Expected value calculator

Weight profit and loss by probability

Expected net is the win probability times winning profit, minus the loss probability times the stake. At a 40% chance and decimal odds of 2.50, a $100 stake has zero expected net value in the stated model.

An estimate is not a known probability

Changing the input probability changes the answer. This tool does not infer an advantage from quoted odds alone. A positive result is not a guarantee of profit, and a short session can differ sharply from its expectation.

Expected loss, RTP and recorded profit

For this binary full-loss model, expected return divided by stake is RTP. One minus RTP is the modeled house edge. Recorded profit is different: subtract actual total stakes from actual total returns, then divide net profit by total stakes for recorded ROI.

Casino RTP, expected loss and gross gaming revenue

For a binary stake S at decimal D and win chance p, expected net is S × (pD−1). Expected gross return divided by stake is pD. An expected loss is the negative of expected net when the result is negative.

At 96% modeled RTP, $10000 total turnover implies $9600 expected gross return and $400 expected loss. Actual results may differ. A general slot paytable requires summing every possible payout, including partial returns; use the slot odds and RTP calculator for an entered outcome table.

Gross gaming revenue is stakes received minus winnings paid over the defined reporting period, before any separately specified costs or deductions. It is not a prediction of a player’s session profit.

Comp value and the underlying theoretical loss

A casino comps estimate applies a stated reward rate to theoretical loss. It does not make the underlying wagering amount profitable. A rakeback estimate instead starts from eligible rake actually paid.

Sports betting ROI and recorded profit

Recorded net profit = total actual returns − total stakes. ROI = net profit / total stakes × 100%. If $1000 was staked and $1120 returned, profit is $120 and ROI is 12%. Enter gross returns including returned stakes, rather than profit-only numbers.

For a lottery with multiple prize tiers and shared jackpots, use the lottery expected value calculator. A high advertised jackpot alone does not establish positive expected value.

See how an uncertain probability changes expected value

The result compares your estimated chance with estimates five percentage points lower and higher, clipped at 0% and 100%. At a $100 stake and decimal 2.00, estimated chances of 45%, 50% and 55% produce expected net values of −$10, $0 and $10 per bet. This is a scenario comparison, not a confidence interval or a forecast. Select American, decimal or fractional odds; the formula is unchanged.