Expected value (EV) tells you what a risky action is worth on average. You take every possible outcome, multiply its value by the chance it happens, and add the results together. If that total is higher than what you paid, the action has positive EV. If it is lower, it has negative EV.
CS2 traders use EV most often for trade-up contracts and case openings. A trade-up has a fixed cost (the ten input skins) and a list of possible outputs, each with a known chance based on the collections you put in. A case opening has a fixed cost (case plus key) and a list of outputs with odds that Valve has published.
How do you calculate expected value for a CS2 trade-up?
List every possible output skin, note its chance and its sell price after fees, then multiply each price by its chance. Add up those numbers to get the EV of one contract. Compare that EV with the total cost of your ten inputs. A contract that costs $10 and has an EV of $11 is worth roughly $1 per attempt on average, though any single attempt can still lose money.
Fees matter here. If you plan to sell the output on the Steam Community Market, subtract the market fee before you count the price. The trade-up calculator does this math for you and shows the EV per contract.
Why does positive EV not guarantee profit?
EV describes the long-run average, not a single result. A trade-up with 80 percent odds of a cheap skin and 20 percent odds of an expensive one can lose money four times in a row and still have positive EV. You only see the average if you can afford to repeat the action many times and accept the swings along the way.
EV also depends on prices that move. A contract that is positive today can turn negative if the output skin drops in price before you sell. Always check current prices and the liquidity of the outputs, not just the raw odds.