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Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet. For example, a bet of £40 at 6 − 4 (fractional odds) will pay out £40 + £60 = £100. The equivalent decimal odds are 2.5; £40 × 2.5 = £100. We can convert fractional to decimal odds by the formula D = (b + a) ⁄ b.
Decimal odds are 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. [13] For example, a quoted odds of 5.00 equals to a probability of 1 / 5.00, that is 0.20 or 20%. Decimal odds are also known as European odds, digital odds or continental odds. [9]
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
A Dutch or an arb is profitable if the sum of the reciprocals of the decimal odds of each selection is less than 1, and each bet is sized such that the payout in each outcome are the same. Additionally, the profitability of a Dutch/arb can be expressed as 1-R, where R is the sum of the reciprocals. [2]
Mathematics – Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%). Mathematics – Poker: The odds of being dealt a three of a kind in poker are 46 to 1 against, for a probability of 0.021 (2.1%).
The values given for Probability, Cumulative probability, and Odds are rounded off for simplicity; the Distinct hands and Frequency values are exact. The nCr function on most scientific calculators can be used to calculate hand frequencies; entering nCr with 52 and 5 , for example, yields ( 52 5 ) = 2 , 598 , 960 {\textstyle {52 \choose 5 ...
For example, the 4-to-1 fractional odds shown above is the same as 5 in decimal odds, while 1-to-4 would be quoted as 1.25. The method for converting moneyline to decimal odds depends on whether the moneyline value is positive or negative. If the moneyline is positive, it is divided by 100 and add 1.
Where more than 1 powerball is drawn from a separate pool of balls to the main lottery (for example, in the EuroMillions game), the odds of the different possible powerball matching scores are calculated using the method shown in the "other scores" section above (in other words, the powerballs are like a mini-lottery in their own right), and ...