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 minus-sign) 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 British-style 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.