combinations that start with a lemon being drawn from bag 1, then once this is done go through all the combinations that start with a Grape being drawn from Bag 1 etc. We have started it for you. No. COMBINATIONS Bag1 Bag2 Bag3 3 OF A KIND? PAIR? 1 L L L 3 Lemons 2 L L G Yes 3 L L T Yes 4 L G L Yes 5 L G G Yes 6 L G T 7 Total 2) What it the likelihood (probability) of drawing a PAIR? Count how many PAIRS there are. To calculate the probability of drawing a PAIR divide the number of PAIRS by the total number of possible COMBINATIONS. You can convert this to a Percentage if you wish by multiplying by ) What it the likelihood (probability) of drawing THREE OF A KIND? Count how many THREE OF A KIND there are, & then divide this by the total number of COMBINATIONS. 4) What it the likelihood (probability) of drawing THREE LEMONS? Use the same method as for 2) & 3) to calculate the probability of drawing THREE LEMONS 5) What is the Probability of drawing THREE OF A KIND excluding LEMONS? This is calculated because THREE LEMONS is now a winning COMBINATION in its own right. Divide the number of 3 OF A KIND except LEMONS by the total number of COMBINATIONS

4 6) What is the Probability of a WIN compared to NOT WINNING? A WIN is either 3 OF A KIND or a PAIR. Use the same method as above to calculate the probability of getting any of the winning COMBINATIONS compared to not winning anything 7) What might affect the combinations being equally likely to be drawn? For instance, think about the organisers being eager for their friends to win a prize. 8) How much money do you think you will raise from GOs in total? Consider, how much you think a player is willing to pay for a GO & how many players you think there will be? You will need to make some estimates & assumptions. For instance, you may hope that each player, on average, will return to your stall 3 times. If you charge 2 for a GO & they only receive 2 pocket money, then they will only have 1 GO on your stall & have nothing left to spend on anything else, which would be a very boring Fete for them. The stall next to yours may only be charging 50p a GO, they would be more likely to go on this stall, especially if the prizes were good in comparison to yours. Experiment with a variety of costs per GO to see how much you might raise. 9) Decide what proportion (percent) of money you want to spend on prizes compared to how much you want to give to your cause. Multiply this percent by the estimates of how much you think you will raise from GOs in 8) above. This gives you an estimate of how much you might raise for your cause & a rough budget for spending on prizes. 10) The amounts you have calculated in 9) above are only estimates. If you spend these amounts on prizes & fewer players turn up than you expected, you may find you are out of pocket. It would be better to estimate how much you have to spend, on average, on prizes per individual GO. This is where it gets difficult First, chose one of the possible amounts to charge per GO from 8) above, 20p for instance, & multiply it by the percentage you decided to spend on prizes in 9) above. Now, calculate how much you have to spend per GO on prizes using the probabilities you calculated in 2) to 6) above. For each winning combination, multiply its probability by an estimate of the value of the prize you might give for it. Then add these together. If the total is less than your budget per prize then you will, on average, cover the cost of prizes. Use this grid OUTCOME A Probability B Suggested Prize THREE LEMONS 3.7% 60p = THREE OF A KIND (excluding Lemons) 7.4% 25p = PAIR 66.7% 5p = NO WIN 22.2% 1p = Total 100% = A X B Note: if you add all the probabilities (expressed as a %) of all possible outcomes together the total will always be 100%. Remember winning nothing is one of the possible outcomes. You will need to use trial & error. Experiment with different prize values and cost per GO and % to spend on prizes versus what to keep for your cause. LOOK AT THE ANSWERS BELOW IF YOU NEED HELP

5 ANSWERS Q1 L = Lemon G = Grape T = Tomato No. COMBINATIONS Bag1 Bag2 Bag3 3 of a KIND PAIRS 1 L L L 3 Lemons 2 L L G Yes 3 L L T Yes 4 L G L Yes 5 L G G Yes 6 L G T 7 L T L Yes 8 L T G 9 L T T Yes 10 G G G 3 Grapes 11 G G L Yes 12 G G T Yes 13 G L G Yes 14 G L L Yes 15 G L T 16 G T G Yes 17 G T L 18 G T T Yes 19 T T T 3 Tomatoes 20 T T G Yes 21 T T L Yes 22 T G T Yes 23 T G G Yes 24 T G L 25 T L T Yes 26 T L G 27 T L L Yes Total 3 18 There are 27 possible COMBINATIONS Q2 There are 18 PAIRS There are 18 chances of getting a PAIR out of 27 total COMBINATIONS Expressed as a percentage this is a 66.7% chance Q3 There are 3 THREE OF A KIND There are 3 chances of getting a THREE OF A KIND out 27 total COMBINATIONS Expressed as a percentage this is a 11.1% chance Q4 There is 1 chance in 27 GOs of getting THREE LEMONS Expressed as a percentage this is a 3.7% chance Q5 There are 2 THREE OF A KIND (excluding LEMONS) There are 2 chances of getting a THREE OF A KIND (excluding LEMONS) out 27 total COMBINATIONS Expressed as a percentage this is a 7.4% chance NOTE: the chance of getting THREE OF A KIND is the same as getting either THREE LEMONS or THREE OF A KIND (excluding LEMONS) 3.7% + 7.4% = 11.1% Q6 There are 6 chances in 27 GOs of winning nothing Expressed as a percentage this is a 22.2% chance This means there are 27 6 = 21 chances of getting any one of the winning combinations. This is a 78.8% chance. Note: If you total the probability of a WIN

6 plus a NO WIN you will get 100%. This is always the case if you total the probability of all the possible outcomes. Q7 One of the organisers might like lemons. Or might have a tendency to pull out the biggest fruit more often. Probable outcomes happen on average, and may only be accurate after a large number of games. Considerations like this could skew the results & affect how many prizes are won. Ensure you allow a margin to cover for this. Q8 There may be 100 children in your school. You may estimate that only half of these children will come to the fete, that s 50, & of these only 80% of them will play on your Fruit Machine, that is 40 (80% X 50). You may estimate that these players will, on average, have 3 GOs each. Based on these assumptions you are expecting 40 X 3 = 120 GOs in total. If you decide to charge 10p for a GO In 120 GOs you will make 120 times 10p = If you decide to charge 20p for a GO In 120 GOs you will make 120 times 20p = If you decide to charge 50p for a GO In 120 GOs you will make 120 times 50p = Q9 If you decided to put 60% of your takings aside for your cause, then at 10p a GO you have 60% X 12 = 7.20 for your cause & approximately 4.80 for prizes 20p a GO you have 60% X 24 = for your cause & approximately 9.60 for prizes 50p a GO you have 60% X 60 = 36 for your cause & approximately 24 for prizes However, these are only estimates so if less players turn up than you expected you will not make as much money. Q10 We have decided on 20p a GO & we want to give 60% to our cause, that is 12p, leaving 8p to spend on prizes per GO. You may have decided otherwise. This means, on average, players cannot win more than 8p per GO on prizes. You will want to give a more attractive prize for combinations that players have a smaller chance of winning. You may also want to give a consolation prize for a NO WIN. This is good for getting players to come back time and time again. Say a 1p sweet. Try with different combinations of prizes and costs per GO until you decide what works for your stall. OUTCOME A Probability B Suggested Prize A X B Probable Prize per GO either THREE LEMONS or 3.7% 60p = 2.22p THREE OF A KIND (excluding Lemons) or 7.4% 25p = 1.85p PAIR or 66.7% 5p = 3.33 NO WIN 22.2% 1p = 0.22p Total 100% = 7.62p NOTE: In probability if the outcome is in terms of either or or etc then you ADD the outcomes. OUR SUGGESTION Cost: 20p for a GO Winning Combinations & Prizes NO WIN = 1p chew A PAIR = 5p sweet THREE OF A KIND (excluding Lemons) = 1 Silver Chocolate Coin costing less than 25p THREE LEMONS = 3 Gold Chocolate Coins coating less than 60p