User Account

All Pages

Business statistics, Applied Statistics

Assignment Help:
Betting on sporting events is big business both in the US and abroad. Consider, for instance, next winter’s American football tournament known as the Superbowl. Billions of dollars will be bet. The vast majority of bets are placed on individual teams, though more complex bets are available. The attached table shows the odds posted on July 15, 2017, by one of the largest on-line betting shops in Great Britain. (Online gambling is illegal in California.) Odds are offered on the 32 potential participants in the tournament. The table is interpreted as follows: the Los Angeles Chargers, for example, have odds of 40. If you bet on the Chargers, the betting shop pays you 40 times your bet and you get your bet back if the Chargers win the Superbowl, and you lose your bet if the Chargers do not win. We say the odds in favor of the LA Chargers winning are 1 to 40. The odds posted are for a team winning: you may not bet on a team losing using its posted odds (though, you could theoretically create a bet on a team losing by using bets for the other teams). There are no ties.
If a bet on the Los Angeles Chargers at these odds were a fair bet, then on average you would neither win nor lose by making this bet. Suppose that you bet £1 on the Chargers. Let p denote the probability of winning implied by a fair bet; hence, (1-p) is the probability of losing. Then, £40p is the anticipated amount to be won, £1(1-p) is the anticipated amount to be lost, and, if the bet is fair,
40p = 1(1-p).
Solving for p yields p = 1/41. More generally, a fair bet with odds of 1 to b implies that the fair bet probability p of winning is p=1/(b+1).
1. Using the odds given in the table, compute the probability implied by a fair bet for each team. Do these numbers you have computed satisfy the rules for probability?
An arbitrage opportunity exists if there is a sequence of gambles at the posted odds that never loses money and wins a positive amount with positive probability. Betting houses try to arrange the bets they accept in order to create and exploit an arbitrage opportunity.
2. Consider several schemes the betting house could use:
(a) accept exactly 32 bets, each of size £1 on each of the thirty two listed teams;
(b) accept exactly 32 bets -- £32 on New England, £31 on Green Bay, … £1 on New York Jets.
Does either of these schemes represent an arbitrage opportunity for the betting house? If not, does an arbitrage opportunity exist, and what might one look like?
(Hint: Consider a scheme that accepts exactly 32 bets, with the amount accepted on each team proportional to the implied fair-bet probability you computed above.)
1 Based on Patrick Larkey, “Fair Bets on Winners in Professional Golf,” Chance, V. 3, N. 4, 1990, 24-26. This case was written by Professor Steven Lippman, UCLA.
Odds Posted on www.paddypower.com on July 15, 2017
New England Patriots
4/1
Arizona Cardinals
25/1
Los Angeles Chargers
40/1
Green Bay Packers
10/1
Minnesota Vikings
25/1
Detroit Lions
40/1
Seattle Seahawks
10/1
Baltimore Ravens
30/1
Washington Redskins
50/1
Pittsburgh Steelers
11/1
Indianapolis Colts
30/1
Jacksonville Jaguars
60/1
Dallas Cowboys
12/1
Houston Texans
30/1
Buffalo Bills
66/1
Atlanta Falcons
12/1
Cincinnati Bengals
33/1
San Francisco 49ers
100/1
Oakland Raiders
18/1
Tampa Bay Buccaneers
33/1
Chicago Bears
100/1
Denver Broncos
20/1
Philadelphia Eagles
40/1
Cleveland Browns
200/1
Kansas City Chiefs
20/1
New Orleans Saints
40/1
Los Angeles Rams
200/1
New York Giants
20/1
Tennessee Titans
40/1
New York Jets
200/1
Carolina Panthers
22/1
Miami Dolphins
40/1

Related Discussions:- Business statistics

Find relative maxima and minima, Q. Find relative maxima and minima? Wh...

Q. Find relative maxima and minima? When finding relative maxima and minima in the Chapters absolute extrema problem, don't forget to use the first or second derivative test to

., differance b/w big M mathod and two phase mathod

differance b/w big M mathod and two phase mathod

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

Combined standard deviation, How to a calculate the combined standard devia...

How to a calculate the combined standard deviation for five groups (samples)?

Team Collaboration: Business Decision Making Project, Collect data about th...

Collect data about the chosen business problem or opportunity at the company. Explain how you obtained a suitable sample of either qualitative or quantitative data. Review data f

Hipotesis, acccpt

acccpt

Mode, Mode The mode is the value which occurs most frequ...

Mode The mode is the value which occurs most frequently in a set of observations on the point of maximum frequency and around which other items of the set cluste

Cluster analysis, Cluster Analysis could be also represented more formally ...

Cluster Analysis could be also represented more formally as optimization procedure, which tries to minimize the Residual Sum of Squares objective function: where μ(ωk) - is a centr

Simple random sampling, Simple Random Sampling In Simple Random Sampli...

Simple Random Sampling In Simple Random Sampling each possible sample has an equal chance of being selected. Further, each item in the entire population also has an equal chan

Confidence interval, for this proportion, use the +-2 rule of thumb to dete...

for this proportion, use the +-2 rule of thumb to determine the 95 percent confidence interval. when asked if they are satisfied with their financial situation, .29 said "very sat

Write Your Message!

Captcha
Order Assignment

Featured Services

Order Now

Popular Subjects

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

Submit Assignment

Academics

Major Subjects

Majors

Get In Touch

whatsapp: +91-977-207-8620

Phone: +91-977-207-8620

Email: [email protected]

TERMS & POLICIES

HELP & SUPPORT

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd