Parimutuel betting (from the French language, Pari Mutuel or mutual betting) is a betting system in which all bets of a particular type are placed together in a pool; taxes and a house "take" or "vig" are removed, and payoff odds are calculated by sharing the pool among all winning bets. In some countries it is known as the Tote after the totalisator which calculates and displays bets already made.

The parimutuel system is used in gambling on horse racing, greyhound racing, jai alai, and all sporting events of relatively short duration in which participants finish in a ranked order. A modified parimutuel system is also used in some lottery games.

Definition

Parimutuel betting differs from fixed-odds betting in that the final payout is not determined until the pool is closed – in fixed odds betting, the payout is agreed at the time the bet is sold.

Parimutuel gambling is frequently state-regulated, and offered in many places where gambling is otherwise illegal. Parimutuel gambling is often also offered at "off track" facilities, where players may bet on the events without actually being present to observe them in person.

Example of parimutuel betting

Consider a hypothetical event which has 8 possible outcomes, in a country using a decimal currency such as dollars. Each outcome has a certain amount of money wagered:

1	$30.00
2	$70.00
3	$12.00
4	$55.00
5	$110.00
6	$47.00
7	$150.00
8	$40.00

Thus the total pool of money on the event is $514.00. Following the start of the event, no more wagers are accepted. The event is decided and the winning outcome is determined to be Outcome 4 with $55.00 wagered. The payout is now calculated. First the commission or take for the wagering company is deducted from the pool, for example with a commission rate of 14.25% the calculation is: $514 × (1 - 0.1425) = $440.76. The remaining amount in the pool is now distributed to those who wagered on Outcome 4: $440.76 / $55 = $8.00 per $1.00 wagered. This payout includes the $1.00 wagered plus an additional $7.00 profit. Thus, the odds on outcome 4 are 7-to-1 (or, expressed as decimal odds, 8).

Often at certain times prior to the event, betting agencies will provide approximates for what should be paid out for a given outcome should no more bets be accepted at the current time. Using the wagers and commission rate above (14.25%), an approximates table in decimal odds would be:

1	$14.69
2	$6.30
3	$36.73
4	$8.00
5	$4.00
6	$9.38
7	$2.94
8	$11.02

In real-life examples such as horse racing, the pool size often extends into millions of dollars with many different types of outcomes (winning horses) and complex commission calculations.

Sometimes the amounts paid out are rounded down to a denomination interval—in the United States and Australia, 10¢ intervals are used. The rounding loss is sometimes known as breakage and is retained by the betting agency as part of the commission.

The above description of the mechanics of parimutuel wagering would suggest that it is impossible for the wagering company (the "house") to lose money, as the commission is deducted before the payouts are calculated. However, in rare circumstances, it is possible for the house to lose money on an event. This situation can occur when there are legal requirements for minimum winning payouts (for example, there may be a legal requirement to pay at least $1.10 on a winning one dollar wager). If the minimum legal winning payout exceeds the payout computed by the standard parimutuel mathematics by a sufficient amount, the house might lose money on this set of wagers.

In horse racing, a practical example of this circumstance might be when an overwhelming favorite wins. The parimutuel calculation results might call for a very small winning payout (say, $1.02 or $1.03 on a dollar bet), but the legal regulation would require a larger payout (e.g., $1.10 on a dollar bet). In North America, this condition is usually referred to as a minus pool.

Algebraic summary

In an event with a set of n possible outcomes, with wagers W₁, W₂, …, W_n the total pool of money on the event is

W_T = \sum^n_{i=1} W_i.

After the wagering company deducts a commission rate of r from the pool, the amount remaining to be distributed between the successful bettors is W_R = W_T(1 − r). Those who bet on the successful outcome m will receive a payout of W_R / W_m for every dollar they bet on it.

History of parimutuel betting

The parimutuel system was invented by Catalan impresario Joseph Oller in 1867.

The large amount of calculation involved in this system led to the invention of a specialized mechanical calculating machine known as a totalisator, "automatic totalisator" or "tote board". The first was installed at Ellerslie Racecourse, Auckland, New Zealand in 1913, and they came into widespread use at race courses throughout the world. The U.S. introduction was in 1927, which led to the opening of the suburban Arlington Racetrack in Arlington Park, near Chicago and Sportsman's Pack in Cicero, Illinois, in 1932.

Parimutuel bet types

There may be several different types of bets, in which case each type of bet has its own pool. The basic bets involve predicting the order of finish for a single participant, as follows:

North America

In Canada and the United States, the most common types of bet on horse races include:

• Win – to succeed the bettor must pick the horse that wins the race.
• Place – the bettor must pick a horse that finishes either first or second.
• Show – the bettor must pick a horse that finishes first, second or third.
• Exacta, perfecta, or exactor –the bettor must pick the two horses that finish first and second, in the exact order.
• Quinella or quiniela – the bettor must pick the two horses that finish first and second, but need not specify which will finish first (similar to an exacta box).
• Trifecta or triactor – the bettor must pick the three horses that finish first, second, and third, in the exact order.
• Superfecta – the bettor must pick the four horses that finish first, second, third and fourth, in the exact order.
• Box – a box can be placed around exotic betting types such as exacta, trifecta or superfecta bets. This places a bet for all combinations of the numbers in the box. A trifecta box with 3 numbers has 6 possible combinations (of the horses in the 'box' 3 can finish first, 2 can finish second, and one can finish third, 3 x 2 x 1) and costs 6 times the betting base amount. A trifecta box with 5 numbers has 60 possible combinations and costs 60 times the betting base amount (5 x 4 x 3). In France, a 'box' gives only the ordered permutations going along an ordered list of numbers such that a trifecta box with 6 numbers would cost 20 times the base amount.
• Any2 or Duet - The bettor must pick the 2 horses who will place first, second or third but can finish in any order. This could be thought of as a double horse show key (see below).
• Double – the bettor must pick the winners of two successive races (a 'running' or 'rolling' double); most race tracks in Canada and the United States take double wagers on the first two races on the program (the daily double) and on the last two (the late double).
• Triple – the bettor must pick the winners of three successive races; like doubles, many tracks offer 'running' or 'rolling' triples. Also called pick three or more commonly, a treble
• Quadrella or Quaddie – The bettor must pick the winners of four nominated races at the same track.
• Sweep – the bettor must pick the winners of four or more successive races. In the US, this is usually called pick four and pick six, with the latter paying out a consolation return to bettors correctly selecting five winners out of six races, and with "rollover" jackpots accumulating each day until one or more bettors correctly picks all six winners.

In Australia, certain exotic bet types can be laid as "flexi" bets. Usually the price of an exotic bet is determined by a set multiple of the outcome, for example $60 for a five horse boxed trifecta at one unit ($1) - or $30 at half unit (50c). If the bet is successful, the bettor will get either the full winning amount shown on the board, or half the winning amount. Under a flexi system the bettor can nominate their desired total wager, and their percentage of payout is determined by this wager's relationship to the full unit price. Using a five horse box trifecta, the bettor may wish to lay only $20 on the outcome. Their percentage of winnings is now calculated as $20/$60 = 33.3%. If the bet is successful, the payout will be 33.3% of the winning amount for a full unit bet.

Win, place and show wagers class as straight bets, and the remaining wagers as exotic bets. Bettors usually make multiple wagers on exotic bets. A box consists of a multiple wager in which bettors bet all possible combinations of a group of horses in the same race. A key involves making a multiple wager with a single horse in one race bet in one position with all possible combinations of other selected horses in a single race. A wheel consists of betting all horses in one race of a bet involving two or more races. For example a 1-all daily double wheel bets the 1-horse in the first race with every horse in the second.

People making straight bets commonly employ the strategy of an 'each way' bet. Here the bettor picks a horse and bets it will win, and makes an additional bet that it will show, so that theoretically if the horse runs third it will at least pay back the two bets. The Canadian and American equivalent is the bet across (short for across the board): the bettor bets equal sums on the horse to win, place, and show.

In Canada and the United States bettors make exotic wagers on horses running at the same track on the same program. In the United Kingdom bookmakers offer exotic wagers on horses at different tracks. Probably the Yankee occurs most commonly: in this the bettor tries to pick the winner of four races. This bet also includes subsidiary wagers on smaller combinations of the chosen horses; for example, if only two of the four horses win, the bettor still collects for their double. A Trixie requires trying to pick three winners, and a Canadian or Super Yankee trying to pick five; these also include subsidiary bets. The term nap identifies the best bet of the day, derived from the Napoleon which was the most valuable French coin at the time the phrase was first used .

A parlay or accumulator consists of a series of bets in which bettors stake the winnings from one race on the next in order until either the bettor loses or the series completes successfully.

Australia

• Win - Runner must finish first.
• Place - Runner must finish first, second or third place. (In events with five to seven runners, no dividends are payable on third place. ("NTD" or No Third Dividend) and in events with 4 or fewer runners, only Win betting is allowed).
• Each-Way - A combination of Win and Place. A $5 bet Each-way is a $5.00 bet to Win and a $5.00 bet to Place, for a total bet cost of $10.
• Exacta – The bettor must correctly pick the two runners which finish first and second.
• Quinella – The bettor must pick the two runners which finish first and second, but need not specify which will finish first.
• Trifecta - The bettor must correctly pick the three runners which finish first, second, and third.
• First4 – The bettor must correctly pick the four runners which finish first, second, third and fourth.
• Running Double – The bettor must pick the winners of two consecutive races at same track.
• Daily Double – The bettor must pick the winners of two nominated races at the same track.
• Treble – The bettor must pick the winners of three nominated races at the same track. This bet type is only available in the states of Queensland and South Australia.
• Quadrella or Quaddie – The bettor must pick the winners of four nominated races at the same track.
• Big 6 – The bettor must pick the winners of six nominated races, which can be at the same track or split over two or more tracks.

Republic of Ireland and Great Britain

• Win - Runner must finish first.
• Place - Runner must finish within the first two places (in a 5-7 runner race), three places (8-15 runners and, in Great Britain, non-handicaps with 16+ runners) or four places (all races with 16+ runners in the Republic of Ireland and handicaps only with 16+ runners in Great Britain).
• Each-way - Charged and settled as one bet to win and another bet to place (for example, a punter asking for a bet of "five pounds each way" will be expected to pay ten pounds).

(Neither Tote Ireland nor the British Tote operates pools on racing in Northern Ireland.)

Strategy and comparison with independent bookmakers

Unlike many forms of casino gambling, in parimutuel betting the gambler bets against other gamblers, not the house. The science of determining the outcome of a race is called handicapping.

It is possible for a skilled player to win money in the long run at this type of gambling, but overcoming the deficit produced by taxes, the facility's take, and the breakage is difficult to accomplish and few people are successful at it.

Independent off-track bookmakers have a smaller take and thus offer better payoffs, but they are illegal in some countries. However, with the introduction of Internet gambling has come "rebate shops". These off-shore betting shops in fact return some percentage of every bet made to the bettor. They are in effect reducing their take from 15-18% to as little as 1 or 2%, still ensuring a profit as they operate with minimal overhead. Rebate shops allow skilled horse players to make a steady income.

The recent WTO decision DS285 against the United States of America by the small island nation of Antigua opens the possibility for offshore horse betting groups to compete legally with parimutuel betting groups.

References

1. Ferran Canyameres, L'Homme de la Belle Époque, Éditions Universelles, Paris, 1946.
2. Steven A. Riess City Games: The Evolution of American Urban Society and the Rise of Sports pg. 188 University of Illinois Press (1991) ISBN 0252062167

See also

• Betting pool
• Bet exchange
• Bookmaker
• Spread betting
• Tote Ireland