Expected value

Expected value

Definition

Expected value is the probability-weighted average payoff of a trade. For a single binary outcome, it equals the probability you assign to the outcome resolving YES multiplied by the payoff if YES occurs, plus the probability of NO multiplied by the payoff if NO occurs. On Polymarket, payoffs are denominated in pUSD and capped at $1.00 per winning outcome token.

In context

You encounter expected value when deciding between candidate arbitrage trades. After you estimate the probabilities of each outcome and account for fees, expected value lets you compare the economic merit of different executions on a common scale. For example, in intra-market binary arbitrage you might compute the EV of buying both legs at available best asks (or buying a complete set in a multi-outcome market) to see whether the probability-weighted payoff justifies capital, time, and settlement risk.

A simple binary EV calculation

• Let p be your estimated probability that YES resolves.
• Let buyPriceYes be the price you pay for YES shares and buyPriceNo for NO shares.
• If you buy both legs for a complete hedge, your payoff is $1.00 when one leg wins and $0.00 on the loser; your net payoff equals $1.00 minus the total amount you paid, adjusted for fees.

Expected value (hedged) = 1.00 - (buyPriceYes + buyPriceNo) - fees

If buyPriceYes + buyPriceNo is less than 1.00, the arithmetic shows a positive EV before accounting for other risks listed below.

Multi-outcome markets

For an N-outcome market, EV of buying a complete set at the sum of best asks is:

Expected value = 1.00 - sum(bestAsk_i) - fees

When you do not buy a complete set but instead buy a single outcome, EV is:

Expected value(single) = p_i * 1.00 - buyPrice_i - fees_on_trade

Practical adjustments

• Fees: subtract taker fees applicable to the category. Polymarket taker fees vary by category (0% to 1.8%) and maker fees are zero. Include builder fees if you route through a Builder.
• Slippage and partial fills: FAK orders can partially fill; account for execution risk and realized price vs. quoted best ask.
• Tick size: tick granularity (usually $0.01, sometimes $0.001 near extremes) can affect achievable prices.
• Resolution and settlement risk: outcomes are resolved by UMA; disputes can pause settlement and delay redeeming winning tokens for pUSD.
• Smart-contract and counterparty risk: although Polymarket uses CTF on Polygon and a sponsored Relayer, those are non-zero operational risks.

See also

• edge

How this affects your trading

Use expected value to compare candidate arb opportunities after you layer in fees and realistic execution assumptions. EV converts probability views and quoted prices into a single metric you can rank across markets or trade sizes. Always pair EV calculations with a checklist of operational risks (slippage, fees, UMA disputes, settlement timing) before sizing a trade.