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"). It is ideal for a bookmaker to price/mark up a book such that the net outcome will always be in his or her 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) 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 or her own 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 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 preferences implying loss aversion and the like). 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.
Types of odds offered
There are three widely used means of quoting odds:
Favoured by bookmakers in the United Kingdom and Ireland, and also common in horse racing, 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. 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 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. 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 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 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.
- 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.
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
- Mathematics of bookmaking
- Parimutuel betting
- Full cover bet
- Even money
- Asian handicap
- Betting strategy
- Spread betting
- Statistical association football predictions
- Gambler's Fallacy