Definition
Implied probability converts a price into the probability that price is asking you to accept. A binary contract pays $1.00 if it wins and $0.00 if it loses, so a YES price of $0.47 means the market is pricing the event at roughly 47%. The NO side of the same event should then sit near $0.53.
Formulas
- Prediction market: implied probability = contract price (a $0.47 contract is 47%)
- Decimal odds: implied probability = 1 / odds (odds of 2.50 are 40%)
Why it matters for arbitrage
If the implied probabilities of every outcome of one event add up to less than 100%, buying all of them costs less than the $1.00 they pay out together. That is the arbitrage condition. Example: YES at $0.46 on one platform (46%) and NO at $0.52 on the other (52%) add up to 98%, a gross gap of 2% before fees. See spread.
Implied probability is not the true probability
A price includes fees, the bid-ask gap and the views of whoever is trading. Two platforms can disagree on the same event without either being "wrong", which is exactly why the gap can exist. Arbitrage doesn't need you to know which platform is closer to the truth: holding both sides pays the same either way.
Watch the overround
Bookmakers build a margin into their odds, so implied probabilities across all outcomes add up to more than 100% (the overround, or vig). Prediction market order books have no built-in margin, but the ask prices of YES and NO on one platform still add up to slightly more than $1.00 because of the bid-ask gap. A gap only counts once it is larger than that cost plus fees.