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Implied Probability  
Implied probability is an important concept in various market based transactions, including the stock, option, bond, futures, currency, and swap markets. It is also a crucial concept in sports betting, whether we are looking at individual game lines, futures, propositions, and live betting markets. Implied probability in sports betting markets is simply a conversion of traditional odds into a percentage, but it also takes into account the house edge and eliminates it to express the odds as the “true odds” of an event occurring. 

Decimal Odds  
Favoured in continental Europe, Australia, New Zealand and Canada, decimal odds quote the ratio of the payout amount, including the original stake, to the stake itself. Therefore, the decimal odds of an outcome are equivalent to the decimal value of the fractional odds plus one. Thus even odds 1/1 are quoted in decimal odds as 2.00. The 4/1 fractional odds discussed above are quoted as 5.00, while the 1/4 odds are quoted as 1.25. This 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 favoured by betting exchanges because they are the easiest to work with for trading, as they reflect the inverse of the probability of an outcome. For example, a quoted odds of 5.00 equals to a probability of 1 / 5.00, that is 0.20 or 20%. 

Fractional odds  
Favoured by bookmakers in the United Kingdom and Ireland, and also common in horse racing, fractional odds quote the net total that will be paid out to the bettor, should he or she win, relative to the stake. Odds of 4/1 would imply that the bettor stands to make a £400 profit on a £100 stake. If the odds are 1/4, the bettor will make £25 on a £100 stake. In either case, having won, the bettor always receives the 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. 

American odds  
American odds are favoured by American bookmakers. The figure quoted is either positive or negative. When American odds are positive, the figure indicates how much money will be won on a $100 wager (this is done for an outcome that is considered less likely to happen than not). For example, a net payout of 4/1 would be quoted as +400. When American odds are negative, the figure indicates how much money must be wagered to win $100 (this is done for an outcome that is considered more likely to happen than not). For example, a net payout of 1/4 would be quoted as 400. American odds are often referred to as Moneyline odds. A "American" wager refers to odds on the straightup outcome of a game with no consideration to a point spread. In most cases, the favorite will have negative American odds (less payoff for a safer bet) and the underdog will have positive American odds (more payoff for a risky bet). However, if the teams are evenly matched, both teams can have a negative line at the same time (e.g,. 110 110 or 105 115), due to house take. Source: Wikipedia 