What is Expected value?
Expected value (EV) is the average amount a bet is mathematically expected to win or lose per wager over many repetitions, calculated from the odds and the payout.
EV multiplies each possible outcome by its probability and adds the results. A £10 straight-up bet on single-zero roulette wins £350 with probability 1/37 and loses £10 with probability 36/37. The expected value is (350 x 1/37) minus (10 x 36/37), about minus 27p, which matches the 2.70% house edge.
Almost every casino bet has a negative expected value for the player. Exceptions are rare, such as the free odds bet in craps, which has zero EV on its own, or situations exploited by advantage players, such as card counting in blackjack.
EV describes the long-run average, not what will happen in one session. Volatility determines how widely individual results scatter around it. Over a handful of bets, actual results will almost always differ from the EV, sometimes by a large amount.
