Fixed-odds gambling - AbsoluteAstronomy.com

Fixed-odds betting is a form of wagering against odds

Odds

The odds in favor of an event or a proposition are expressed as the ratio of a pair of integers, which is the ratio of the probability that an event will happen to the probability that it will not happen...

offered by a bookmaker

Bookmaker

A bookmaker, or bookie, is an organization or a person that takes bets on sporting and other events at agreed upon odds.- Range of events :...

, an individual, or on a bet exchange

Bet exchange

A betting exchange is an entity which provides "trading" facilities for retail or bookmaker customers to buy and sell contracts. Contracts are structured as binary options. Some betting exchanges may also offer CFD products...

Calculating fixed odds

It is customary with fixed-odds gambling to know the odds at the time of the placement of the wager (the "live price"), although this category also includes wagers whose price is determined only when the race or game starts (the "starting prices

Starting Prices

In horse racing, the starting price is the odds prevailing in the on-course fixed-odds betting market at the time a race begins. The method by which SPs are set for each runner varies in different countries but is generally by consensus of an appointed panel on the basis of their observations of...

"). It is ideal for a bookmaker to price/mark up a book such that the net outcome will always be in his favour, i.e. the sum of the probabilities quoted for all possible outcomes will be in excess of 100%. The excess over 100% (or overround

Mathematics of bookmaking

In betting parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The term originates from the practice of recording such wagers in a hard-bound ledger and gives the English language the term bookmaker for the person laying the bets and thus...

) represents profit to the bookmaker in the event of a balanced/even book. In the more usual case of an imbalanced book, the bookmaker may have to pay out more winnings than what is staked, or he may earn more than mathematically expected. An imbalanced book may arise since there is no way for a bookmaker either to know the true probabilities for the outcome of competitions left to human effort or to predict the bets that will be attracted from others by fixed odds compiled on the basis of his own personal view and knowledge.

With the advent of Internet and bet exchange

Bet exchange

betting, the possibility of fixed-odds arbitrage

Arbitrage

In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

actions and Dutch book

Dutch book

In gambling a Dutch book or lock is a set of odds and bets which guarantees a profit, regardless of the outcome of the gamble. It is associated with probabilities implied by the odds not being coherent....

s against bookmakers and exchanges has expanded significantly. Betting exchanges in particular act like a stock exchange

Stock exchange

A stock exchange is an entity that provides services for stock brokers and traders to trade stocks, bonds, and other securities. Stock exchanges also provide facilities for issue and redemption of securities and other financial instruments, and capital events including the payment of income and...

, allowing the odds to be set in the course of trading between individual bettors, usually leading to quoted odds that are reasonably close to the "true odds."

In making a bet where your expected value is positive, you are said to be getting "the best of it". For example, if you were to bet $1 at 10 to 1 odds (you could win $10) on the outcome of a coin flip, you would be getting "the best of it" and you should always make the bet (assuming you are rational and risk-neutral with linear utility curves and have no susceptibility to such fallacies as loss aversion). However if someone offered you odds of 10 to 1 that a card chosen at random from a regular 52 card deck would be the ace of spades, then you would be getting "the worst of it" because the chance is only 1 in 52 that the ace will be chosen. It is mathematically disadvantageous to make a bet where you are getting "the worst of it."

When making a bet where you must put more at stake than you stand to win, you are laying the odds or laying the bet. So, for example, if you bet $1000 that it will rain tomorrow, and if you win you will only win $200 but if you lose you will lose your entire $1000, then you are laying a bet. It is possible that you could be getting "the best of it" or "the worst of it" when you lay a bet; the fact that you are laying a bet does not necessarily mean you are getting "the worst of it". A lay bet is a bet that something won't happen, so if you lay $50 on a horse then you are betting the horse won't win.

Providers for fixed odd betting would include ChoiceOdds

ChoiceOdds

ChoiceOdds is a UK based company specialising in online financial betting. The company head quarters are at Sugar Quay, London.-History:The company was founded by Felix Riley in 2006 along with co founders Paul Laight and Michelle Bass...

, Ladbrokes

Ladbrokes

Ladbrokes plc is a British based gambling company. It is based in Rayners Lane in Harrow, London owned by Bhavin Kakaiya. From 14 May 1999 to 23 February 2006, when it owned the Hilton hotel brand outside the United States, it was known as Hilton Group plc...

, Paddy Power

Paddy Power

Paddy Power is Ireland’s largest bookmaker. Offline it conducts business through a chain of licensed betting offices and by operating Ireland's largest telephone betting service. Online it offers sports betting, online poker, online bingo, online casino games and spread betting...

, and William Hill plc.

Fractional odds

Favoured by bookmaker

Bookmaker

A bookmaker, or bookie, is an organization or a person that takes bets on sporting and other events at agreed upon odds.- Range of events :...

s in the United Kingdom

United Kingdom

The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

and Ireland

Ireland

Ireland is an island to the northwest of continental Europe. It is the third-largest island in Europe and the twentieth-largest island on Earth...

, and also common in horse racing

Horse racing

Horse racing is an equestrian sport that has a long history. Archaeological records indicate that horse racing occurred in ancient Babylon, Syria, and Egypt. Both chariot and mounted horse racing were events in the ancient Greek Olympics by 648 BC...

, fractional odds quote the net total that will be paid out to the bettor, should he win, relative to his stake. Odds of 4/1 ("four-to-one" or less commonly "four-to-one against") would imply that the bettor stands to make a £400 profit on a £100 stake. If the odds are 1/4 (read "one-to-four", or "four-to-one on"), the bettor will make £25 on a £100 stake. Should he win, the bettor always receives his original stake back, so if the odds are 4/1 you would actually receive a total of £500 in return (£400 plus the original £100). Odds of 1/1 are known as evens or even money. This would result in the bettor making £100 profit, and receiving back £200 in total, should he win.

Not all fractional odds are traditionally read using the lowest common denominator

Lowest common denominator

In mathematics, the lowest common denominator or least common denominator is the least common multiple of the denominators of a set of vulgar fractions...

. Perhaps most unusual is that odds of 10/3 are read as "one-hundred-to-thirty".

Fractional odds are also known as British odds, UK odds or in that country, traditional odds.

Decimal odds

Favoured in continental Europe

Europe

Europe is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...

, Australia

Australia

Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

and Canada

Canada

Canada is a North American country consisting of ten provinces and three territories. Located in the northern part of the continent, it extends from the Atlantic Ocean in the east to the Pacific Ocean in the west, and northward into the Arctic Ocean...

, decimal odds differ from fractional odds in that the bettor must first part with their stake in order to make a bet, the figure quoted is the winning amount that would be paid out to the bettor

Bettor

A Bettor is a person who makes bets based on particular information, or feeling, on sporting or other events in the hope of gaining financial profit.-Low Vs. High-stake bettors:...

. Therefore, the decimal odds of an outcome are equivalent to the decimal value of the fractional odds plus one. Thus even odds 1/1 are quoted in decimal odds as 2. The 4/1 fractional odds discussed above are quoted as 5, while the 1/4 odds are quoted as 1.25. This is considered to be ideal for parlay

Parlay (gambling)

A parlay or accumulator is a single bet that links together two or more individual wagers and is dependent on all of those wagers winning together. The benefit of the parlay is that there are much higher payoffs than placing each individual bet separately since the difficulty of hitting it is much...

betting, because the odds to be paid out are simply the product of the odds for each outcome wagered on. Decimal odds are also favoured by betting exchanges because they are the easiest to work with for trading.

Decimal odds are also known as European odds, or continental odds in the UK.

Moneyline odds

Moneyline odds are favoured by American bookmakers. There are two possibilities, the figure quote can be either positive or negative.

Moneyline odds are often referred to as American odds. Moneyline refers to odds on the straight-up outcome of a game with no consideration to a point spread

Spread betting

Spread betting is any of various types of wagering on the outcome of an event, where the pay-off is based on the accuracy of the wager, rather than a simple "win or lose" outcome, such as fixed-odds betting or parimutuel betting. A spread is a range of outcomes and the bet is whether the outcome...

.

Positive figures

If the figure quoted is positive, the odds are quoting how much money will be won on a $100 wager (this is done if the odds are better than even). Fractional odds of 4/1 would be quoted as +400, while fractional odds of 1/4 cannot be quoted as a positive figure.

Negative figures

If the figure quoted is negative, then the moneyline odds are quoting how much money must be wagered to win $100 (this is done if the odds are worse than even). Fractional odds of 1/4 would be quoted as -400, while fractional odds of 4/1 cannot be quoted as a negative figure.

Even odds

Even odds are quoted as +100 or -100. Some bookmakers display the negative symbol while others do not.

Odds Conversion

To convert fractional odds to decimal, take the fractional number, convert it to decimal by doing the division, and then add 1. For example, the 4-to-1 fractional odds shown above is the same as 5 in decimal odds, while 1-to-4 would be quoted as 1.25.

The method for converting moneyline to decimal odds depends on whether the moneyline value is positive or negative. If positive, divide by 100 and add 1. +400 moneyline is the same as 5.0 in decimal odds. If the moneyline is negative, divide 100 by the absolute moneyline amount, then add 1. For example, -400 moneyline is 100/400 + 1 in decimal, or 1.25

Decimal	Fractional	Moneyline	Win% (to Break Even)	Return (minus stake)
1.01	1/100	-10,000	99.01%	1.00%
1.11	1/9	-900	90.00%	11.11%
1.33	1/3	-300	75.00%	33.33%
1.50	1/2	-200	66.67%	50.00%
2.00	1/1	+/-100	50.00%	100.00%
3.00	2/1	+200	33.33%	200.00%
4.00	3/1	+300	25.00%	300.00%
10.00	9/1	+900	10.00%	900.00%
101.00	100/1	+10,000	0.99%	10,000.00%

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