Editing Fixed-odds betting (section)

==Calculating fixed odds==
It is customary with fixed-odds gambling to know the odds at the time of the placement of the wager (the "live price"), but the category also includes wagers whose price is determined only when the race or game starts (the "[[starting prices]]"). It is ideal for bookmakers to price/mark up a book such that the net outcome will always be in their favour: the sum of the probabilities quoted for all possible outcomes will be in excess of 100%. The excess over 100% (or [[Mathematics of bookmaking|overround]]) represents profit to the bookmaker in the event of a balanced/even book. In the more usual case of an imbalanced book, the bookmaker may have to pay out more winnings than what is staked or may earn more than mathematically expected. An imbalanced book may arise since there is no way for a bookmaker to know the true probabilities for the outcome of competitions left to human effort or to predict the bets that will be attracted from others by fixed odds compiled on the basis personal view and knowledge.

With the advent of Internet and [[bet exchange]] betting, the possibility of fixed-odds [[arbitrage]] actions and [[Dutch book]]s against bookmakers and exchanges has expanded significantly. Betting exchanges in particular act like a [[stock exchange]], allowing the odds to be set in the course of trading between individual bettors, usually leading to quoted odds that are reasonably close to the "true odds".

==="The best of it"===
In making a bet where the expected value is positive, one is said to be getting "the best of it". For example, if one were to bet $1 at 10 to 1 odds (one could win $10) on the outcome of a coin flip, one would be getting "the best of it" and should always make the bet (assuming a rational and risk-neutral attitude with linear [[utility curve]]s and have no preferences implying [[loss aversion]] or the like). However, if someone offered odds of 10 to 1 that a card chosen at random from a regular 52 card deck would be the ace of spades, one would be getting "the worst of it" because the chance is only 1 in 52 that the ace will be chosen.

In an entry for ''[[Encyclopédie|L'Encyclopédie]]'' (the Enlightenment-era "French Encyclopedia"), [[Denis Diderot]] cites a similar example in which two players, Player A and Player B, wager over a game of dice that involves rolling two six-sided dice. Player A wins if the dice add up to 12, of which there is only one possible case. Player B wins if the dice fall in any other combination, of which there are 35 possibilities.<ref>{{cite journal | url=http://quod.lib.umich.edu/cgi/t/text/text-idx?c=did;cc=did;rgn=main;view=text;idno=did2222.0001.120 | title=Wager | journal=Encyclopedia of Diderot & d'Alembert - Collaborative Translation Project | date=June 2009 | publisher=University of Michigan Library | access-date=1 April 2015}}</ref> It is mathematically disadvantageous to make a bet if one gets "the worst of it". Accordingly, for the bet to be "fair", the amount each player could potentially lose or gain from the wager should be adjusted, depending on the odds of their success.

===Laying odds===
When making a bet in which one must put more at risk than one can win, one is ''[[Wiktionary:lay odds|laying the odds]]''. Rational bettors will do so only if the actual chances of an adverse outcome are low enough that the expected outcome even after deduction of taxes and any [[transaction costs]] is favorable to the person placing the bet. For example, if one bets $1,000 that it will rain tomorrow and can win only $200 but can lose the entire $1,000, one is laying odds that will rain tomorrow. Laying odds is reflected in the [[Wiktionary:colloquial|colloquial]] expression "[I would] [[Wiktionary:bet a dollar to a doughnut|dollars to doughnuts]]" – with which the speaker is expressing a willingness to risk losing something of value in exchange for something worthless, because winning that bet is a certainty.<ref>''Listening to America'', [[Stuart Berg Flexner]] (Simon and Schuster, New York, 1982).</ref>

===Lay betting===
"Lay betting" is a bet that something will ''not happen'', so "laying $50 on a horse" is betting the horse will ''not'' win. Bookmakers sell bets based on the odds of a specific outcome, but lay betting allows the bettor (in some English-speaking countries, the "punter") to reverse roles with the bookmaker, using odds to sell the opposite outcome to the bookmaker. In this context, "lay" is used in the sense of "layman", i.e., a bet sold by someone who does not sell bets professionally. {{citation needed|date=January 2022}}