Expected value: price, probability and costs

What an expected value is

It is not the outcome of a single trade. For n binary shares paying $1 on success, price c, probability p and total costs F, the expected net result is n × (p − c) − F, assuming the position is held to resolution. The probability p is a subjective assumption you supply, not a fact embedded in the market price. The Expected value calculator lets you vary p and see how the arithmetic changes. Use the Prediction markets overview first if you need the basic setup.

Two realized outcomes sit underneath that average. With n = 100 shares, c = $0.40, p = 0.60 and F = $2, the outlay is $42. If YES resolves, the position pays $100, so the net gain is $100 − $42 = $58. If NO resolves, the position pays nothing, so the net loss is −$42. The expected net is 100 × (0.60 − 0.40) − 2 = $18, which is an average over hypothetical repetitions, not the result of this one position. Under ordinary binary resolution a winning token redeems for 1 USD and a losing token has no payout, so those are the only two terminal outcomes for a held position.

Total costs, not just the price

The formula subtracts F, so total costs affect both the average and the threshold. Some markets charge taker fees, and the parameters depend on the market; intermediaries can have separate charges. A gross illustrative return before costs is not a net return. Check the current market's fee parameters rather than assuming every trade is free. In the 100-share example, F = $2 is purely illustrative; it is not an actual platform commission. Changing variable fees or execution prices falls outside this simplified calculation.

The break-even assumption

Set the expected net to zero and solve for p: n × (p − c) − F = 0, so p = c + F/n. In the 100-share example that is 0.40 + 2/100 = 0.42, or 42%. If you believe the true probability is above 42%, the assumed expected net is positive before considering any nonordinary settlement. If you believe it is below 42%, the assumed expected net is negative. The market rules, not the question title, determine how the contract resolves, and cases involving disputes or nonordinary settlement are outside this simplified calculator. To see how probability errors affect scoring more generally, the Brier score calculator can help. The break-even figure is an arithmetic consequence of your own inputs, not a recommendation or a promise about any real market.