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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
Fixed-odds betting. Fixed-odds betting is a form of gambling where individuals place bets on the outcome of an event, such as sports matches or horse races, at predetermined odds. In fixed-odds betting, the odds are fixed and determined at the time of placing the bet. These odds reflect the likelihood of a particular outcome occurring.
Thus if expressed as a fraction with a numerator of 1, probability and odds differ by exactly 1 in the denominator: a probability of 1 in 100 (1/100 = 1%) is the same as odds of 1 to 99 (1/99 = 0.0101... = 0. 01), while odds of 1 to 100 (1/100 = 0.01) is the same as a probability of 1 in 101 (1/101 = 0.00990099... = 0. 0099). This is a minor ...
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.
The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one.
UK format (fractional odds) are used by British bookmakers. They are the ratio of the amount won to the stake – the solidus "/" is pronounced "to"; for example, 7/1 is "seven to one". Fractional odds of 1/1 are an even bet. US format odds are the amount won on a 100 stake when positive, and the stake needed to win 100 when negative.
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An explanation of logistic regression can begin with an explanation of the standard logistic function. The logistic function is a sigmoid function, which takes any real input , and outputs a value between zero and one. [ 2 ] For the logit, this is interpreted as taking input log-odds and having output probability.