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BETTING RATES - CAN THEY BE USEFUL?

BETTING RATES - CAN THEY BE USEFUL?. Magdalena Hykšová CTU Prague 2011. Which pair has the greates chance for the win in the competition StarDance 2010?. e.g., Kříž/Stodůlková: stake 1 EUR  win 2,55 EUR or nothing. Similarly in the following cases:.

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BETTING RATES - CAN THEY BE USEFUL?

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  1. BETTING RATES- CAN THEY BE USEFUL? Magdalena Hykšová CTU Prague 2011

  2. Which pair has the greates chance for the win in the competition StarDance 2010? e.g., Kříž/Stodůlková: stake 1 EUR win 2,55 EUR or nothing

  3. Similarly in the following cases:

  4. Where should we bet for the football match Spain – Honduras at the world championship 2010? Numbers in the table: how much the bookmaker’s pays for 1 EUR in the case of the sake on the right result

  5. Where should we bet for the football match Spain – Honduras at the world championship 2010? Whatever happens,Tipsport pays the mostThe highest chance for the win: Spain

  6. We bet for all alternatives to obtain 100 EUR in any case.How many percent of the stake will we get back? Return – e.g., forFortuna: To win 100 EUR in the case of the win of Spain, we have to bet 100/1,12 on it In total we pay:

  7. We bet for all alternatives to obtain 100 EUR in any case.How many percent of the stake will we get back? Return – e.g., forFortuna: In total we pay:

  8. betting ratep ... how much the bettor has to bet on the event A to win 1 EUR, if A occurs Hockey championschip 2010, finalCZE – RU pCZE = 1/4, pRU = 9/10 To win S=100 CZK, I have to bet 100  1/4 = 25 EUR ... winof the Czech Republic 100  9/10 = 90 EUR ... win of Russia

  9. betting ratep ... how much the bettor has to bet on the event A to win 1 EUR, if A occurs Hockey championschip 2010, finalCZE – RU pCZE = 1/4, pRU = 9/10 To win S=100 CZK, I have to bet 100  1/4 = 25 EUR ... winof the Czech Republic 100  9/10 = 90 EUR ... win of Russia I will pay 115 EUR, win 100 EUR  return:

  10. Hockey championschip 2010, finalCZE – RU pCZE = 1/4, pRU = 9/10 To win S=100 CZK, I have to bet 100  1/4 = 25 EUR ... winof the Czech Republic 100  9/10 = 90 EUR ... win of Russia I will pay 115 EUR, win 100 EUR  return: pCZE + pRU>1 the bettor loses  fair bett

  11. FAIR BETT the bookmaker specifying p must be in danger of getting into the role of the better  we admit positive and negative betts values the bettor pays: pCZES + pRUS, obtains: S pCZE + pRU>1 ... bettor chooses S < 0and wins pCZE + pRU<1 ... bettor chooses S > 0 and wins  pCZE + pRU = 1

  12. FAIR BETT S ... the value of the win if A occurs (positive or negative) Bettor’s profit: Z(A) = S – pS = (1 – p) S Z(A) = – pS In total we can write:Z = (|A| – p) S Fornevents: Z = (|A1| – p1) S+ (|A2| – p2) S+ ... + (|An| – pn) S

  13. Bookmaker’s estimation of probability P(A): e.g., P(A)=0,5 no danger of changing the roles it is profitable to propose e.g.p=0,75 Consider S = 100 win 100 CZKif A occurs ... bett 75 EUR repetition: bookmaker’s guessabout bettor’s profit ca. 1/2 cases:Aoccurs Z = 100 – 75 = 25 EUR ca. 1/2 cases:Adoes not Z = – 75 EUR Average profit:

  14. Bookmaker’s estimation of probability P(A): Mean bettor’s profit: S > 0meanbettor’s profit Z < 0  bookmaker benefits  fair bett Fair bett: we allow S < 0 p ... probability that the bookmaker franklyassigns to the event A

  15. BETTING RATES DETERMINATION bettor’s profit: Z(A) =S–pS=(1–p)S Z(A)=–pS coherent betting rates: profit Z cannot be always positive, no matter which event occurs (sure win of the bettor) coherence requirement basic axioms of probability theory i.e., to prevent a sure loss, bookmaker’s rates p have to satisfy axioms of probability theory

  16. BETTING RATES  Warning – who can profit from them? • Application of probability – determination of rates (although the bets are not fair)  The meaning of axioms of probability theory  Broadening of probability conception

  17. SUBJECTIVE INTERPRETATION PROBABILITY = measure of personal conviction or belief in the occurence of someevent Václav Šimerka (1818 – 1887), 1882 Frank Plumpton Ramsey (1903 – 1930), 1931 (1926) Bruno de Finetti (1906 – 1985), 1931, 1937 Leonard Jimmie Savage (1917 – 1971), 1954

  18. SUBJECTIVE INTERPRETATION Everyday considerations • No traffic jam probably occurs on the highway this time. • Our hockey team has no chance against Russia. • This drug should be effective in your case. • The election will be probably won by CSSD. • If I set out at 16:10, I will perhaps catch the train. • CNB predicts the 1.8% VAT growin 2012.

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