The Math Behind Betting Odds & Gambling

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Gambling games implied form

Postby Tazil В» 01.03.2020

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In gambling parlance, making a book is the practice of laying bets on the various possible outcomes of a single event. The term originates from the practice of recording such wagers in a hard-bound ledger the 'book' and gives the English language the term bookmaker for the person laying the bets and thus 'making the book'. A bookmaker strives to accept bets on the outcome of an event in the right proportions in order to make a profit regardless of which outcome prevails.

See Dutch book and coherence philosophical gambling strategy. This is achieved primarily by adjusting what are determined to be the true odds of the various outcomes of an event in a downward fashion i. The odds quoted for a particular event may be fixed but are more likely to fluctuate in order to take account of the size of wagers placed by the bettors in the run-up to the actual event e.

This article explains the mathematics of making a book in the simpler case of the former event. For the second method, see Parimutuel betting. It is important to understand the relationship between fractional and decimal odds. Decimal odds are a single value, greater than 1, representing the amount to be paid out for each unit bet. The equivalent decimal odds are 2. In considering a football match the event that can be either a 'home win', 'draw' or 'away win' the outcomes then the following odds might be encountered to represent the true chance of each of the three outcomes:.

These odds can be represented as implied probabilities or percentages by multiplying by as follows:. The bookmaker, in his wish to avail himself of a profit, will invariably reduce these odds.

Consider the simplest model of reducing, which uses a proportional decreasing of odds. For the above example, the following odds are in the same proportion with regard to their implied probabilities :. Examining how he potentially achieves this:. In reality, bookmakers use models of reducing that are more complicated than the model of the "ideal" situation.

Bookmaker margin in English football leagues decreased in recent years [6]. When a punter bettor combines more than one selection in, for example, a double , treble or accumulator then the effect of the overround in the book of each selection is compounded to the detriment of the punter in terms of the financial return compared to the true odds of all of the selections winning and thus resulting in a successful bet.

To explain the concept in the most basic of situations an example consisting of a double made up of selecting the winner from each of two tennis matches will be looked at:. In Match 1 between players A and B both players are assessed to have an equal chance of winning.

The situation is the same in Match 2 between players C and D. In a fair book in each of their matches, i. However, a bookmaker would probably offer odds of for example on each of the two possible outcomes in each event each tennis match. This results in a book for each of the tennis matches of The decimal odds of a multiple bet is often calculated by multiplying the decimal odds of the individual bets, the idea being that if the events are independent then the implied probability should be the product of the implied probabilities of the individual bets.

This represents an implied probability of Thus the overround has slightly more than doubled by combining two single bets into a double.

This is why bookmakers offer bets such as Lucky 15 , Lucky 31 and Lucky 63 ; offering double the odds for one winner and increasing percentage bonuses for two, three and more winners. In general, for any accumulator bet from two to i selections, the combined percentage overround of books of B 1 , B 2 , In settling winning bets either decimal odds are used or one is added to the fractional odds: this is to include the stake in the return.

The place part of each-way bets is calculated separately from the win part; the method is identical but the odds are reduced by whatever the place factor is for the particular event see Accumulator below for detailed example.

All bets are taken as 'win' bets unless 'each-way' is specifically stated. Non-runners are treated as winners with fractional odds of zero decimal odds of 1. Fractions of pence in total winnings are invariably rounded down by bookmakers to the nearest penny below. Calculations below for multiple-bet wagers result in totals being shown for the separate categories e. Each-Way multiple bets are usually settled using a default " Win to Win, Place to Place " method, meaning that the bet consists of a win accumulator and a separate place accumulator Note: a double or treble is an accumulator with 2 or 3 selections respectively.

However, a more uncommon way of settling these type of bets is " Each-Way all Each-Way " known as " Equally Divided ", which must normally be requested as such on the betting slip in which the returns from one selection in the accumulator are split to form an equal-stake each-way bet on the next selection and so on until all selections have been used.

Double [11] [12]. Note: " Win to Win, Place to Place " will always provide a greater return if all selections win, whereas " Each-Way all Each-Way " provides greater compensation if one selection is a loser as each of the other winners provide a greater amount of place money for subsequent selections. Treble [11] [12].

Accumulator [11] [12]. Note: 'All up to win' means there are insufficient participants in the event for place odds to be given e. The only 'place' therefore is first place, for which the win odds are given. Trixie , Yankee , Canadian , Heinz , Super Heinz and Goliath form a family of bets known as full cover bets which have all possible multiples present.

Examples of winning Trixie and Yankee bets have been shown above. The other named bets are calculated in a similar way by looking at all the possible combinations of selections in their multiples.

Note: A Double may be thought of as a full cover bet with only two selections. Should a selection in one of these bets not win, then the remaining winners are treated as being a wholly successful bet on the next 'family member' down.

For example, only two winners out of three in a Trixie means the bet is settled as a double; only four winners out of five in a Canadian means it is settled as a Yankee ; only five winners out of eight in a Goliath means it is settled as a Canadian. The place part of each-way bets is calculated separately using reduced place odds.

Thus, an each-way Super Heinz on seven horses with three winners and a further two placed horses is settled as a win Trixie and a place Canadian. Virtually all bookmakers use computer software for ease, speed and accuracy of calculation for the settling of multiples bets. Patent , Lucky 15 , Lucky 31 , Lucky 63 and higher Lucky bets form a family of bets known as full cover bets with singles which have all possible multiples present together with single bets on all selections.

An examples of a winning Patent bet has been shown above. The other named bets are calculated in a similar way by looking at all the possible combinations of selections in their multiples and singles. For example, only two winners out of three in a Patent means the bet is settled as a double and two singles; only three winners out of four in a Lucky 15 means it is settled as a Patent ; only four winners out of six in a Lucky 63 means it is settled as a Lucky Thus, an each-way Lucky 63 on six horses with three winners and a further two placed horses is settled as a win Patent and a place Lucky The overall 'odds multiplier' is a combined decimal odds value and is the result of all the individual bets that make up a full cover bet, including singles if needed.

This is equivalent to the OM for a Patent treble: abc ; doubles: ab , ac and bc ; singles: a , b and c plus 1. Now multiply by the unit stake to get the total return on the bet. The winning Patent described earlier can be more quickly and simply evaluated by the following:.

For the family of full cover bets that do not include singles an adjustment to the calculation is made to leave just the doubles, trebles and accumulators. In effect, the bet has been calculated as a Lucky 15 minus the singles.

In the days before software became available for use by bookmakers and those settling bets in Licensed Betting Offices LBOs this method was virtually de rigueur for saving time and avoiding the multiple repetitious calculations necessary in settling bets of the full cover type. A Round Robin with 3 winners is calculated as a Trixie plus three Up and Down bets with 2 winners in each. A Round Robin with 2 winners is calculated as a double plus one Up and Down bet with 2 winners plus two Up and Down bets with 1 winner in each.

Flag and Super Flag bets may be calculated in a similar manner as above using the appropriate full cover bet if sufficient winners together with the required number of 2 winner- and 1 winner Up and Down bets.

Note: Expert bet settlers before the introduction of bet-settling software would have invariably used an algebraic-type method together with a simple calculator to determine the return on a bet see below.

From Wikipedia, the free encyclopedia. This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources. Expected Values and variance in bookmaker payouts: A Theoretical Approach towards setting limits on odds. Journal of Prediction Markets. Mathematical Methods in Economis - Conference Proceedings : — See: Gambling games.

Gambling mathematics Mathematics of bookmaking Poker probability. See: Gambling terminology. Casino game Game of chance Game of skill List of bets Problem gambling. Category Commons Wiktionary WikiProject. Categories : Gambling mathematics Wagering. Hidden categories: Articles needing additional references from February All articles needing additional references. Namespaces Article Talk. Views Read Edit View history. Languages Italiano Edit links. By using this site, you agree to the Terms of Use and Privacy Policy.

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Yokazahn
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Re: gambling games implied form

Postby Kagrel В» 01.03.2020

Million Dollar Blackjack. Players, known as comp hustlers or comp wizards, who play games with a low house advantage or low bet size such as penny slots, can get more than their expected loss in free items from implier casino. For the family of full cover bets that do not include singles an adjustment to the iplied is made to leave just the doubles, click at this page and accumulators. Converting odds to their implied probabilities is perhaps the most interesting part.

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Re: gambling games implied form

Postby Meztikora В» 01.03.2020

Thus, an each-way Super Heinz on seven horses with three winners and a further two placed horses is settled as a win Trixie and a place Canadian. Bookmaker margin in English football leagues decreased in recent years [6]. Gambling mathematics Mathematics of bookmaking Poker probability.

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