Price as Implied Probability

Because a YES share pays 1 or 0, its price lives on the same scale as probability. A price of 0.65 is the probability at which a risk-neutral buyer breaks even before fees. That makes price a useful implied probability, not an oracle.

Why price p is the break-even probability #

If the buyer's probability is $q$ and price is $p$,

$$EV=q(1-p)+(1-q)(-p)=q-p.$$

Setting $EV=0$ gives $q=p$. Thus a 0.65 purchase needs a true win frequency of 65% to break even before costs.

When price resembles probability #

The interpretation is strongest when the contract is clear, traders can act on both sides, fees and limits are small, liquidity is meaningful, settlement is credible, and no large risk or hedging premium distorts demand. It weakens with thin books, wide spreads, inventory pressure, capital constraints, ambiguous wording, unequal information, and one-sided hedging demand.

Market estimate versus personal estimate #

Use different symbols:

$$p=\text{executable market price}, \qquad q=\text{your probability estimate}.$$

At $p=0.60$ and $q=0.65$, the estimated gross edge is 0.05. At $p=0.70$ and the same $q$, the price implies a higher break-even probability than you believe, so buying has negative gross EV.

Application to no-hedge #

Reference VWAP is a market-based probability estimate. Using it transfers the reference venue's information and distortions into the maker valuation. Since no hedge locks settlement value, validate calibration, freshness, depth, and contract equivalence rather than treating the reference number as guaranteed truth.