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1. 1/2 As A Decimal Betting
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3. 1 2 As A Decimal Betting Rules

Fixed-odds betting is a form of wagering against odds offered by a bookmaker or an individual or on a bet exchange. It involves betting on an event in which there is no fluctuation on the payout. In Australia, the practice is usually known as 'SP betting'.

Calculating fixed odds[edit]

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.

Decimal odds of 2.0 represents even money (1/1) and anything less than 2.0 is an odds on bet. So for example 1.50 will see you win half your stake and to continue the example of Chelsea from above. Wagering 1 at 1:1 (Evens) pays out 2 (1+1) and wagering 1 at 1:2 pays out 3 (1+2). These example may be displayed in many different forms: Fractional odds with a slash: 5 (5/1 against), 1/1 (Evens), 1/2 (on) (short priced horse). Tote boards use Decimal or Continental odds, the ratio of total paid out to stake: 6.0, 2.0, 1.5; In the US Moneyline. There are two steps to convert decimal odds into a fraction. Step 1) Convert decimals odds into a fraction by subtracting 1, and using 1 as the denominator. Example: 3.40 – 1 = 2.40. This creates the decimal odds of 2.40/1. While this is a perfectly good fraction, bookmakers never use numbers with decimal points in fractionals. That is why we need step two. Step 2) We now need to turn this fraction into its most simple form. Find the nearest whole integer (i.e. Decimal - 1 divided by the decimal odds, multiplied by 100 to give a percentage e.g. Decimal odds of 2 = (1/2). 100 = 50%. Fraction - 1 divided by (the fractional odds plus 1), multiplied by 100 to give a percentage. Fractional odds of 3/1 = (1 / ( (3/1) + 1)). 100 = 25%.

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.'

'The best of it'[edit]

1/2 As A Decimal Betting

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 or 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.

In an entry for L'Encyclopédie (the Enlightenment-era 'French Encyclopedia'), Denis Diderot cites a similar example 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.^[1] 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.

Laying odds[edit]

When making a bet in which one must put more at risk than one can win, one is laying the odds. Rational bettors will do so only if the actual chances of an adverse outcome are low enough that the expected outcome even after deduction of taxes and any transaction costs is favorable to the person placing the bet. For example, if one bets $1,000 that it will rain tomorrow and can win only $200 but can lose the entire $1,000, one is laying odds that will rain tomorrow. Laying odds is reflected in the colloquial expression '[I would] dollars to doughnuts' — with which the speaker is expressing a willingness to risk losing something of value in exchange for something worthless, because winning that bet is a certainty.^[2]

Lay betting[edit]

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'Lay betting' is a bet that something will not happen, so 'laying $50 on a horse' is betting the horse will not win. Bookmakers sell bets based on the odds of a specific outcome, but lay betting allows the bettor (in some English-speaking countries, the 'punter') to reverse roles with the bookmaker, using odds to sell the opposite outcome to the bookmaker. In this context, 'lay' is used in the sense of 'layman', i.e., a bet sold by someone who does not sell bets professionally.

Types of odds offered[edit]

There are three widely used means of quoting odds:

Fractional odds[edit]

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 bettor relative to the stake. The term 'fractional odds' is something of a misnomer, especially when visually reinforced by using a slash (as opposed to, e.g., a colon or the word 'to' or 'on') to separate a potential gain from the amount that a bettor must wager in order to receive it upon a win, because the 'fraction' in question represents not the odds of winning or even the reciprocal of the odds of winning but rather the fraction (for any odds longer than 'even money' or chances of winning less than 50%, an improper fraction) of the amount at stake that the upside outcome represents. This fraction may be derived by subtracting 1 from the reciprocal of the chances of winning; for any odds longer than 'even money,' this fraction will be an improper one.^[3][4] 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 alternatively 'four-to-one on' or 'four-to-one in favor'), the bettor stands to 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,^[5] or, in that country, traditional odds.

Decimal odds[edit]

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.^[4][6] Therefore, the decimal odds of an outcome are equivalent to one plus the decimal value of the fractional odds; in the absence of built-in house advantage to cover overhead, profit margins, or (for an illegal enterprise) compensation for the fact that both chances of prosecution and penalties in the event of conviction tend to be higher for bookmakers than for clients, the decimal odds associated with a given outcome would be the decimal expression of the reciprocal of what the offering party assesses to be the outcome's chance of occurring.^[7] 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 known as European odds, digital odds or continental odds and tend to be favoured by betting exchanges because they are the easiest to work with for trading, in this case the purchase and sale of upside and downside risk.^[5]

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Moneyline odds[edit]

Moneyline odds are favoured by United States bookmakers and as such are sometimes called American Odds.^[4] 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 positive symbol.

Odds conversion[edit]

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.

See also[edit]

References[edit]

1. ^'Wager'. University of Michigan Library. Retrieved 1 April 2015.
2. ^Listening to America, Stuart Berg Flexner (Simon and Schuster, New York, 1982).
3. ^'Betting School: Understanding Fractional & Decimal Betting Odds'. Goal. 10 January 2011. Retrieved 27 March 2014.
4. ^ ^abcCortis, Dominic (2015). Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds. Journal of Prediction Markets. 1. 9.
5. ^ ^ab'Betting Odds Format'. World Bet Exchange. Archived from the original on May 2, 2014. Retrieved 27 March 2014.
6. ^D., Chris. 'What is Fixed odds betting and Due Column betting?'. TBR. Retrieved 27 March 2014.
7. ^'Fractional Odds'. betstarter.com/. Archived from the original on April 2, 2014. Retrieved 27 March 2014.

External links[edit]

For most British punters, odds are best understood as being fractional. It’s simple to work out that if something is 5/1 then for every £1 you bet you’ll get £5 back. Yet as more and more foreign bookmakers are entering the UK market they’re also offering decimal odds more readily than fractional ones, confusing people that have never dealt with them before.

In actuality, decimal odds are just as easy to understand as their fractional cousins. The decimal format is used across Europe, with only British bookmakers steering away from them. The key thing to remember is that the unit stake of 1 is always included, so decimal odds of 1.97 mean that you’ll get 97p back on top of your £1 stake.

Decimal Odds

The decimal way of displaying odds is the favoured manner of doing so across continental Europe as well as in countries such as Australia, New Zealand, Singapore and Canada. Defectively any country that uses metric measurement will generally use decimal odds.

Learning how they work is also useful for you’re looking at a betting exchange, therefore, but also if you want to place bets when you’re abroad and don’t want to have to convert things into fractional odds.

Simply put, decimal odds give you the payout amount that includes the stake. As a result, the decimal odds of an event are the same as fractional odds converted to decimal and adding 1. Even odds, therefore, come out as 2.00 in decimal. If you opted for something like 4/1 then it would be displayed as 5.00, whereas 1/4 would be 1.25.

Whilst chucking formula into the conversation is unlikely to make things easier, here’s how to think of decimal odds:

Return = Initial Wager x Decimal Value

In other words, returns on a £100 bet on Liverpool to beat Manchester United at decimal odds of 2.00 would be £100 x 2.00, or £200. To phrase it differently, simply multiply your stake by the odds and you’ll get your return. So a £100 bet on a wager with odds of 1.25 would return £125. That’s why they’re favoured on the exchange, because they’re so easy to calculate.

Working Out The Odds

Odds are another way of discussing the implied chances of something happening. Let’s say that darts player A is going up against darts player B and the bookmakers have decided that A has an 80% chance of winning. This obviously means that B has a 20% chance of winning, meaning that our fair bookie needs to price it up 80% / 20%.

In order to come up with the decimal odds our bookmaker takes the total chance of all outcomes happening, or 100, then divides it by the 80% chance they think player A has got. 100/80 is 1.25, so they’re player A’s decimal odds. For player B, meanwhile, we divide 100 by 20%, or 100/20. That equals 5.00, so they’re that player’s odds.

In order to figure out the probability given to an event, you simply need to reverse engineer that line of thinking. If something has been given odds of 6.00 then the math is 100/6, which works out at 16.6%. The reason 2.00 is the equivalent of Evens is that 100/2.00 equals 50%. Odds of 1.5 in decimal means the probability of that happening is 100/1.5, or 66.6%.

Decimal v Fractional Odds

The trouble with decimal odds is that they seem more complex than they actually are for people that have grown up using fractional odds in betting. In reality, of course, it’s much easier to figure out your total return using decimal odds as opposed to fractional, because with fractional odds you need to add your stake in afterwards.

To put it another way, fractional odds are good at working out your net profit, whereas decimal odds are best for figuring out your total return for your bet. In decimal odds, Evens is 2.00. That means anything above 2.00 is you getting a larger return than just your stake and anything less than 2.00 is the equivalent of getting your money back plus less then what you bet.

If you’re using a bookmaker that is offering fractional odds and you want to figure out what that would be in decimal then you simply divide the first number by the second and then add 1. So odds of 1/4 is 1 divided by 4, or 0.25, plus 1 for 1.25. Equally you might find yourself in a position where the odds are decimal but you want to know what they’d be in fractions.

When that is the case, the easiest way to do it is to take 1 away from the decimal and then convert what’s left into the most simplified fraction possible. So odds of 6.00 would be 6.00-1, which is 5 and becomes 5/1. To use a more complex example, 8.50 as decimal odds would be 8.50-1, which is 7.50. The most simplified fraction would be 15/2.

The table at the top show a list of the most obvious odds as both decimal and their fractional equivalents.

Having read the above, you might be able to see the table making a bit more sense. A £1 bet at 5/2, for example, would return £2.50 plus your initial £1 stake. That amounts to £3.50, which is why the decimal odds equivalent of 5/2 is 3.50. Equally, a £1 stake on something with fractional odds of 1/3 would mean that you’d get 33 pence back plus your £1 stake, of £1.33. The fractional odds are 1.33.

The key thing with this is not to overly test yourself. Most bookmakers will give you the choice about whether you’d like to see your odds displayed as fractional or decimal, so figure out which one is for you and then go from there. You don’t need to sit and do maths problems to work out what you’re betting, but it’s handy to know how it all works.

If you are interested in American Odds and how they work see our dedicated article.