The Math of Parimutuel Odds: Implied Probability, Pool Share Pricing, and the Kelly Criterion

1. Deconstructing Implied Odds on PredictWin

In PredictWin's parimutuel architecture, odds are determined purely by the capital distribution between the two outcome pools. If Pool YES contains $P_Y$ and Pool NO contains $P_N$, the market's implied probability of YES is simply:

$$\pi_{YES} = \frac{P_Y}{P_Y + P_N}$$

And conversely:

$$\pi_{NO} = \frac{P_N}{P_Y + P_N} = 1 - \pi_{YES}$$

The gross decimal payout multiple $M_{YES}$ for a winning YES share is:

$$M_{YES} = \frac{P_Y + P_N}{P_Y} \times (1 - \text{Fee})$$

With PredictWin's 2% total fee, this becomes: $M_{YES} = 0.98 \times \left(1 + \frac{P_N}{P_Y}\right)$.

2. Calculating Expected Value (+EV)

A bet should only be executed if its Expected Value is strictly positive ($EV > 0$). Let $p$ be your independently assessed true probability of outcome YES occurring. The Expected Value of risking 1 unit of capital is:

$$EV = [p \times (M_{YES} - 1)] - [(1 - p) \times 1]$$

Finding markets where $EV > +0.10$ (a 10% expected return on investment) is the bedrock of professional prediction trading.

3. Optimal Position Sizing: The Kelly Criterion

The famous Kelly Criterion formula establishes the mathematically optimal fraction $f^*$ of your total capital to risk on a single trade:

$$f^* = \frac{b \cdot p - q}{b}$$

Where $b$ is the net decimal odds received on the wager ($b = M_{YES} - 1$), $p$ is your true probability of winning, and $q = 1 - p$. Quantitative traders employ Half-Kelly ($0.5 \times f^*$) to safely dampen volatility and survive adverse drawdowns.