Converting Betting Odds
The odds converter below can be used to convert American moneyline, European decimal, UK fraction or implied probability odds to the other three formats. In this article I'll explain how each odds format works and then cover the basic math behind the various conversions.
American Moneylines - In this odds format the odds are expressed as either a positive or negative number. When positive this represents how much winnings are paid on a $100.00 stake. So for example odds +150 means risk $100 to win $150, if your bet wins you're paid the $150 in winnings plus your $100 stake. When the odds are negative this represents how much you will need to stake to win $100. For example: -225 is risk $225 to win $100. If your bet wins you'll get paid the $100 in winnings plus your $225 stake. I cover how to calculate payouts for non-$100 increment stakes in my article on moneyline betting.
Decimal Odds - This is the most popular odds format outside of the United States and is sometimes referred to as European odds. Decimal odds are listed as a whole number usually followed by decimals. The odds stated are how much a winning ticket will return (stake + win) for each unit wagered. So for example bet 1 unit on odds 2.45, if your bet wins you get back 2.45 units. 1 unit was your stake and 1.45 units is your win. For another example, bet €100 on odds 1.903. If you win you get back €190.30 of which €100 was you stake and €90.30 was profit.
Fraction Odds - This odds format is mostly only popular in the UK, though is used sometimes by American local bookies for baseball, and in parts of South East Asia for fight and horse race betting. The odds are displayed as a fraction. The first number is how much you'll be paid in winnings per the second number staked. So for example 7/5 is win 7 for every 5 staked and 10/11 is win 10 for every 11 staked. To calculate your payout for any stake, simply solve the fraction and multiply your stake by it. So, if the fraction odds are 7/5, you solve 7 divided 5 = 1.4. If you were to bet £100 on odds 7/5 your payout would be 100*1.4=$140 plus return of your £100 stake.
Implied Probability - This is a fancy term for how often a bet must win to average breakeven. For example, American odds +100, decimal odds 2.00 and fraction odds 1/1 all have a 50% implied probability. This is because these are even money propositions - Risk 1 to win 1. If half the time you lose 1, and half the time you win 1, then so long you win 50% of the time you're averaging breakeven.
Important Tip on Odds Conversions
If you live in the US, you can get by fine knowing only American odds, due to the limited number of gambling sites available for US residents. For everyone else, you'll want to get into the practice of using the primary odds format the bookmaker you're betting with uses. This is because conversions are not exact, and the bookmaker will round in their favor. For example, when betting point spreads American betting sites charge -110 on each side. If you instead change to having the odds in decimal format you'll be often be given odds 1.90, even though the true conversion rate is 1.9091. Look to their betting rules pages, bonus terms etc. to understand which odds format is their primary one used.
Odds Conversion Math
Our odds converter can be used to change the odds between formats. However, the need to visit our webpage over and over to convert odds is silly. There are times you'll want to be able to do this on a windows calculator or even in your head while visiting a Las Vegas sportsbook or High Street bookmaker. For this reason I'll run through the math required to convert each odds format to the other three.
Converting American Odds
To change American odds to decimal odds it depends if the odds are negative or positive. For positive odds we use Decimal Odds = (Positive US Odds + 100) / 100. So to calculate +175 we enter (175+100)/100=2.75. For negative odds we ignore the minus and use the formula Decimal Odds = (US Odds + 100) / US Odds. For example on -110 this would be (110+100)/110=1.909.
To convert American odds to fraction odds it again depends if the odds are negative or positive. In the case the odds are positive use American/100 and then if possible simplify. For example odds +140 we'd use 140/100 which we could simplify to 14/10. In the case the odds are negative use 100/American and then again simplify. For example -110 is 100/110 which simplifies to 10/11.
The formula for implied probability is always risk/return=implied probability, where return is stake + win. So in the case of -175 this is risk $175 to win $100, the return is $275 ($175 stake + $100 win) so here the math is 175/275= 0.636, which in percentage format is an implied probability of 63.60%.
Converting Decimal Odds
To convert decimal odds to American it depends if the odds are between 1.01 and 2.0, or are greater than 2.0. In case they're 1.01 to 2.0 use the formula 100/(odds-1) and then add a negative sign to it. So if the odds are 1.95 the formula would be 100/(1.95-1)=105.26, so rounding and adding the negative the American line is -105. In the cases where the odds are greater than 2.0 we use the formula (odds-1)*100 and then add a plus sign to it. So if the odds are 2.45 we calculate this as (2.45-1)*100=145, adding the plus sign we get American odds +145.
To convert decimals odds to fraction odds, we need to form a fraction using: (odds-1)/1. This will come out ugly in most cases so we will need to do some multiplication and simplifying. For example odds 1.45 are (1.45-1)/1 which is 0.45/1. Considering we can't leave this as a fraction that uses a decimal multiply both sides by 100 to get 45/100; from here, we simply the fraction to 9/20.
To convert decimal odds to an implied probability, use the formula 1/odds=implied probability. For example odds 2.14 is 1/2.14= 0.467 which as a percentage is an implied probability of 46.7%.
Converting Fraction Odds
To first note fraction are formatted as numerator/denominator. To convert fraction odds to American odds it depends whether the numerator or denominator is larger. In cases where the numerator is larger use the formula (odds)*100, and add a positive sign. So in the case of odds 7/5 our formula is (7/5)*100=140, adding the positive sign this is American odds +140. In cases where the denominator is larger we use the formula 100/(odds) and then add a negative sign. So for fraction odds 5/7 the formula is 100/(5/7)=140 - adding the negative this is American odds -140.
To convert fraction odds to a decimal use the formula (odds)+1. For example, for fraction odds 11/10 we use calculate using (11/10)+1=2.10.
To convert fraction odds to an implied probability use denominator/(numerator + denominator). So in a case where the odds are 10/13 we use 13/(10+13)= 0.565 which as a percentage is an implied probability of 56.5%.
Converting Implied Probabilities
To convert an implied probability to American odds format it depends whether the probability is over 50% or not. In cases where it is we use the formula 100*p/(1-p) and then add a negative sign. In this formula: p is the probability as a decimal, example 56.5% is 0.565. If we are solving for 56.5% we use (100*0.565)/1-0.565=129.89 which rounding and adding a negative is American odds -130. In cases where the probability is 50% or less, we use the formula 100*(1-p)/p and add a positive plus sign. So for 47.43% it would be 100*(1-0.4743)/0.47.43=110.83, which rounding and adding the plus sign is American odds +111.
To convert an implied probability to decimal odds simply use 1/p. So for an implied probability of 52.38% use 1/0.5238= 1.909.
To convert an implied probability to fraction odds we need to first change our percentage to a decimal. Example 35% is 0.35. Let's call this decimal X and calculate the numerator as (100/X)-1. We then use 1 as the denominator. So in the case of 35% this is (100/35)-1= 1.86, so it gives us 1.86/1 which is ugly so let's convert to 186/100 which can simplify no smaller than 93/50.
Understanding Vig
When you bet on sports it is extremely important to understand both what it is you're betting, and what it is the bookmaker is charging. Let me use decimal odds for the example. Let's say for a draw no bet soccer market the bookmaker is offering Team A 3.85 / Team B 1.31. How much vig is built into these odds? For most bettors this is a mystery. However figuring it out is rather simple.
Our odds converter shows 3.85 has an implied probability of 25.97% and 1.31 has an implied probability of 76.34%. The two probabilities total 102.31%. The extra 2.31% is because the bookmaker needs an advantage and therefore has added vig to the lines. To remove vig we need to divide both implied probabilities by the overall percent market of 102.31%. So in this case: 25.97%/102.31%=25.38% and 76.34/102.31%=74.62%. As you can see these two probabilities now total 100%; we've now calculated each team's no-vig win probability.
Expected Value Equation
The equation for calculating expected value is (win probability*amount won) - (loss probability * bet amount)=expected value. Going back to our earlier example, the bookmaker was offering 1.31, so, if we bet €100 our payout is €131 of which €31 is the amount won. We also know the no-vig win probability is 74.62% and therefore the no vig loss probability is the difference, 25.38%. So we can now plug these figures into our EV formula as (0.7462*€31)-(0.2538*€100)=-2.25. We're losing €2.25 for each €100 bet and therefore it can be stated the bookmaker has a 2.25% advantage. He has that same advantage no matter which side someone bets so if he attracts balanced action this what he profits on all bets.
Using Vig Knowledge for Profit
Now that you understand the bookmaker advantage (vig) you can profit from it. The trick is to shop dozens of online betting sites looking to see which sites are charging the lowest vig. The reason we want to know this is bookmakers charging low vig (also called reduced juice) have far less of a margin of error to work with. If we can compare no-vig odds at two or three of the sites offering low vig, we should get a very strong idea of a team's overall chances of winning. If we then incorporate in betting bonuses and only make the tiny -EV wagers (which are bonus more than covers) we stand a great chance of meeting our rollover requirements while still having free bonus cash. For a deeper discussion of vig and betting strategy I strongly suggest reading my article on handicapping the betting market.