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.

Parimutuel Pool Basics

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.

Fixed Odds Betting

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.

Parimutuel Pools vs Fixed Odds

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.

Calculating Parimutuel Payoffs

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:

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, …, W_n the total pool wagered on the event is:

After the pool operator 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 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.

Live Parimutuel Pools

Here are some links where users can try their hand with real life parimutuel pools. Each of these examples uses bitcoins as the currency, but new users without bitcoins can actually try for free on two of these sites.

CoinRoster

CoinRoster is a betting site that features fixed odds bets and parimutuel pools. Join for free to receive a small amount of bitcoin to play with, just make sure to use the promo code on the main page. There are parimutuel pools running for each week’s PGA Tour golf tournament. Check out the Golf Props category. CoinRoster also usually has a few parimutuel pools in the User Generated category, which is a category where any type of pool can be created by users who have made a deposit.

FreeBitco.in

This is a site with a bitcoin faucet, so if you don’t already have some bitcoin, you can signup to FreeBitco.in and receive some free bitcoin to play with. FreeBitco.in has a few cool features including the ability to bank your bitcoins for interest, but they also host a variety of parimutuel pools on a variety of topics. Once you have signed up for the site, scroll to the betting tab to view the different parimutuel pools available. Click here to try FreeBitco.in

BetMoose

BetMoose is a bitcoin betting site with parimutuel and fixed odds bets. They do not have a freeplay option, so you can only try BetMoose if you already have bitcoin. Like CoinRoster, BetMoose allows users to create their own parimutuel and fixed odds bets. But unlike CoinRoster and more like FreeBitco.in, BetMoose adds a time weighted factor to their parimutuel pools. This is done to encourage early betting. Since with parimutuel pool betting, there is no benefit to betting before the time when the pool closes since its the bettors advantage to bet at the last moment the pool will close in order to use all possible information about the odds from the pool size. Click Here to try BetMoose.

More Questions about Parimutuel Pools

If you have more questions about parimutuel betting, please leave your comment to this post and I will respond directly or write a post specifically to answer your question.

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