Dominos vs. US Pizza Essay Example for Free

Dominos vs. US Pizza Essay The research report you have authorized us to write on â€Å"Dominos vs. US Pizza† is now ready and follow this letter. This report is the result of work completed at SKIPS. During our work term as other student, we were engaged to assist in related topic collection. In the course of this work we gained knowledge about this topic. It is the detailed information and data which is the subject of this report. Through the course of the term, we were given the opportunity to learn much about the strategic model of Dominos. We feel that this knowledge will be helpful in future work terms, and in our career. We would like to thank our mentor Mr. Manish Thaker for his patience and good judgement, as well as classmates who were always willing to help. Sincerely Parul Kapoor (43) Sejal Rathod (55) Table of contents Contents Executive summary Introduction Research methodology Analysis of research data Findings Conclusions Recommendation Annexure Executive Summary This report contains the detailed research about the ‘strategies of Dominos vs US Pizza’. The research was an exploratory one. The aim of the research was to find the out the strategies adopted by Dominos to attract customer towards it. The research was conducted in the period of March to April. The target population of the research was the pizza consumers. Out of this the sample size of 100 were drawn based on convenient sampling technique. The research was done by filling the questionnaire which was fully drawn on the basis of the research objectives. The conclusion for the research was almost drawn during the data collection itself. 100% of respondents like pizza. Out of sample size of 100, 68% of respondents visit more to Dominos. 35% of respondents lie in age group of 20-25 years, visit these restaurants with their friends in free hours. Respondents prefer Dominos because the quality of the food offered by Dominos is good. Awareness of preferred restaurant came from friends and T. V add. This shows that people are attracted more towards Dominos because quality of food offered by Dominos is better than Quality offered by US Pizza. INTRODUCTION Problem Definition: Both (Dominos and US Pizza), provide same kind of facility. They have huge varieties in pizza as well as other items. Us pizza has unlimited scheme packages and price of its items are also reasonable whereas Dominos doesn’t have any unlimited packages and price of all the items are also high as compare to U. S. Pizza. Still people attracted towards Dominos, more than US Pizza. Research Objectives: The key objectives of the research are identified as following: To study the strength of Dominos business model. To study the strength of US Pizza’s business model. To find out ‘why people are attracted more towards Dominos than US Pizza’ Research Design: This is an exploratory type of research. It’s a problem of general nature, numbers and statistics are used to support this research. The primary source of data is in questionnaire and short interview. Research design is the that phase where researcher has to detail a plan in which alternatives are going to be chose at each of the following stages. Selection of type of research. Selection of measures and measurement techniques. Selection of sample size and sampling techniques. Selection of methods of data analysis. Research Methodology: Primary Data: Data is collected through structured questionnaire by conducting survey. Mode of collection Online questionnaire Offline questionnaire Methods of Data Analysis The questionnaire of 22 variables (2 dependants and 18 independents) was administered through advanced data analysis of utilities of SPSS. 1. Hypothesis To achieve these objectives, the following hypotheses are formulated:- 1. H0 :- More Frequency of customer towards Dominos Pizza H1:- Frequency is more towards other restaurant 2. H0 :- All parameters are equality important H1:- At least 1 Parameter is Important 3. H0:- Customers are satisfied for all Parameter H1:- Customers are Satisfied for At least One Parameter Data analysis and interpretation: Exhibit-1 1)Like restaurants Frequency Percent Valid Percent Cumulative Percent Valid YES 100 100. 0 100. 0 100. 0 Interpretation: From Exhibit -1 we can conclude that 100% people like to go to restaurant. Exhibit-2 2)Visit time Frequency Percent Valid Percent Cumulative Percent. Valid ONCE OR TWICE IN WEEK 23 23. 0 23. 0 23. 0 ONCE OR TWICE IN 15 DAYS 27 27. 0 27. 0 50. 0 ONCE OR TWICE IN A MONTH 37 37. 0 37. 0 87. 0 OCCATIONNALY 13 13. 0 13. 0 100. 0 Total 100 100. 0 100. 0 Interpretation:- From above chart 37% people go to restaurant once or twice in a month, 27% people go to restaurant once or twice in a 15 days, 23% people go to restaurant once or twice in a week and only 13% people like to go to restaurant occasionally. Exhibit-3 3)No. of visit Frequency Percent Valid Percent Cumulative Percent Valid 1-5 91 91. 0 91. 0 91. 0 5-10 7 7. 0 7. 0 98. 0 MORE THAN 10 2 2. 0 2. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: looking above graph 91% respondent visit restaurant 1-5 times in a month Exhibit-4 4)Prefer Frequency Percent Valid Percent Cumulative Percent Valid PIZZA 59 59. 0 59. 0 59. 0 CHAT 6 6. 0 6. 0 65. 0 SANDWITCH 25 25. 0 25. 0 90. 0 OTHER 10 10. 0 10. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: From above Exhibit more preference given to pizza then other snacks. Exhibit-5 5)Like pizza Frequency Percent Valid Percent Cumulative Percent Valid YES 100 100. 0 100. 0 100. 0. Interpretation: Above diagram conclude that thought respondents like other snacks like sandwitch, chats etc, they also like pizza. Exhibit-6 6) Preferred rest. Frequency Percent Valid Percent Cumulative Percent Valid DOMINOS 68 68. 0 68. 0 68. 0 US PIZZA 26 26. 0 26. 0 94. 0 PIZZA WORLD 2 2. 0 2. 0 96. 0 PIZZA ZONE 2 2. 0 2. 0 98. 0 OTHER 2 2. 0 2. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: Respondents like to go many restaurant like dominos, us pizza, pizza world, pizza zone etc but they give more preference to dominos. Exhibit-7 7)Reason for visit Frequency Percent Valid Percent Cumulative Percent Valid QUALITY IS GOOD 86 86. 0 86. 0 86. 0 PRICE IS LOW 8 8. 0 8. 0 94. 0. SERVICE IS GOOD 2 2. 0 2. 0 96. 0 4 2 2. 0 2. 0 98. 0 5 2 2. 0 2. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: Above diagram conclude that people give more preference to dominos because food quality of dominos is better than other restaurant. Cross-tab Q-9 Q-10. Important factor satisfaction level 8. (a) Quality * 9. (b)Price Crosstab Count 9. (b)Price Total Satisfied least satisfied 8. (a)Quality very imp 54 46 100 Total 54 46 100 Interpretation: From above cross tab 54% respondents to whom quality is very important and they are also satisfied by the price which they are paying for the quality. 8. (a) Quality * 9. (c)Service Crosstab Count 9. (c)Service Total Satisfied 8. (a)Quality very imp 100 100 Total 100 100 Interpretation: Almost all the respondent to whom quality is very important they all satisfied by the service given by the restaurant. 8. (a) Quality * 9. (d)Ambience Crosstab Count 9. (d)Ambience Total Satisfied normal 8. (a)Quality very imp 79 21 100 Total 79 21 100 Interpretation:- Above table conclude that respondents to whom quality is very important they are also satisfied by the ambience in the restaurant. 8. (a)Quality * 9. (e)Customization Crosstab Count 9. (e)Customization. Total Satisfied normal least satisfied 8. (a)Quality very imp 77 21 2 100 Total 77 21 2 100 Interpretation: respondents who gives very important to quality also satisfied by the customization adopted by their favourite restaurant. 8. (b)Price * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied 8. (b)Price very important 46 46 IMPORTANT 23 23 least important 31 31 Total 100 100 Interpretation: In this table respondents who gives very important to the price, they are also very satisfied by the quality they are getting in that price. 8. (b)Price * 9. (b)Price Crosstab Count 9. (b)Price. Total satisfied least satisfied 8. (b)Price very important 0 46 46 IMPORTANT 23 0 23 least important 31 0 31 Total 54 46 100 Interpretation:- Respondents who gives very important to the price they are least satisfied by the price adopted by their favourite restaurant. 8. (b)Price * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (b)Price very important 46 46 IMPORTANT 23 23 least important 31 31 Total 100 100 Interpretation: This table conclude that respondents to whom price is very important they also satisfied by the services delivered by restaurant. 8. (b)Price * 9. (d)Ambience Crosstab. Count 9. (d)Ambience Total satisfied normal 8. (b)Price very important 46 0 46 IMPORTANT 2 21 23 least important 31 0 31 Total 79 21 100 Interpretation: Respondents also satisfied by the ambience presents in their favourite restaurant. 8. (b)Price * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (b)Price very important 46 0 0 46 IMPORTANT 0 21 2 23 least important 31 0 0 31 Total 77 21 2 100 Interpretation:- Respondents to whom price are very important they also satisfied by the customization. 8. (c)Service * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied 8. (c)Service very important 52 52 important 48 48 Total 100 100 Interpretation: Respondents who give much important to the service they are also satisfied by the quality. 8. (c)Service * 9. (b)Price Crosstab Count 9. (b)Price Total satisfied least satisfied 8. (c)Service very important 52 0 52 important 2 46 48 Total 54 46 100 Interpretation: Respondents to whom service are very important they are satisfied by the price which they are paying. 8. (c)Service * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (c)Service very important 52 52 important 48 48 Total. 100 100 Interpretation:- Respondents to whom service is very important they also satisfied by the service offered by their favourite restaurant. 8. (c)Service * 9. (d)Ambience Crosstab Count 9. (d)Ambience Total satisfied normal 8. (c)Service very important 31 21 52 important 48 0 48 Total 79 21 100 Interpretation: respondents who gives important to the service they are also satisfied by the ambience in the restaurants. 8. (c)Service * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (c)Service very important 31 21 0 52 important 46 0 2 48 Total 77 21 2 100. Interpretation: Respondents to whom service is important they are satisfied by the customization. 8. (d)Brand * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied 8. (d)Brand very important 31 31 Important 23 23 least important 46 46 Total 100 100 8. (d)Brand * 9. (b)Price Crosstab Count 9. (b)Price Total satisfied least satisfied 8. (d)Brand very important 31 0 31 Important 23 0 23 least important 0 46 46 Total 54 46 100 8. (d)Brand * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (d)Brand very important 31 31 Important 23 23 least important 46 46 Total 100 100 8. (d)Brand * 9. (d)Ambience Crosstab. Count 9. (d)Ambience Total satisfied normal 8. (d)Brand very important 31 0 31 Important 2 21 23 least important 46 0 46 Total 79 21 100 8. (d)Brand * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (d)Brand very important 31 0 0 31 Important 0 21 2 23 least important 46 0 0 46 Total 77 21 2 100 Interpretation: Respondents gives least important to the brand but they are satisfied by quality, price, service, ambience and customization delivered by their favourite restaurant. 8. (e)Ambience * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied 8. (e)Ambience important 33. 33 least important 67 67 Total 100 100 8. (e)Ambience * 9. (b)Price Crosstab Count 9. (b)Price Total satisfied least satisfied 8. (e)Ambience important 33 0 33 least important 21 46 67 Total 54 46 100 8. (e)Ambience * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (e)Ambience important 33 33 least important 67 67 Total 100 100 8. (e)Ambience * 9. (d)Ambience Crosstab Count 9. (d)Ambience Total satisfied normal 8. (e)Ambience important 33 0 33 least important 46 21 67 Total 79 21 100 8. (e)Ambience * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (e)Ambience important 31 0 2 33. least important 46 21 0 67 Total 77 21 2 100 Interpretation: Respondents who gives least important to the ambience but they are satisfied by the quality, price, service ambience customization. 8. (f)Customization * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied 8. (f)Customization very important 2 2 important 98 98 Total 100 100 8. (f)Customization * 9. (b)Price Crosstab Count 9. (b)Price Total satisfied least satisfied 8. (f)Customization very important 2 0 2 important 52 46 98 Total 54 46 100 8. (f)Customization * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (f)Customization very important 2 2. important 98 98 Total 100 100 8. (f)Customization * 9. (d)Ambience Crosstab Count 9. (d)Ambience Total satisfied normal 8. (f)Customization very important 2 0 2 important 77 21 98 Total 79 21 100 8. (f)Customization * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (f)Customization very important 0 0 2 2 important 77 21 0 98 Total 77 21 2 100 Interpretation: Almost all the respondents gives important to the customization and they are also satisfied by the quality, price, service, ambience, customization. 8. (g)Nearness * Satis. In Quality Crosstab Count Satis. In Quality Total very satisfied. 8. (g)Nearness very important 58 58 least important 42 42 Total 100 100 8. (g)Nearness * 9. (b)Price Crosstab Count 9. (b)Price Total satisfied least satisfied 8. (g)Nearness very important 52 6 58 least important 2 40 42 Total 54 46 100 8. (g)Nearness * 9. (c)Service Crosstab Count 9. (c)Service Total satisfied 8. (g)Nearness very important 58 58 least important 42 42 Total 100 100 8. (g)Nearness * 9. (d)Ambience Crosstab Count 9. (d)Ambience Total satisfied normal 8. (g)Nearness very important 37 21 58 least important 42 0 42 Total 79 21 100 8. (g)Nearness * 9. (e)Customization Crosstab Count 9. (e)Customization Total satisfied normal least satisfied 8. (g)Nearness very important 37 21 0 58 least important 40 0 2 42 Total 77 21 2 100 Interpretation: Almost all the respondents prefer to go to nearness restaurant and they are also satisfied by it. Exhibit-10 10)Visit with whom Frequency Percent Valid Percent Cumulative Percent Valid Friends 87 87. 0 87. 0 87. 0 Family 4 4. 0 4. 0 91. 0 g. f/b. f 9 9. 0 9. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: respondents mostly go to the restaurant with their friends. Exhibit-11 11)Scheme Frequency Percent Valid Percent Cumulative Percent Valid unlimited 65 65. 0 65. 0 65. 0 By one get one free 5 5. 0 5. 0 70. 0 Discount 11. 11. 0 11. 0 81. 0 coupons 7 7. 0 7. 0 88. 0 Other 12 12. 0 12. 0 100. 0 Total 100 100. 0 100. 0 Exhibit-12 12)Awareness Frequency Percent Valid Percent Cumulative Percent Valid Friends 68 68. 0 68. 0 68. 0 TV adds 17 17. 0 17. 0 85. 0 news paper adds 9 9. 0 9. 0 94. 0 Posters 4 4. 0 4. 0 98. 0 Internet 2 2. 0 2. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: looking to the above diagram respondents aware about the restaurant by their friends and by TV adds. Exhibit-13 13)Frequency Frequency Percent Valid Percent Cumulative Percent Valid occationally 28 28. 0 28. 0 28. 0 once or twice in a week 15 15. 0 15. 0 43. 0 once or twice in a month. 57 57. 0 57. 0 100. 0 Total 100 100. 0 100. 0 Intr Interpretation: respondents visit dominos once or twice in a month. Exhibit: 14 14)Visit reason Frequency Percent Valid Percent Cumulative Percent Valid In your free hours 66 66. 0 66. 0 66. 0 For meetings 6 6. 0 6. 0 72. 0 For parties 21 21. 0 21. 0 93. 0 For someone parties 7 7. 0 7. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: Respondents mostly like to go to Dominos in their free time for Parties. Exhibit-15 15)Freq. visit reason Frequency Percent Valid Percent Cumulative Percent Valid Quality of food is good 53 53. 0 53. 0 53. 0 Has good friendly atmosphere. 32 32. 0 32. 0 85. 0 It is near your house 10 10. 0 10. 0 95. 0 Other 5 5. 0 5. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: Above diagram conclude that respondents like to go to Dominos because the quality of the food offer by dominos is better. Exhibit-17 17) age Frequency Percent Valid Percent Cumulative Percent Valid 20-25 35 35. 0 35. 0 35. 0 25-30 17 17. 0 17. 0 52. 0 30-40 29 29. 0 29. 0 81. 0 above 40 19 19. 0 19. 0 100. 0 Total 100 100. 0 100. 0 Interpretation: looking to the above exhibit mostly young generation, who come under the age of 20-25 preferred to go to the Dominos. Findings conclusions. 1) From above analysis we can conclude that 68% respondents prefer to go to the Dominos then other restaurants. 2) Respondents prefer to go to the Dominos because the quality of the food is good over there. 3) People give very important to the quality, price and services. They give important to the customization but they give least important to the brand ambience. But comparison to all factor more preference given to quality price. They are satisfied by the quality in their favourite restaurant but they are least satisfied by the price. 4) Out of the respondents most number of respondents visits dominos with their friends family. 5) Respondents also aware about Dominos by their friends and TV adds. 6) Out of respondents mostly they prefer to visit Dominos once or twice in a month in their free time and for parties so we can conclude that they are regular customer. 7) Dominos attracts all kind of generation like those who come in age 20-25, 25-30, and above 30 also. But more attracted by 20-25 years old people. Conclusion 1) People gives more important to price and they also least satisfied by the price in dominos but they are attracted to Dominos because they are satisfied by the quality offered by the Dominos and for that they are not paying high price. 2) People are not attracted towards Dominos because it is an international brand. People are not giving important to the brand but they are giving important to the quality and price. 3) Mostly people go to Dominos with their friends and family. But people go to there with family rarely because of the price factor. They prefer to go U. S. Pizza with family because it offer unlimited scheme which is enable them to spend less. 4) People also aware about the Dominos by their friend and TV adds also by the banners. 5) Dominos attracted all kind of generation like youngster adult. Strategies Following are the strategies adopted by Dominos to attract the customer towards it. 1) They maintain the quality of the food same in every store because there quality is main factor to influence the customer. 2) They maintain same taste in every store. 3) They also maintain hygiene level. 4) They have monopoly in 5 types of pizza which is thin crust, hand toast, cheese burst, deep dish, 3 cheese. 5) They come up with new product every 3-4 months. 6) They contacted their customer and ask about their choice taste and they launch new product according to customer preference. 7) People give more preference to the nearness restaurant so they open their branches in 15 areas. 8) They give free delivery in just 30 minute. If it is not delivered in 30 minute they give pizza free of cost. 9) Mostly college going student and working people go to Dominos so they open there branches in 2. 5km 3 km near to the college and office area. Recommendation 1) People give more important to the price if dominos reduce their price then people they can capture almost all market share. 2) If dominos don’t want to reduce the price than it can also offer some discount or unlimited scheme. People attracted towards US pizza because of it unlimited scheme. Here people already satisfied by quality if they offer some scheme then they can attract more people who go restaurant with their family. 3) They also offer salads or other customization product. Annexure Dominos vs us Pizza Questionnaire Respected Sir/ Madam We, 1st year PGDM student from St Kabir Institute of Professional Studies , conducting a research on ‘Dominos vs US Pizza’. We want to know your views about these restaurants. The information provided by you is purely for research purpose and will be strictly kept confidential. Top of Form. 1) Do you like to go Restaurants? Yes No 2) When do you go to Restaurants? Once or Twice a week Once or Twice in 15 days Once or twice in a month Occasionally 3) How many times in previous month did you visit the restaurant? 0 1-5 5-10 More than 10 4) What do you prefer in snacks? Pizza Chat Sandwich Others 5) Do you like Pizza? Yes No 6) Where do you like the most to go for Pizza? Dominos US Pizza Pizza world Pizza zone Others 7) Why you like to go in above mention Pizza restaurant? Quality is good Price is low Service is good Others 8) How much importance do you give to the following factors when you go for eating pizza? Very Important Important Least Important Not at all Important Quality Price Service Brand Ambience Customization Nearness 9) How much are you satisfied with the following factors in your preferred pizza restaurant? Very satisfied Satisfied Normal least Satisfied Not Satisfied Quality Price Service Ambience Customization 10) With whom you like to go in this restaurant? Friends Colleague Family G. F/ B. F Others 11) Is there any scheme in above pizza restaurant? Unlimited By one get one free Discount Price Coupon Others No scheme s 12) How did you know above restaurant? Friends T. V Add. Newspaper adds. poster. Internet Other 13) How frequently you go to this restaurant? Occationally Once or twice in week Once or twice in month rarely 14) When you prefer to go? In your free hours For meetings For parties For someone’s parties 15) What is the main reason you frequently go a particular restaurant? Quality of food is good Has a good friendly atmosphere your family children like it It is near your house Other 16) Name 17) Age 15-20 20-25 25-30 30-40 above 40 18) Area where you belong: 19) Contact No 20) Gender Male Female 21) Occupation Student Job Business Other 22) You’re monthly Income? 20000 Bottom of Form.

Lord Hastings: A Justification To Omit Regret :: essays research papers fc

Lord Hastings: A Justification to Omit Regret We, the audience, lend our ears and nod our heads at the exactness of Lord Hastings's uttering: I think there's never a man in Christendom, Can lesser hide his love or hate than he, For by his face shall you know his heart. (3.4.51-53). Ironically, we do not assent to his words because they are exactly in the right, but because they are exactly in the wrong. By Act III, Richard III exhibits a pallet of personalities including the devoted brother, the witty wooer, and the loyal subject. We see that these almost Platonic ideals are tarnished black under the rule of Richard's perfectly evil intent to manipulate. Lord Hastings, however, could not see until it was too late. The time to weigh the validity of the supernatural signs and omens in Stanley’s dream had past. Before his death, Lord Hastings misperceives the "subtle, false, and treacherous" Richard, and only saw the face (i.e. the theatrical abilities of Richard), not the heart (1.1.37). Why, then, do we nod at wrongness? The answer lies in the fact that we are plummeted into absolute awe. We have reached a catharsis of our emotions in response to the summit of Richard’s manipulative character, where Lord Hastings had actually believed tha t Richard was a man incapable of manipulating. Our response is a sign of assent because Lord Hastings is completely justified for trusting Richard and ignoring Stanley’s forebodings entirely. If Lord Hastings had the chance to relive his death scene, he would have two choices: to reiterate his regret for not listening to Stanley, or take a different course, and omit his regret. The study of this paper involves what types of justification Lord Hastings could offer if he had the opportunity to omit regret. His justification would necessarily contain an assessment of Richard’s compelling theatrical abilities. In other words, Lord Hastings would have to prove that Richard was too good of an actor for anyone to realize his acting. Lord Hastings now carries the burden of proof on his shoulders. Lord Hastings would probably refer to the ideal representation of brotherly love Richard shows to Clarence. â€Å"We are not safe Clarence, we are not safe,† Richard says, probably placing his hand on his brother’s shoulder while stressing â€Å"we†(1.1.70). In those words, Clarence felt warmth, despite the cold chains draping from his wrists; felt security, despite his insecurities about the reason as to why he was placed under arrest.

Adolescents With Food Allergy Health And Social Care Essay

Aim: To develop and formalize the Food Allergy Quality of Life Questionnaire-Teenager Form ( FAQLQ-TF ) in the Dutch linguistic communication. Methods: Ten nutrient allergic striplings ( 13-17 old ages ) were interviewed and generated 166 HRQL points. The most of import points were identified by 51 nutrient allergic striplings utilizing the clinical impact method, ensuing in the FAQLQ-TF incorporating 28 points ( mark scope 1 ‘no damage ‘ to 7 ‘maximal damage ‘ ) . The FAQLQ-TF, the Food Allergy Independent Measure ( FAIM ) and a generic HRQL questionnaire ( CHQ-CF87 ) were sent to 98 nutrient allergic striplings for cross-sectional proof of the FAQLQ-TF. Consequences: Construct cogency was assessed by the correlativity between the FAQLQ-TF and the FAIM ( rho 0.57, P & A ; lt ; 0.001 ) . The FAQLQ-TF had first-class internal consistence ( Cronbach ? 0.92 ) and discriminated between striplings who differed in figure of nutrient allergic reactions ( 1 nutrient allergic reaction vs. & A ; gt ; 2 nutrient allergic reactions, entire FAQLQ-TF mark, 4.3 vs. 3.5 ; p=0.037 ) , but did non know apart between reported anaphylaxis or non. The FAQLQ-TF correlated decrepit with 6 of the 11 CHQ-CF87 graduated tables, showing convergent/discriminant cogency. Decision: The FAQLQ-TF is the first self-administered, disease-specific HRQL questionnaire for nutrient allergic striplings. It has good concept cogency and first-class internal consistence and discriminates between striplings who differ in figure of nutrient allergic reactions. The FAQLQ-TF is short and easy to utilize and may hence be a utile tool in clinical research.Clinical DeductionsThe Food Allergy Quality of Life Questionnaire-Teenager Form ( FAQLQ-TF ) is dependable, valid, short and easy to utilize and therefore a utile tool in clinical research.Capsule sum-upThe FAQLQ-TF is the first self-administered, disease-specific HRQL questionnaire for nutrient allergic striplings. It is dependable and valid and hence a utile tool in clinical research in which HRQL is the result of involvement.Key wordsAdolescents EuroPrevall Food allergic reaction Health-related quality of life AdolescentsAbbreviationsHRQL Health-Related Quality of Life FAQLQ-TF Food Allergy Quality of Life Questionnaire – Adolescent Form FAQLQ-CF Food Allergy Quality of Life Questionnaire – Child Form FAQLQ-PF Food Allergy Quality of Life Questionnaire – Parent Form MI Mean Importance OI Overall Importance FAIM Food Allergy Independent Measure EO Expectation of Outcome IM Independent Measure CHQ-CF87 Children ‘s Health Questionnaire – Child Form AADR Allergen Avoidance and Dietary Restrictions EI Emotional Impact RAE Risk of Accidental Exposure DBPCFC Double-Blind Placebo-Controlled Food ChallengeIntroductionHaving a nutrient allergic reaction can be fatal and striplings are at the highest hazard of decease from nutrient allergic reaction ( 1-3 ) . It is estimated that 2.3 % of striplings are nutrient allergic ( 4 ) . The lone effectual signifier of intervention of nutrient allergic reaction is rigorous turning away of the implicated nutrient ( s ) and proviso of medicines for exigency intervention ( 5 ) . In malice of the high hazard of decease, nutrient allergic striplings really reported societal isolation as the most distressing facet of their disease ( 6 ) . In add-on, some striplings reported depression as a consequence of nutrient allergic reaction and this may take to troubles in school public presentation and leisure activities ( 7 ) . Therefore, nutrient allergic striplings need to be continuously watchful as to what they are eating in legion state of affairss and scenes and, along with the fright of allergic reac tions, this may hold a negative impact on quality of life. At present, no validated self-administered, food-allergy-specific health-related quality of life ( HRQL ) questionnaire exists for usage in striplings. A few surveies have reported that nutrient allergic reaction has a negative impact on HRQL in striplings. However, three restrictions arise when construing these surveies. First, no differentiation was made between striplings and younger kids ( 8-13 ) , whereas HRQL in striplings demands to be addressed individually, because HRQL may be influenced by the phase of neurocognitive and emotional development of an person ( 14 ; 15 ) . Second, HRQL questionnaires were administered to parents therefore mensurating parents ‘ perceptual experiences ( 8-13 ) . However, kids and parents differ in their positions and judgements about quality of life ( 16 ) . Finally, surveies used generic HRQL questionnaires ( 11-13 ; 17 ) or disease-specific questionnaires which have non been validated ( 8 ; 10 ) , whereas generic HRQL questionnaires are n on every bit sensitive as disease-specific HRQL questionnaires ( 18 ) and proof is highly of import in order to find whether the questionnaire is mensurating that portion of quality of life which is determined by the mark upset ( 19 ) . Therefore, we have developed and cross-sectionally validated the first self-administered, food-allergy-specific HRQL questionnaire for striplings, the Food Allergy Quality of Life Questionnaire-Teenager Form ( FAQLQ-TF ) . This questionnaire has been developed as portion of the EuroPrevall undertaking, a European multi-center research undertaking on nutrient allergic reaction. The FAQLQ-TF complements the late developed self-administered Food Allergy Quality of Life Questionnaire-Child Form ( FAQLQ-CF ) for kids aged 8 to 12 old ages ( 20 ) and the parent-administered Food Allergy Quality of Life Questionnaire-Parent Form ( FAQLQ-PF ) for parents of nutrient allergic kids aged 0 to 12 old ages ( 21 ) .MethodParticipants and processDuring point coevals, participants were recruited merely from our outpatient pediatric allergic reaction clinic. Two striplings were approached during a double-blind placebo-controlled nutrient challenge ( DBPCFC ) and, based on patient records, eight strip lings were approached by phone. All approached striplings ( niˆ?10 ) agreed to take part in an interview on the impact of nutrient allergic reaction on their day-to-day life. During point decrease and cross-sectional proof, participants were recruited from our outpatient pediatric allergic reaction clinic ( based on patient records or assignments for DBPCFC ) or were recruited by advertizement in local intelligence documents and through nutrient allergy support organisations ( the Dutch Foundation for Food Allergy and the Dutch Anaphylaxis Network ) . A missive of invitation, the questionnaire and a pre-paid return envelop was sent to suited striplings from our clinic and to striplings who responded to the advertizement. The missive of invitation stressed that engagement was wholly voluntary. When the questionnaire was non returned within a month, the stripling was contacted by phone as a reminder. Adolescents were non paid for their engagement in any phase of questionnaire development or proof. Before cross-sectional proof, the questionnaire was pre-tested in three striplings ( aged 13, 15 and 17 old ages ) . No major jobs emerged during this pre-test. Thereafter, the FAQLQ-TF, the Food Allergy Independent Measure ( FAIM ) and the CHQ-CF87, a generic quality of life questionnaire, were sent by mail to 98 nutrient allergic striplings. Some of them had participated in the point coevals ( 10 % ) or point decrease ( 49 % ) . Descriptive features were asked sing age, sex, type and figure of nutrient allergic reactions, type of symptoms and diagnosing. For the striplings recruited from our clinic, we checked patient records to find whether nutrient allergic reaction had been diagnosed by a DBPCFC. During all phases of questionnaire development and proof, all common nutrient allergic reactions and different types and badnesss of symptoms were represented. The survey was approved by the local medical moralss review committee ( METc 2005/051 ) who deemed that permission from the committee was non required.DevelopmentItem coevals For the development and proof of the FAQLQ-TF, the same methodological analysis was used as for the development and proof of the FAQLQ-CF, which is described in more item elsewhere ( 20 ) . Briefly, possible points for the new questionnaire were generated by questioning 10 nutrient allergic striplings ( aged 13-17 old ages ) . In add-on, literature reappraisal and adept sentiment were consulted. This resulted in an drawn-out point questionnaire of 166 points. Item decrease The drawn-out point questionnaire was sent to a different group of 51 nutrient allergic striplings to place the most of import points by utilizing the clinical impact method ( 22 ; 23 ) . The striplings were asked to bespeak the importance of applicable points utilizing a five-point graduated table. Frequency ( per centum ) was multiplied by average importance ( MI ) , ensuing in the overall importance ( OI ) of each point. The maximum possible OI was 5.0 ( 24 ; 25 ) . Items with the greatest OI were selected for the FAQLQ-TF, except one of any brace of points with an inter-item correlativity & A ; gt ; 0.85 and/or overlapping content ( face cogency ) . The selected points were worded as inquiries holding a seven-point response graduated table runing from ‘not troubled ‘ to ‘extremely troubled ‘ ( 23 ; 25 ) . A psychologist and a linguist reviewed the FAQLQ-TF for lucidity and easiness of usage.Cross-sectional proofConstruct cogency Construct cogency was investigated by computation of correlativity coefficients for the FAQLQ-TF with the Food Allergy Independent Measure ( FAIM ) . This attack has already been successfully implemented to formalize disease-specific HRQL questionnaires ( 9 ; 20 ; 21 ; 25 ) and it is particularly utile in anaphylactic upsets where no nonsubjective measuring of the extent or badness of disease exists ( 26 ) . The FAIM, which was besides used to formalize the FAQLQ-CF ( 20 ) , includes four Expectation of Outcome ( EO ) inquiries and two Independent Measure ( IM ) inquiries. The EO inquiries are based on the sensed outlook of patients of what will go on following exposure which is likely to be a impulsive force of quality of life ( 26 ) . The IM inquiries are based on the same rule and inquire about the sensed figure of nutrients one needs to avoid and sensed impact on societal life. We expected moderate correlativity coefficients ( 0.40-0.60 ) for the FAQLQ-TF with the FAIM. The proof of the FAQLQ-TF was carried out in the Dutch linguistic communication. The English version of the FAQLQ-TF and the FAIM are presented as Figure E1 and Figure E2 in the Online Repository. The Dutch FAQLQ-TF and the FAIM were translated into English by a native English talker and back translated by a native Dutch talker, harmonizing to the guidelines of the World Health Organization ( 27 ) . The original Dutch version was compared with the back translated Dutch version. No of import differences in content or significance of inquiries emerged. Discriminative ability To set up the discriminatory ability of the FAQLQ-TF, we compared the entire FAQLQ-TF mark for striplings who reported anaphylaxis ( i.e. striplings who reported two or more of the undermentioned cardiovascular symptoms ; giddiness, experiencing your bosom round fast, loss of vision, inability to stand, light headedness, prostration, loss of consciousness/passing out ) versus striplings who did non, for striplings who reported many nutrient allergic reactions versus striplings who reported few nutrient allergic reactions, for male childs versus misss ( 28 ) and for striplings who were recruited from our clinic versus striplings who were recruited by advertizement. Dependability The dependability of the FAQLQ-TF was assessed by administrating the questionnaire to 34 striplings on two occasions 10-14 yearss apart. Convergent and discriminant cogency To look into convergent and discriminant cogency, a generic HRQL questionnaire was administered: the Children ‘s Health Questionnaire-Child Form ( CHQ-CF87 ) ( 29 ; 30 ) . This questionnaire is self-administered by striplings and contains 87 points divided into 12 graduated tables. We expected weak correlativity coefficients ( 0.20-0.40 ) for the FAQLQ-TF with the CHQ-CF87.Statistical analysesThe natural FAQLQ-TF and FAIM scores 0 to 6 were recoded as 1 to 7. The entire FAQLQ-TF mark is the average mark of all points with a scope of 1 ‘no damage ‘ to 7 ‘maximal damage ‘ . To measure concept cogency, Spearman ‘s correlativity coefficients were calculated between the FAQLQ-TF and the FAIM. The allotment of the points of FAQLQ-TF into spheres was based on factor analysis ( chief constituent analysis with Varimax rotary motion ) ( 31 ) and face cogency determined by a clinical expert panel ( BMJFdB, JNGOE and AEJD ) ( 14 ; 32 ) . To look into the inter nal consistence of the FAQLQ-TF and the spheres, Cronbach ‘s ? were calculated. An ? greater than 0.70 indicates good internal consistence ( 33 ) . The Mann-Whitney trial was used for mensurating the discriminatory ability of the FAQLQ-TF. The dependability of the FAQLQ-TF was assessed by ciphering the intraclass correlativity coefficient of the repeated FAQLQ-TF measuring ( 34 ) . Finally, convergent and discriminant cogency were assessed by ciphering Spearman ‘s correlativity coefficients between the FAQLQ-TF and the CHQ-CF87 graduated tables. Statistical analyses were performed with SPSS for Windows 14.0 ( SPSS Inc. , Chicago, IL, USA ) .ConsequenceDevelopmentDescriptive features of the striplings involved in the point coevals and point decrease are shown in Table 1. The drawn-out point questionnaire was returned by 46 striplings ( response rate 90 % ) . The OI tonss of all 166 points of the drawn-out point questionnaire ranged from 0.00 to 2.89. The point decrease re sulted in the choice of 28 points ( OI & A ; gt ; 1.37 ) for the FAQLQ-TF ( Table 2 ) .Cross-sectional proofParticipants The questionnaire bundle including the FAQLQ-TF, the FAIM and the CHQ-CF87 were returned by 75 striplings ( response rate 77 % ) . One stripling was excluded because the descriptive features were losing from the questionnaire, ensuing in 74 assessable questionnaires for the cross-sectional proof. Forty-three striplings ( 58 % ) were recruited from our clinic, of which 19 ( 26 % ) had a nutrient allergic reaction confirmed by a DBPCFC. The other striplings from our clinic had a physician-diagnosed nutrient allergic reaction ( skin asshole and/or blood trial ) and the bulk was expecting DBPCFC. All striplings recruited by advertizement ( 42 % ) reported physician-diagnosed nutrient allergic reactions. Descriptive features of the striplings involved in the cross-sectional proof are shown in Table 1. There were no important differences in descriptive features between male childs and misss, between striplings recruited from our clinic and striplings recruited by advertizement or between s triplings with a physician-diagnosed nutrient allergic reaction and striplings with a nutrient allergic reaction diagnosed by DBPCFC. Construct cogency Most points of the FAQLQ-TF correlated significantly with at least one of the FAIM inquiries and with the mean of the FAIM inquiries. Five points did non correlate with any of the FAIM inquiries and were hence excluded from the questionnaire. The validated FAQLQ-TF therefore consists of 23 inquiries. As expected, we found moderate correlativity coefficients between the FAQLQ-TF and the FAIM. The entire FAQLQ-TF mark correlated significantly with the average FAIM ( rho 0.57, P & A ; lt ; 0.001 ) and with the single FAIM inquiries ( Table 3 ) . This important correlativity coefficient was found for striplings with a nutrient allergic reaction diagnosed by DBPCFC and for striplings with a physician-diagnosed nutrient allergic reaction ( entire FAQLQ-TF mark with the average FAIM, rho 0.76, P & A ; lt ; 0.000 and rho 0.52, P & A ; lt ; 0.000, severally ) . These consequences support the concept cogency of the FAQLQ-TF. That is, the FAQLQ-TF steps that portion of quality of life that is a ffected by nutrient allergic reaction. Expectation of Outcome inquiry 3 ( EO3 ) did non correlate with any of the single HRQL points and is therefore improbable to be an appropriate independent step for nutrient allergic reaction in striplings. Therefore, we excluded this inquiry from farther analyses.Sphere construction and internal consistenceThe 23 points of the FAQLQ-TF were subjected to factor analysis ( chief constituent analysis ) , which revealed 5 factors with characteristic root of a square matrixs & A ; gt ; 1. To assistance in the reading of these factors, Varimax rotary motion was performed for 5, 4 and 3 factors. These groupings were reviewed by an adept panel, and based on face cogency the grouping of 3 factors made the most sense. This grouping revealed the undermentioned spheres: Allergen Avoidance and Dietary Restrictions ( AADR ) , Emotional Impact ( EI ) and Risk of Accidental Exposure ( RAE ) . These three factors showed a figure of strong burdens ; all exceed 0 .300, which is regarded as an acceptable standard ( 31 ) . The adept panel allocated 3 points to a more appropriate sphere based on face cogency. The FAQLQ-TF and the spheres had first-class internal consistence with Cronbach ‘s ? transcending 0.70 ( Table 3 ) .Discriminative abilityAdolescents who reported two or more nutrient allergic reactions reported a significantly more impaired HRQL than striplings who reported merely one nutrient allergic reaction ( entire FAQLQ-TF mark 4.3 vs. 3.5 ; p=0.037 ) . There was no important difference in entire FAQLQ-TF mark between striplings who reported anaphylaxis ( cardiovascular symptoms ) and striplings who did non describe anaphylaxis ( 4.5 vs. 4.0 ; p=0.184 ) or between male childs and misss ( 4.0 vs. 4.3 ; p=0.324 ) . Adolescents who were recruited by advertizement reported a significantly more impaired HRQL than striplings recruited from our clinic ( entire FAQLQ-TF mark 4.6 vs. 3.9 ; p=0.015 ) . Dependability The entire FAQLQ-TF mark intraclass correlativity coefficient was 0.98 ( 95 % assurance interval, 0.95-0.99 ) , bespeaking first-class test-retest dependability. Convergent and discriminant cogency The entire FAQLQ-TF mark correlated weakly with 6 of the 11 CHQ-CF87 graduated tables. In add-on, the spheres of the FAQLQ-TF correlated weakly with several CHQ-CF87 graduated tables ( Table 4 ) . This indicates that both questionnaires step constructs that are partially related ( i.e. convergent cogency ) . However, as expected the correlativities are weak and sometimes even absent because the CHQ-CF87 is a generic quality of life questionnaires and hence non every bit sensitive as the disease-specific FAQLQ-TF ( i.e. discriminant cogency ) .DiscussionWe have developed and validated the first health-related quality of life ( HRQL ) questionnaire particular for striplings with nutrient allergic reaction, the Food Allergy Quality of Life Questionnaire-Teenager Form ( FAQLQ-TF ) . We found that the FAQLQ-TF has good concept cogency and first-class internal consistence ( Table 3 ) . In add-on, the FAQLQ-TF discriminates between striplings who differ in figure of nutrient allergic reacti ons. Finally, the FAQLQ-TF showed convergent/discriminant cogency ( Table 4 ) , which supports the demand for a disease-specific quality of life questionnaire for nutrient allergic striplings. It is known that HRQL may be influenced by the current phase of cognitive, societal and emotional development of an person. Therefore, it has been argued that HRQL in striplings should be measured by agencies of a specific instrument ( 14 ; 15 ) . The FAQLQ-TF was specifically designed for nutrient allergic striplings aged 13 to 17 old ages. Age rightness was ensured by bring forthing and including merely points that were regarded as of import by nutrient allergic striplings ( clinical impact method ) . The FAQLQ-TF focal points on the perceptual experiences of the striplings themselves, because the questionnaire is self-administered. Many of the points in this instrument are specific to striplings. An illustration is ‘Carrying an Epipen ‘ . The Epipen issue in nutrient allergic striplings is in harmony with the literature. It has been reported that striplings raise concerns about its size and portability ( 35 ) and sometimes striplings do non transport it based on societal fortunes and sensed hazards ( 36 ) . Despite our age specific attack and the separate development of kid and adolescent questionnaires, it is striking that about two tierces of the adolescent inquiries in the FAQLQ-TF correspond to the kid inquiries in the FAQLQ-CF ( 20 ) . Therefore, although we generated many age specific points, there are seemingly ‘general ‘ nutrient allergic reaction points that are of import in kids and striplings. Furthermore, we found that the three most of import points that impair quality of life were the same in kids and adolescents ( ‘Always be alert as to what you are eating ‘ , ‘The ingredients of a merchandise alteration ‘ , ‘Able to eat fewer merchandises ‘ ) . An unexpected determination was that EO3 ( Chance of deceasing when by chance exposed ) was non correlated with any of the points of the FAQLQ-TF. This may bespeak that fright of deceasing of nutrient allergic reaction is non a driving force of quality of life in striplings, which may be characteristic and specific for striplings. It has been reported that striplings perceived their anaphylaxis as ‘no large trade ‘ ( 35 ) . In add-on, striplings are at the highest hazard of decease from nutrient allergic reaction ( 1-3 ) . This high hazard may be the consequence of underestimate of the badness of nutrient allergic reaction and the belief of striplings that they will non decease from any cause, including their nutrient allergic reaction. In fact, there were no striplings in this survey who reported ‘always ( 100 % opportunity ) ‘ of deceasing when by chance exposed, whereas this was reported by 5 % of kids and 4 % of grownups in other FAQLQ proof surveies ( non shown ) . Although non statistically important, this is a notable observation. The wrong belief of immortality of striplings may ensue in risk-taking behaviour that may increase the hazard of deceasing from a nutrient allergic reaction. Therefore, doctors and other health-care suppliers should be cognizant that underestimate of nutrient allergic symptoms may be of import when reding striplings with nutrient allergic reaction. When comparing the discriminatory consequences of the FAQLQ-TF with the FAQLQ-CF ( 20 ) , two interesting observations emerged. First, there was no important difference in entire FAQLQ-TF mark between striplings who reported anaphylaxis ( cardiovascular symptoms ) and striplings who did non. The same consequence was found in kids ( 20 ) . Second, striplings who were recruited by advertizement reported a significantly more impaired HRQL than striplings recruited from our clinic. This difference was non important in kids, although a tendency was seen ( 20 ) . It may be that striplings see safety and security by being looked after in the clinic, whereas striplings outside the clinic experience more uncertainness and insecurity about their nutrient allergic reaction ( 37 ) . Most striplings recruited from our clinic were known to us for many old ages ( average figure of old ages since first visit 12.5 ( SD 5.4 ) ) . In add-on, it has late been shown that parental trait anxiousness is hig her in parents of kids with a suspected nutrient allergic reaction who refused to take part in a DBPCFC than parents who did take part ( 38 ) . Since it is known that parental anxiousness is related to child anxiousness ( 39 ) , it may be that the striplings in our survey recruited by advertizement have higher degrees of trait anxiousness than striplings recruited from our clinic and may therefore hold more damage in quality of life. This survey may hold some restrictions. First, the proof of the FAQLQ-TF was carried out in the Dutch linguistic communication. The FAQLQ-TF was carefully translated into English utilizing the guidelines of the World Health Organization. The cogency of the English linguistic communication version of this questionnaire is presently being investigated every bit good as versions in several other European linguistic communications. Our experience with the Dutch Vespid Allergy Quality of Life Questionnaire was that the English interlingual rendition validated good ( 25 ) . It is possible, nevertheless, that cultural differences may act upon the ability of our questionnaire to place the most of import points for nutrient allergic patients in different cultural or lingual scenes. Second, patients were recruited at our clinic and by advertizement. These patients may differ from each other, for illustration in footings of degree of information about their nutrient allergic reaction. However, we did non happen important differences in the descriptive features between these groups and other possible differences would non hold adversely influenced the proof process, where a spectrum of badness is good to obtain optimum correlativities. Third, some of the points in this questionnaire are likely to be clip sensitive in the long tally. For illustration, new labelling Torahs could do the labelling points included in this questionnaire obsolete. It is likely that in clip, this questionnaire will necessitate some updating and version. Finally, this study describes merely the cross-sectional proof of the FAQLQ-TF. Currently, the longitudinal proof of the questionnaire is being investigated ( i.e. the capacity of the FAQLQ-TF to mensurate differences in HRQL over clip ) . In drumhead, we have developed and validated the first HRQL questionnaire particular for nutrient allergic striplings, the Food Allergy Quality of Life Questionnaire-Teenager Form ( FAQLQ-TF ) . We found that this questionnaire is valid and dependable and it is short and easy to utilize. The FAQLQ-TF will be therefore a suited questionnaire for clinical research in nutrient allergic striplings in which HRQL is the result of involvement.RecognitionsThis work was funded by the EU through the EuroPrevall undertaking ( FOOD-CT-2005-514000 ) . We would wish to thank Dr. GFEC van Linden new wave lair Heuvell, medical psychologist, and Karel Verbeek, linguist, for reexamining the drawn-out point questionnaire and the FAQLQ-TF and Tina van der Velde for executing the test-retest of the FAQLQ-TF.

What Is the St. Petersburg Paradox

You’re on the streets of St. Petersburg, Russia, and an old man proposes the following game. He flips a coin (and will borrow one of yours if you don’t trust that his is a fair one). If it lands tails up then you lose and the game is over. If the coin lands heads up then you win one ruble and the game continues. The coin is tossed again. If it is tails, then the game ends. If it is heads, then you win an additional two rubles. The game continues in this fashion. For each successive head we double our winnings from the previous round, but at the sign of the first tail, the game is done. How much would you pay to play this game? When we consider the expected value of this game, you should jump at the chance, no matter what the cost is to play. However, from the description above, you probably wouldn’t be willing to pay much. After all, there is a 50% probability of winning nothing. This is what is known as the St. Petersburg Paradox, named due to the 1738 publication of Daniel Bernoulli Commentaries of the Imperial Academy of Science of Saint Petersburg. Some Probabilities Lets begin by calculating probabilities associated with this game. The probability that a fair coin lands heads up is 1/2. Each coin toss is an independent event and so we multiply probabilities possibly with the use of a tree diagram. The probability of two heads in a row is (1/2)) x (1/2) 1/4.The probability of three heads in a row is (1/2) x (1/2) x (1/2) 1/8.To express the probability of n heads in a row, where n is a positive whole number we use exponents to write 1/2n. Some Payouts Now lets move on and see if we can generalize what the winnings would be in each round. If you have a head in the first round you win one ruble for that round.If there is a head in the second round you win two rubles in that round.If there is a head in the third round, then you win four rubles in that round.If you have been lucky enough to make it all the way to the nth round, then you will win 2n-1 rubles in that round. Expected Value of the Game The expected value of a game tells us what the winnings would average out to be if you played the game many, many times. To calculate the expected value, we multiply the value of the winnings from each round with the probability of getting to this round, and then add all of these products together. From the first round, you have probability 1/2 and winnings of 1 ruble: 1/2 x 1 1/2From the second round, you have probability 1/4 and winnings of 2 rubles: 1/4 x 2 1/2From the first round, you have probability 1/8 and winnings of 4 rubles: 1/8 x 4 1/2From the first round, you have probability 1/16 and winnings of 8 rubles: 1/16 x 8 1/2From the first round, you have probability 1/2n and winnings of 2n-1 rubles: 1/2n x 2n-1 1/2 The value from each round is 1/2, and adding the results from the first n rounds together gives us an expected value of n/2 rubles. Since n can be any positive whole number, the expected value is limitless. The Paradox So what should you pay to play? A ruble, a thousand rubles or even a billion rubles would all, in the long run, be less than the expected value. Despite the above calculation promising untold riches, we would all still be reluctant to pay very much to play. There are numerous ways to resolve the paradox. One of the simpler ways is that no one would offer a game such as the one described above. No one has the infinite resources that it would take to pay someone who continued to flip heads. Another way to resolve the paradox involves pointing out how improbable it is to get something like 20 heads in a row. The odds of this happening are better than winning most state lotteries. People routinely play such lotteries for five dollars or less. So the price to play the St. Petersburg game should probably not exceed a few dollars. If the man in St. Petersburg says that it will cost anything more than a few rubles to play his game, you should politely refuse and walk away. Rubles aren’t worth much anyway.