# Parimutuel betting explanation

Parimutuel betting, also known as mutual betting or pool betting, is a way for players to bet against each other without odds fixed by a central bookmaker.

The winning multiplier for your bet depends on the bets placed by other players, and it often happens to be higher than expected compared to the real probability of the event. You may want to compare your potential return with the fixed odds available at traditional bookmakers for the same event, and play where the return is higher. Sometimes betting arbitrage opportunities arise between traditional bookies and parimutuel bookmakers.

Let's begin with explaining the most simple form of parimutuel winning distribution. Suppose the event is: "Will Manchester Utd. beat Liverpool?" , and the punters have to choose between two results: YES or NO. In our first example, there are 4 punters, 2 of them choose YES and the other 2 pick NO. The ones that chose NO place 1 Bitcoin stake each. The ones that chose YES place 1 Bitcoin and 0.5 Bitcoin. So the total amount bet is 3.5 BTC.

If Manchester wins, the result is YES, so the bettors that chose YES will proportionally share the total 3.5 BTC stake. But in which manner it is proportional? In the simplest form of parimutuel scheme , explained in this example, each winner's share is proportional just to his stake. The first winner placed 1 BTC, while the second one placed 0.5 BTC, which is half. So the latter has the right to receive half the prize of the first winner. Hence the shares are: the first winner receives 2 thirds of the total ( 3.5 * 2 / 3 = 2.333 BTC) , while the second winner receives one third ( 3.5 / 3 = 1.166 BTC ).

Now, that was a very simple form of parimutuel you can find on some bookies. But our version is slightly more complex, as it takes into account not only the stake of each player, but also the date and time of the bet; players that place their bets early have an advantage over the ones that come later. This is what most parimutuel bookmakers do, because it is logical to think that the more you wait for an event to be near resolution, the more information you have about the possible outcome. Thinking about the soccer match of our example, one week before the match there is very little insight information about it, but a few hours from the start more info is available about the weather, athletic condition of the team players, etc.

For the nerds who want to dig more, let us express into formulas everything we covered in this article. First we have the calculation done for the simple parimutuel, the one that only takes into account the stakes ( no time factor ) :

My Winning (simple parimutuel)=My StakeXSum Of All Stakes/Sum Of All Winners' Stakes

And now our algorithm, the complete parimutuel that takes into account the time of bet. First, we introduce the time factor of a bet which is called Weight of the bet, calculated as this:

Weight=Time Left To Event Close Time/Total Time That The Event Has Been Open

The first operand on the right is the number of seconds left from the bet time till the match start (or in general, the event close time, i.e. the moment when no more bets are accepted). The denominator is the time span, in seconds, from the moment the event was published on the site till the event close time. In other words, it is the total time that the event has been open (accepting bets). The resulting Weight is going to be a number between 0.0 and 1.0.

Now, each player's Weight is used to calculate a "weighted" value of his bet. We call this the player's Weighted Bet:

My Weighted Bet=My StakeXMy Weight/Sum Of All Winners' Weights

And finally, our return:

My Winning=My Stake+ (My Weighted BetXSum Of All Losing Stakes/Sum Of All Winners' Weighted Bets)

The Losing Stakes are the stakes of the losing bettors, and the sum of them is the total net earnings to be shared among winners. The whole formula shown above is the one we actually use to distribute the winnings.

Now you should understand why the actual return cannot be precisely estimated prior to the event close time, as it is necessary to know all the bets placed to do the calculation, but a winning calculator is still available to you , for having an estimation assuming that no more punters will come after you.

This whole topic may seem hard to grasp compared to traditional odds decided by bookmakers, but the smartest gamblers can take advantage of parimutuel for arbitrage and other clever techniques we may talk about in this blog , if you are interested.

Lastly, you may notice that we support multiple cryptocurrencies, but in this article we assumed that the betting pool only accepts Bitcoin and everyone uses Bitcoin. That assumption was made to keep the explanation simple, but we want to point out that actually you can use altcoins as well when you bet. Pay attention: you actually are playing only against the players that use the same currency as yours. So you only win from the losing players that used the same currency you used. We can say there are separated and independet betting pools, one for each currency, and a player is in a different pool based on the currency he is using. If that was not clear, read our multi-cryptocurrency pool betting explanation to have a better understanding.