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BETTING RATES - CAN THEY BE USEFUL?

Exploring the concept of betting rates and their significance in determining probabilities, betting stakes, and potential profits for bettors. Analyzing examples from sports events to illustrate betting strategies and outcomes.

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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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