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"), but the category also includes wagers whose price is determined only when the race or game starts (the "starting prices"). It is ideal for bookmakers to price/mark up a book such that the net outcome will always be in their favour: the sum of the probabilities quoted for all possible outcomes will be in excess of 100%. The excess over 100% (or overround) 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 may earn more than mathematically expected. An imbalanced book may arise since there is no way for a bookmaker 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 personal view and knowledge.
With the advent of Internet and bet exchange betting, the possibility of fixed-odds arbitrage actions and Dutch books against bookmakers and exchanges has expanded significantly. Betting exchanges in particular act like a stock exchange, 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 the expected value is positive, one is said to be getting "the best of it". For example, if one were to bet $1 at 10 to 1 odds (one could win $10) on the outcome of a coin flip, one would be getting "the best of it" and should always make the bet (assuming a rational and risk-neutral attitude with linear utility curves and have no preferences implying loss aversion and the like). However if someone offered odds of 10 to 1 that a card chosen at random from a regular 52 card deck would be the ace of spades, one would be getting "the worst of it" because the chance is only 1 in 52 that the ace will be chosen.
Diderot cites a similar example in La Encyclodie, in which two players, Player A and Player B, wager over a game of dice that involves rolling two six-sided dice. Player A wins if the dice add up to 12, of which there is only one possible case. Player B wins if the dice fall in any other combination, of which there are 35 possibilities. It is mathematically disadvantageous to make a bet if one gets"the worst of it." Accordingly, for the bet to be "fair," the amount each player could potentially lose or gain from the wager should be adjusted, depending on the odds of their success.
When making a bet that one must put more at stake than can to win, one is laying the odds or laying the bet. So, for example, if one bets $1000 that it will rain tomorrow and can win only $200 or lose the entire $1000, one is laying a bet.
It is possible to be getting "the best of it" or "the worst of it" during lay a bet; laying a bet does not necessarily mean getting "the worst of it". A lay bet is a bet that something will not happen so laying $50 on a horse is betting the horse will not win.
Types of odds offered
There are three widely used means of quoting odds:
Favoured by bookmakers in the United Kingdom and Ireland and common in horse racing, fractional odds quote the net total that will be paid out to the winning better, relative to the 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. In either case, against or on, should he win, the bettor always receives his original stake back so if the odds are 4/1 the bettor receives a total of £500 (£400 plus the original £100). Odds of 1/1 are known as evens or even money.
Not all fractional odds are traditionally read using the lowest common denominator. 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.
Favoured in Continental Europe, Australia, New Zealand and Canada, decimal odds differ from fractional odds by taking into account that the bettor must first part with their stake to make a bet; the figure quoted, therefore, is the winning amount that would be paid out to the bettor. 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. It is considered to be ideal for parlay 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, digital odds or continental odds.
Moneyline odds are favoured by United States bookmakers and as such are sometimes called American Odds. There are two possibilities: the figure quote can be either positive or negative. Moneyline refers to odds on the straight-up outcome of a game with no consideration to a point spread.
- Positive figures
- If the figure quoted is positive, the odds are quoting how much money will be won on a $100 wager (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, 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 but not all bookmakers display the negative symbol.
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 the moneyline is positive, it is divided by 100 and add 1. Thus, +400 moneyline is the same as 5.0 in decimal odds. If the moneyline is negative, 100 is divided by the absolute moneyline amount (the minus signed is removed), and then 1 is added. For example, -400 moneyline is 100/400 + 1, or 1.25, in decimal odds.
- Mathematics of bookmaking
- Parimutuel betting
- Full cover bet
- Even money
- Asian handicap
- Betting strategy
- Spread betting
- Statistical association football predictions
- Gambler's Fallacy
- Fixed odds betting terminal
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- "Betting Odds Format". World Bet Exchange. Retrieved 27 March 2014.
- D., Chris. "What is Fixed odds betting and Due Column betting?". TBR. Retrieved 27 March 2014.
- "Fractional Odds". http://betstarter.com/. Retrieved 27 March 2014. External link in