期待値（EV） is a fundamental concept in probability and statistics that represents the average or 平均値 of a random variable over numerous trials or occurrences. It is a calculated measure that helps in predicting the likely outcomes of uncertain events.
The expected value is computed by taking the sum of all possible outcomes, each multiplied by its 発生確率を表します。数学的には、次のように表されます：
EV = Σ (x * P(x))
ただし：
- x 可能な結果を表します。
- P(x) 各結果の確率です。
例えば、公平な六面体のサイコロを振る簡単なゲームがある場合、振ったときの期待値は次のように計算できます：
EV = (1/6 * 1) + (1/6 * 2) + (1/6 * 3) + (1/6 * 4) + (1/6 * 5) + (1/6 * 6) = 3.5
これは、多くの回数振った場合、平均結果が3.5に近づくことを意味します。
様々な分野で finance, economics, and gambling, the expected value helps in making informed decisions by weighing the risks and benefits of different options. A positive expected value indicates a potentially profitable decision, while a negative expected value suggests a loss over time. Therefore, understanding expected value is crucial for effective decision-making 。