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Quick links: Odds formats  Odds conversion  Odds back to probability  Table of conversions
Odds (sometimes called price) are numbers which are used to calculate how much money we win with our stake on a certain event. Rule is higher the odds for a given outcome less the probability of that outcome. Odds are just probability percentages converted in numbers. Three formats of odds are widely used. European (decimal), British (fractions) or American (whole) format. Some bookmakers support more than one format. Conversion between formats is possible.
Odds formats
Here is example of how odds are presented in different formats. We are comparing odds for a soccer match between Brazil and England, with Brazil being the favorite and England the underdog.
EXAMPLE EVENT: Brazil Vs England  
European 
British 
American 

Brazil (1):  1.40 
2/5 
250 

Draw (X):  3.75 
11/4 
+275 

England (2):  5.00 
4/1 
+400 
Now let's make some calculations to better explain odds formats. It is important to distinguish between payout to betting account and winning. Payout is total amount of money won together with stake and winnings are real money won, or payout minus our stake.
We bet 100$ or Brazil.
European Odds (decimal)
We calculate payout by multiplying stake with odds offered. The odds show how many units bookie pays out for one unit staked. To make it simple European odds show us total amount of money we win together with our stake. In this case it's 100$ x 1.40 = 140$.
British Odds (fractions)
British odds show winnings, or how much money we win minus our stake. 100$ x 2/5 (0.4) = 40$. We see that with 100$ betted on Brazil we earn extra 40$.
American Odds (whole)
American odds are divided in negative and positive odds. Like British odds they show us our winnings not the payout. Negative odds show how big stake is needed for a winning of 100 units, when betting on favourite. Positive odds show how winnings are if we bet 100 units on underdog.
Negative Odds (necessary stake for a winning of 100 units):
Example: Home win to Brazil over England, US odds 250
Stake x (100/US odds)
100$ x (100/250) = 40$
Notice that the negative sign in front of the odds is changed in the calculation. The number has to be positive.
Positive Odds (winning with a stake of 100 units):
Example: Draw in Brazil vs. England, US odds +275
Winning: Stake x (US odds/100)
100$ x (275/100) = 275$
Odds conversion
Converting American style odds to European odds and vice versa
To convert American odds to European, simply divide an underdog's price (positive odds) by 100 and add 1, or divide the favorite's price (negative odds) into 100 (after dropping the minussign) and add 1. To convert decimal odds of less than 2.0 to American, subtract 1 and divide into 100. For odds greater than 2.0, subtract 1 and multiply by 100.
If we use odds from our general example above, American odds offered for a Brazil win (a favorite so American odds are negative)are 250. We lose the minus sign and it's (100 / 250) + 1 equals 1.40. And for positive odds we take England to win, an underdog, odds are +400, it's (400/100) + 1 equals 5.00.
To convert European odds to American we take odds for a Brazil win which is offered at 1.40, so under 2.00. It's 100/ (1.40  1) equals 250. Now for odds over 2.00 we take England to win at odds 5.00, so it's (5.00  1) x 100 equals 400.
Converting British odds to European odds and vice versa
Now this is more simple. We just divide two sides (left and right number) of British odds to get a fraction and add 1. Brazil win in British odds is valued at 2/5. It's 2/5 equals 0.4 + 1 equals 1.40. Simple. When converting decimal odds to fractions some round off error may occur, since some odds don't have an exact translation into Britishstyle fractions.
Converting British odds to American and vice versa
American odds that start with a + sign (+150) show you how much money you will make for every $100 bet, not including your original $100. To work out the fractional odds simply divide the expected profit by 100. (150/100 = 1.5/1). And now multiple both sides with 10 and you get 15/10. To work out the decimal odds just add the two fractional odds together (1.5 +1 = 2.5).
And back to percentages
Odd represent probability of certain outcome for a selected event. Probability is expressed in percentages. To make it easier for punters bookmakers present probability in odds. So it is easier to calculate how much money we win at offered odds. But sometimes we want to convert odds back to percentages. Maybe we need probability for finding value bets or for discovering bookie margin. Whatever our reasons are here is how to convert decimal odds back to percentages. This is done by dividing 100 with given odds. So for our general example above a probability of Brazil winning the match is 100/1.40 equals 71.42%. Probability for draw is 100/3.75 = 26.67% and for England win 100/5 = 20%. If we sum all percentages we get 118.09% what means that our imagination bookie operates with 18% margin, or on every 1$ bet bookie earns 0.18 cents. Nice ha? Of course probabilities that we get this way are just bookie expectations that don't have to be correct.
Table of conversions
To make thing simple, you can use this table to convert between odds formats and percentages.
UK 
U.S.A. 
Europe 
% 
2/7  350  1.29  77.80 
3/10  330  1.30  76.70 
1/3  300  1.33  75.00 
4/11  275  1.36  73.33 
2/5  250  1.40  71.43 
4/9  225  1.44  69.23 
1/2  200  1.50  66.67 
8/15  190  1.53  65.50 
4/7  175  1.57  63.64 
8/13  161  1.65  61.90 
2/3  150  1.67  60.00 
8/11  137  1.73  57.89 
4/5  125  1.80  55.56 
5/6  120  1.83  54.55 
9/10  111  1.90  52.63 
10/11  110  1.91  52.38 
1/1  100  2.00  50.00 
21/20  105  2.05  48.78 
11/10  110  2.10  47.62 
10/9  111  2.11  47.37 
6/5  120  2.20  45.45 
5/4  125  2.25  44.44 
13/10  130  2.30  43.48 
27/20  135  2.35  42.55 
11/8  137  2.37  42.11 
7/5  140  2.40  41.67 
3/2  150  2.50  40.00 
8/5  160  2.60  38.46 
13/8  162  2.62  38.10 
17/10  170  2.70  37.04 
7/4  175  2.75  36.36 
9/5  180  2.80  35.71 
15/8  187  2.87  34.78 
19/10  190  2.90  34.48 
2/1  200  3.00  33.33 
21/10  210  3.10  32.26 
11/5  220  3.20  31.25 
9/4  225  3.25  30.77 
23/10  230  3.30  30.30 
12/5  240  3.40  29.41 
5/2  250  3.50  28.57 
13/5  260  3.60  27.78 
27/10  270  3.70  27.03 
11/4  275  3.75  26.67 
14/5  280  3.80  26.32 
3/1  300  4.00  25.00 
10/3  333  4.33  23.08 
7/2  350  4.50  22.22 
4/1  400  5.00  20.00 
9/2  450  5.50  18.18 
5/1  500  6.00  16.67 
11/2  550  6.50  15.38 
6/1  600  7.00  14.29 
13/2  650  7.50  13.33 
7/1  700  8.00  12.50 
15/2  750  8.50  11.76 
8/1  800  9.00  11.11 
17/2  850  9.50  10.53 
9/1  900  10.00  10.00 
10/1  1000  11.00  9.09 
11/1  1100  12.00  8.33 
12/1  1200  13.00  7.69 
14/1  1400  15.00  6.67 
16/1  1600  17.00  5.88 
18/1  1800  19.00  5.26 
20/1  2000  21.00  4.76 
22/1  2200  23.00  4.35 
25/1  2500  26.00  3.85 
28/1  2800  29.00  3.45 
33/1  3300  34.00  2.94 
40/1  4000  41.00  2.44 
50/1  5000  51.00  1.96 
66/1  6600  67.00  1.49 
80/1  8000  81.00  1.23 
100/1  10000  101.00  0.99 
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