Calculating Payoffs from a Parimutuel Pool

Parimutuel betting is a wagering system in which all bets of a particular type are placed together in a pool and payoff odds are calculated by sharing the pool among all winning bets. Parimutuel betting differs from fixed-odds betting in how the final payout is not determined until the pool is closed. With fixed odds betting, the payout is agreed to at the time the bet is placed. Another difference between parimutuel betting and fixed-odds betting is the way risk is assumed and odds are set.

In a parimutuel pool, the pool operator assumes none of the outcome/event risk because the odds are set by the betting participants. Conversely, a fixed-odds betting “book” sets the odds for each bet and assumes the outcome/event risk. Since a fixed-odds book assumes the responsibility for setting the odds and paying off the bettors at a certain pre-determined price, a fixed-odds book is more likely to be interested in getting “action” between the various potential outcomes of an event. A fixed-odds book operator attempts to balance their book by attempting to offer odds that as closely as possible match the theoretical chances of the various outcomes an in turn expects bettors to wager on the odds in a proportionate way. A fixed-odds book handicaps these odds in a variety of ways including using both fundamental and technical methods.

Although a parimutuel pool avoids many of the risks that a fixed-odds book operator faces since a parimutuel pool does not get involved in setting the wagering odds or assuming any of the event risk; bettors in a parimutuel pool face uncertain payoffs compared to a fixed-odds betting method. Since the payouts from a parimutuel pool aren’t determined until betting is complete, a bettor does not know their actual payoff odds until after wagering has ended.  This creates greater uncertainty for the parimutuel pool bettor compared to accepting fixed-odds from a bookmaker, since the bettor knows for certain what their payoff will be using a fixed-odds wagering method prior to the close of wagering on an event.

Parimutuel payoffs are calculated using a simple method. Before an event takes place, wagers are accepted by the pool on the various possible outcomes. Then, after the event takes place and an outcome is determined, the amount in the pool is distributed between those who wagered on that outcome. For example, consider the following table where a certain amount is wagered on each of the following outcomes:

1 $60
2 $140
3 $24
4 $110
5 $220
6 $94
7 $300
8 $80

The total pool of money wagered on the event is $1028. Following the start of the event, no more wagers are accepted. The event is then decided and the winning outcome is determined to be Outcome 4 with $110.00 wagered. The rake for the pool operator is first deducted from the pool. With a rake of 14.25%, the calculation is: $1028 × 0.1425 = $146.49. This leaves $881.51 remaining in the pool. This remaining amount in the pool is now distributed to those who wagered on Outcome 4: $881.51 / $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).

Expressed algebraically, in an event with a set of n possible outcomes, with wagers W1, W2, …, Wn the total pool wagered on the event is:

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

After the pool operator 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 amount they bet on it.

To calculate the payoffs on types of bets that have more than one outcome, such as “place” and “show” bets, a pool must be created for each type of bet and pooled wagers distributed between each winning outcome. For example, assume $1,000 is bet on “place” bets where the betting an outcome will be either first or second place. Further assume $100 is bet on “X” outcome and $200 is bet on “Y” outcome. The pool operator takes a 17% commission, leaving $830 in the wagering pool. X and Y each place in the event, and so winning bets of $300 are deducted from the pool leaving $530 to pay those who wagered on X and Y. Half of the $530 remaining in the pool will be paid to the winners of each X and Y. The expressed odds are a ratio of payoffs to wagers on X which is $265/$100 = 2.65 and on Y which is $265/$200 = 1.325. As you can see from these odds, we can assume the pool expected outcome X to be a bit unlikely and outcome Y to be a bit likely.


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