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In probability theory, odds provide a measure of the probability of a particular outcome. Odds are commonly used in gambling and statistics.For example for an event that is 40% probable, one could say that the odds are "2 in 5", "2 to 3 in favor", or "3 to 2 against".
Given that Alice is 90% credent, this level of belief can be expressed as gambling odds in the following ways: 90% credence; 1 / 9 fractional odds (1 to 9) 1.11 decimal odds; −900 moneyline odds; The return on a $100 wager is $11.11 (plus the $100 initial wager). See the article odds for conversion equations.
E.g. £100 each-way fivefold accumulator with winners at Evens ( 1 ⁄ 4 odds a place), 11-8 ( 1 ⁄ 5 odds), 5-4 ( 1 ⁄ 4 odds), 1-2 (all up to win) and 3-1 ( 1 ⁄ 5 odds); total staked = £200 Note: 'All up to win' means there are insufficient participants in the event for place odds to be given (e.g. 4 or fewer runners in a horse race).
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. Thus, +400 moneyline is the same as 5.0 in decimal odds.
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.
These are wagers offered as alternatives to money line wagers in baseball, hockey, or soccer, respectively. These bets are effectively point spread bets that have the same money line odds on either side of the wager (i.e., industry standard of −110 to −115). Sportsbooks will occasionally shift the moneyline by a few points on either side of ...
If one decides that John Smith is 12.5% likely to win—an arbitrary valuation—one might then set an odds of 7:1 against. This arbitrary valuation — the "operational subjective probability" — determines the payoff to a successful wager. $1 wagered at these odds will produce either a loss of $1 (if Smith loses) or a win of $7 (if Smith wins).
The odds strategy is optimal, that is, it maximizes the probability of stopping on the last 1. The win probability of the odds strategy equals w = Q s R s {\displaystyle w=Q_{s}R_{s}} If R s ≥ 1 {\displaystyle R_{s}\geq 1} , the win probability w {\displaystyle w} is always at least 1/ e = 0.367879... , and this lower bound is best possible .