A technical overview of a Dynamic Parimutuel (DPM) betting system with support for limit orders.

Basics

• Markets are structured around a question with a binary outcome.
• Traders can place a bet on either YES or NO. The trader receives some shares of the betting pool. The less likely the outcome, the more shares the trader receives per dollar.
• When the market is resolved, the traders who bet on the correct outcome are paid out of the final pool in proportion to the number of shares they own.

Probability

If y is the total number of outstanding shares of YES and n is the total number of outstanding shares of NO, the instantaneous implied probability of the market is

$$ P(y, n) = \frac{y^2}{y^2 + n^2} $$

Betting

We introduce a cost function C which captures the total amount wagered by all traders given the current shares of YES and NO:

$$ C(y, n) = \sqrt{y^2 + n^2} $$

If a trader places a bet of $b on YES, they add $b to the YES pool and receive s shares of the final pool if YES is the outcome, where s satisfies

$$ b = C(y + s, n) - C(y, n) $$

Antes

The market creator chooses an initial probability p and an ante amount to initialize the betting pool:

$$ p = \frac{y_{start}^2}{y_{start}^2 + n_{start}^2} \quad \text{s.t.} \quad \sqrt{y_{start}^2 + n_{start}^2} = ante, \quad y_{start}, n_{start} > 0 $$

Market Resolution

I. Typical case: Resolving YES or NO

Suppose the market resolves YES. The payout for a YES bet of s shares (with y total YES shares) is

$$ payout = \frac{s}{y} \cdot pool $$