2. Odds formats

Decimal, fractional (UK), American format

The world’s three big betting cultures describe the same odds, which betting jargon often simply calls the price, in three different ways. The good news: all three answer the same question (how much does the bet pay?), only their reference point differs. Once you understand their logic, conversion is just arithmetic. We give you formulas and practice exercises for that in subchapter 2.3, the section Conversion with formulas.

The decimal (European) format is the multiplier of the total payout: stake × odds = payout, stake included. €100 at 2.50 pays €250, of which €150 is profit, because you get your €100 stake back as well. You already know it from chapter 1: it is the most transparent format, which is why the course and the platform use it throughout. Lock in two of its properties: it can never go below 1.00, and the larger the number, the smaller the chance the bookmaker gives that outcome. This estimate of the chance behind the number is what the jargon calls pricing.

The fractional (UK) format is the heritage of British racecourses. It tells you how much the pure profit is relative to the stake, counted in units. A unit here simply means whatever amount you happen to be betting: if 1 unit = €10, then 5/1 means that a €10 stake wins €50 of profit and €60 comes back. 6/4 says that four units of stake bring six units of profit, that is, one unit staked brings one and a half. It does not include the stake, so its decimal counterpart is always one greater: 5/1 = 6.00, 6/4 = 2.50, 1/2 = 1.50. If the top number of the fraction is smaller than the bottom one (for example 1/2), the winnings are smaller than the stake: English calls this odds-on, and it always signals a heavy favourite.

The American (moneyline) format relates everything to 100 and works with a sign. The positive number tells you how much profit you get on a 100-unit stake: at +150, a 100 stake brings 150. The negative number tells you how much you must risk for 100 units of profit: at -200, you need a 200 stake for 100 of profit. The dividing line is +100 (2.00 in decimal). Plus prices mark the less likely outcome (the underdog or outsider, bigger winnings), minus prices the more likely one (the favourite, smaller winnings). The same price at a few familiar levels, in three languages:

• 1Strong favourite: 1.50 decimal = 1/2 fractional = -200 American. €100 stake → €50 profit.
• 2Even money: 2.00 = 1/1 (evens) = +100. €100 stake → €100 profit.
• 3Slight underdog: 2.50 = 6/4 = +150. €100 stake → €150 profit.
• 4Big outsider: 6.00 = 5/1 = +500. €100 stake → €500 profit.

Whatever format you meet, first translate it to decimal: that is the common language. And remember the lesson of chapter 3 in advance: the odds are not really about money but about probability; the format is just packaging. Odds of 2.00, for example, mark an outcome that comes in roughly every second time, and 4.00 roughly every fourth time, in reality slightly less often, because of the bookmaker’s margin; exactly how that is calculated is what we look at in chapter 3.

Exotic formats: Hong Kong, Malay, Indonesian

The Asian betting markets use their own formats, and you can meet them not only at exotic bookmakers: odds comparison sites and Asian handicap markets often write prices this way too. A market in betting simply means what you can bet on within the same match: the final result, the number of goals, the number of corners and so on. The Asian handicap is one such market, where one team starts with a goal advantage or disadvantage and there is no draw outcome; we cover both in detail in chapter 6. All three formats relate to a 1-unit stake; the only difference is what they take as the reference point and when they change sign.

The Hong Kong format is the simplest: the pure profit on a 1-unit stake, that is exactly the decimal odds minus 1. 2.50 in Hong Kong is 1.50, and 1.50 is 0.50. In money: Hong Kong 1.50 means that a €100 stake wins €150 of profit. It is the decimal cousin of the fractional format: always positive, with no trick in it.

The Malay format always moves between -1 and +1, endpoints included. The positive number is the favourite side’s language: it says how much the profit is on a 1-unit stake (+0.50 = 1.50 decimal). In money: Malay +0.50 means that a €100 stake wins €50 of profit. If the profit would exceed the stake, that is, if we went above 2.00 in decimal, the number turns negative. From then on it says how much you must risk for 1 unit of profit: -0.50 means half a unit of stake brings one unit, which is 3.00 in decimal. In money that means a €50 stake wins €100 of profit, so €150 comes back. The number changes sign above 2.00 precisely so that it never leaves the band between -1 and +1, and that is why the same 0.50 marks two very different prices depending on whether a plus or a minus stands in front of it.

The Indonesian format is the scaled-down copy of the American: the same numbers divided by a hundred, so -200 becomes -2.00. The negative number is the favourite’s (-2.00 says you must risk two units for one unit of profit, 1.50 in decimal), the positive is the underdog’s (+1.50 is one and a half units of profit on a 1-unit stake, 2.50 in decimal). The same price at all four levels you already saw in the previous section:

• 1Decimal 1.50: Hong Kong 0.50, Malay +0.50, Indonesian -2.00.
• 2Decimal 2.00 (even money, that is, an even chance): 1.00 in all three formats, and for Malay this is the top end of the band.
• 3Decimal 2.50: Hong Kong 1.50, Malay approx. -0.67, Indonesian +1.50. The Malay -0.67 is a rounded value: 1 divided by 1.50 is 0.666..., which is why we write approximately.
• 4Decimal 3.00: Hong Kong 2.00, Malay -0.50, Indonesian +2.00.

A quick recognition rule for negative numbers: a value between -1 and 0 can only be Malay; a value below -1 is Indonesian (or American on the scale of hundreds). The trap is that the Malay and Indonesian minus signs mean different things, so with an Asian price always check which format you are looking at and convert to decimal.

Conversion with formulas

Every conversion runs through decimal: whatever you see, you first translate to decimal, and if needed onward to the target format. In the formulas d is the decimal odds, and every other format is denoted by its own letter: a and b for fractional, A for American, HK for Hong Kong, M for Malay, I for Indonesian. One more piece of notation: the two vertical bars (|A|, |M|, |I|) simply mean that we look at the number without its sign, so -200 becomes 200 and -125 becomes 125.

• 1Fractional (a/b), where a is the top number of the fraction (the profit) and b is the bottom one (the stake): d = 1 + a/b. So for 7/4, a = 7 and b = 4, their quotient is 1.75, and the stake is added to that, giving 2.75. Going back, you write the value d − 1 as a fraction: 2.75 minus 1 is 1.75, and 1.75 is seven quarters, because 1.75 × 4 = 7, hence 7/4. If the number does not come out neatly, bookmakers round to the nearest customary fraction.
• 2American (A): for positive, d = 1 + A/100; for negative, d = 1 + 100/|A|, that is, you divide 100 by the number without its sign and add one. Going back: if d is at least 2.00, then A = +100 × (d − 1); if smaller, then A = −100 / (d − 1).
• 3Hong Kong (HK): d = HK + 1, going back HK = d − 1. 0.50 becomes 1.50, and 1.50 goes back to 0.50.
• 4Malay (M): for positive d = M + 1, for negative d = 1 + 1/|M|. Going back, if the decimal is 2.00 or below, the Malay value is the decimal minus 1 (at 1.50 that is +0.50); if it is above 2.00, you divide minus one by the decimal minus 1 (at 2.50 that is minus 1 divided by 1.50, so -0.67).
• 5Indonesian (I): for positive d = I + 1, for negative d = 1 + 1/|I|. Going back it is exactly the other way round: if the decimal is 2.00 or above, the Indonesian value is the decimal minus 1 (at 2.50 that is +1.50); if it is below, you divide minus one by the decimal minus 1 (at 1.25 that is minus 1 divided by 0.25, so -4.00).

Notice that Malay and Indonesian use the same two formulas; the difference is which side gets the plus sign. For Malay the positive number belongs to the favourite (below 2.00 decimal), for Indonesian to the less likely outcome (above 2.00). That is precisely why it is dangerous to mix them up: the same number can mean two very different prices.

Practice exercises: first calculate in your head or on paper, only then check the solution.

• 17/4 fractional to decimal. Solution: 1 + 7/4 = 2.75.
• 2-125 American to decimal. Solution: the number without its sign is 125, and 100/125 = 0.80, plus the stake: 1 + 100/125 = 1.80.
• 33.40 decimal to American. Solution: 3.40 is bigger than 2.00, so the result is positive: +100 × (3.40 − 1) = +100 × 2.40 = +240.
• 4Malay -0.40 to decimal. Solution: 1 divided by 0.40 is 2.50, plus the stake: 1 + 1/0.40 = 1 + 2.50 = 3.50.
• 5Indonesian -2.50 to decimal. Solution: 1 divided by 2.50 is 0.40, plus the stake: 1 + 1/2.50 = 1 + 0.40 = 1.40.
• 61.25 decimal in all the other formats. Solution: fractional 1/4, American -400, Hong Kong 0.25, Malay +0.25, Indonesian -4.00.

The calculation questions of the end-of-chapter test draw new values on every attempt: it is worth repeating until you switch between the formats without thinking. The next chapter brings the real point: the probability hidden behind the odds.