Parimutuel betting

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Parimutuel betting (from the French: 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 the "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.

Betting on the Favorite, an 1870 engraving


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.


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


Thus, the total pool of money on the event is $1028.00. 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 $110.00 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: $1028 × (1 - 0.1425) = $881.52. The remaining amount in the pool is now distributed to those who wagered on Outcome 4: $881.52 / $110.00 = 8.01 ≈ $8 per $1 wagered. This payout includes the $1 wagered plus an additional $7 profit. Thus, the odds on Outcome 4 are 7-to-1 (or, expressed as decimal odds, 8.01).

Prior to the event, betting agencies will often provide approximates for what will 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:


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.

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[edit]

In an event with a set of n possible outcomes, with wagers W1, W2, …, Wn 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 WR = WT(1 − r). Those who bet on the successful outcome m will receive a payout of WR / Wm for every dollar they bet on it.


The parimutuel system was invented by Catalan impresario Joseph Oller in 1867.[1]

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", invented by the Australian engineer, George Alfred Julius. 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 Park in Cicero, Illinois, in 1932.[2]

Strategy and comparison with independent bookmakers[edit]

Unlike many forms of casino gambling, in parimutuel betting the gambler bets against other gamblers, not the house. The science of predicting 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 World Trade Organization decision DS285[3] 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.

Parimutuel bet types[edit]

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[edit]

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

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. There are also other bets which are large combinations of singles, doubles, trebles and accumulators some of them are called Lucky 15, Lucky 31, Heinz, Super Heinz, Goliath. The term nap identifies the best bet of the day.

A parlay, accumulator or roll-up 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/New Zealand[edit]

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.

In recent times the "Roving Banker" variant for Trifecta and First4 betting is now offered. For a Roving Banker First4 the player selects one, two or three runners they believe will definitely finish 1st, 2nd, 3rd or 4th, and up to three selections as Roving Banker(s) with other runners to fill the remaining place(s). A Roving Banker Trifecta is where the player believes that one or two runners will definitely finish 1st, 2nd or 3rd. The bet can be placed by picking the player's favourite runner to finish in any place within the bet and complete the Trifecta with any number of other runners to fill the other placing(s).[4]


The following pools are operated at meetings in mainland Britain:


Tote Ireland operates the following pools:


Bet types for harness racing (trotting):

Hong Kong[edit]

The Hong Kong Jockey Club (HKJC) operates the following bet types and pools.[5]


In Japan, Keiba (競馬, horse racing), Keirin (競輪, professional cycling), Kyōtei (競艇, hydroplane racing), and Auto Race (オートレース, motorcycle racing) operate the following bet type.[6][7][8][9] Wager must be a multiple of 100 yen except Each-way.


The following bet type are offered by the government-controlled betting agency Paris Mutuel Urbain (PMU).[10][11]

Tiercé, Quarté+ and Quinté+ bets are typically only offered on the largest race of the day.

See also[edit]


  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 0-252-06216-7
  3. ^ "DS285". 
  4. ^ "First4". 
  5. ^
  6. ^ "How to Bet (JRA)". Japan Racing Association. Retrieved 20 May 2014. 
  7. ^ Your Guide to Keirin for Beginners - JKA
  8. ^ BASIC KNOWLEDGE of BOAT RACE - Boat Race Promotion Association
  9. ^ Types of betting tickets - JKA
  10. ^ "Translation of the French Betting Rules". PMU. Retrieved 18 December 2014. 
  11. ^ "List of the French Racing Bets Proposed by Eurotierce". EuroTiercé. Retrieved 18 December 2014.