Betting By Billy Lai and Charlie Law
Probability and Percentage Gambling is the wager of something of material value on an event with an uncertain outcome with the primary intent of winning additional material goods
Presentation Outline • Expected value • Pari-mutuel betting
Mark Six -- Background • Lottery Betting • Organized by the Hong Kong Jockey Club (HKJC) Since 1975 • 3 Times a Week (Tuesday, Thursday and Saturday or Sunday)
Hong Kong Jockey Club(香港賽馬會) • Non-profit organization founded in1884 • Provides betting entertainment in HK such as horse racing and Mark Six • Largest taxpayer (~$1billion each year)
What is Mark Six? • Lottery Style Game with 49 colored balls numbered from 1 to 49 • In each game, 7 balls are drawn from these 49 balls • Name of First Six Numbers Drawn: Drawn Number Name of Last One Drawn: Extra Number
Rules Of Mark Six • Rule 1: Choose 6 out of 49 numbers • Rule2: Wager $10 on each Selection • For example, in the ticket, Selection 1: Selection 2: Total wager : $10 x = $ 0 http://www.youtube.com/watch?v=DFYSUX-L9jU Ticket of Mark Six
What is the winning probability? • Example. (winning probability of 6th prize[3 Drawn Numbers + Extra Number]) • Number of possible way to buy a selection: • Number of possible way to win 6th prize: • Winning probability of 6th prize: Remarks:
Question The Prize Qualification on 17/2/2011 is listed below, What is the expected value of the winnings of one selection? A: E(X)=>10 B: 7.5<E(X)<10 C: 5<E(X)<=7.5 D: 2.5<E(X)<=5 E: 0<E(X)<=2.5
Expected Value • Expected Value ( denoted by E[X] ) is the average value an experiment is expected to produce if it is repeated a large number of times. where is the amount of payout of the (i)th prize and is the probability of getting the (i)th prize
Example (Expected Value of Mark Six) What is the answer? Tips: Ans: E(X) = (1st Prize) x (Probability of 1st Prize) + (2nd Prize) x (Probability of 2nd Prize) + (3rd Prize) x (Probability of 3rd Prize) + (4th Prize) x (Probability of 4th Prize) + (5th Prize) x (Probability of 5th Prize) + (6th Prize) x (Probability of 6th Prize) + (7th Prize) x (Probability of 7th Prize) It is unfair!!! = $5.5446 < $10 which is the wager!!!
Pari-mutuel Game – Horse Racing Instructions: • Two people (or one person if necessary) in a group • Each group receives a paper on which there is an amount you can wager on 1 out of the 4 horses provided • Place your paper into the collection box
Assumptions • You guys are basically gambling addicts so please wager every penny you have on one horse • One group can only wager on one horse
How to calculate the payout? Calculate: • Total Pool (TP) • The amount wagered on the winning horse (W) • Then, the payout (P) (per $1 wagered)
Assumptions Made The operator does not make any profit i.e. TP is distributed to all winners
Reality • In reality, the operator usually takes away a certain percentage of the TP as the commission • In Hong Kong, under the Betting Duty Ordinance (BDO), the duty accounts for a certain percentage of the proceeds from horse racing
Payout distributed By the HKJC Calculate: • Total Pool (TP) • The amount wagered on the winning horse (W) • Commission (C) and Duty (D) • Then, the payout (P) (per $1 wagered)
An extract from the HKJC’s website concerning place betting: • The Net Pool will be divided into two or three parts, according to whether two Place Betting or three Place Betting is being conducted, then each such divided part will be divided by the number of Unit Bets on the horse to which the divided part relates.
The Inventor Joseph Oller
Invented pari-mutuel betting in 1867 • Sentenced to prison in 1874 • Pari-mutuel betting system legalized by the French authorities in 1891 • Focused on the entertainment industry from 1876
Additional Information • The website of the HKJC: • http://www.hkjc.com/english/betting/betting_rule.htm
Homework(Question1) • Based on the Prize Qualification of Mark Six on 17/02/2011, Calculate the expected income (expected value) of the Jockey Club if the total turnover is $ 46,613,470.
Homework(Question2) • Using the figures in the game (which will be provided in the uploaded ppt), calculate the rate of payout if the game was organized by the HKJC, given the commission is 5.5% of TP
Homework (Extra Credit Problem) • Given that the total turnovers in a Mark Six game and a horse racing game are the same and the prize qualification of both games and the BDO(in P.18) are the same as shown in questions 1 and 2. Then, from which game, Mark Six or horse racing, does the Hong Kong Jockey Club receive more commission? State your reasons.