Random variables

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Business Plan for Dart Game

Paul Elam

Essay The purpose of this business plan is to show the profitable use of our dart game

The game dispenses tickets for various scores as shown in Table 1 below The possible point values for each throw of the dart are shown in the first column with the number of tickets dispensed in the second column The third column shows the probability of scoring a specific point value on a given throw of the dart

Points

Tickets Probability

Probability per Throw Dispensed Score /Throw in 32 Throws in 32 throws per Throw

50 5 1 /32 1 50 1 .56

40 4 1 /16 2 80 2 .50

30 3 1 /8 4 120 3 .75

20 2 1 /4 8 160 5 .00

10 1 1 /2 16 160 5 .00

0 0 1 /32 1 0 0 .00 32 570 17 .81 Table 1 . Scoring and win probabilities

The probability of each score for 32 throws is shown in the fourth column , while the probability of points scored for 32 throws is shown in the fifth column . Dividing the by the number of throws of the dart resulted in an average of 17 .81 probable points per throw . From table 1 it can be seen that each dispensed ticket has a value of ten points . The number of throws per win will be equal to the number of points required for a win divided by the probable points per throw . The profit will be a function of the number of throws per win times the cost per throw minus the cost of the cost of the stuffed animal

The profit per win versus costs per dart ranging from .25 to 3 .00 is shown in Chart 1 for 10 , 15 , and 20 tickets required to win a stuffed animal , based on a 3 .00 stuffed animal cost

Chart 1 . Profit per win versus various costs per throw

From this data , three business plans for using the dart game for profit will be proposed

Plan 1

Plan 1 would charge 0 .50 per dart throw and require 20 tickets (200 points ) to win a stuffed animal . In this case , the average number of throws to win a stuffed animal would be twelve . Twelve dart throws 0 .50 per throw would yield an income of 6 .00 . Take out the 3 .00 cost of the bear would leave 3 .00 profit per win of a stuffed animal

Plan 2

Plan 2 would charge 0 .75 per dart throw and require 15 tickets (150 points ) to win a stuffed animal . In this case , the average number of throws to win a stuffed animal would be nine . Nine dart throws 0 .75 per throw would yield an income of 6 .75 . Take out the 3 .00 cost of the bear would leave 3 .75 profit per win of a stuffed animal

Plan 3

Plan 3 would charge 1 .00 per dart throw and require 10 tickets (100 points ) to win a stuffed animal . In this case , the average number of throws to win a stuffed animal would be six . Six dart throws 1 .00 per throw would yield an income of 6 .00 . Take out the 3 .00 cost of the bear would leave 3 .00 profit per win of a stuffed animal

Conclusion

Plan 3 is recommended . The possibility of winning a stuffed animal with just two darts will be enticing to customers . In addition , the 1 .00 cost per throw would greatly reduce the need for handling coins . In summary , Plan 3 would entice the customer to play , enjoy the use of mostly currency , and still provide an acceptable profit

References

1 . MMA1- Project 15 table

Table of scoring probabilities

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