Expectation
The probability-weighted average of all possible values; also known as Expected Value.
In the context of gambling and probability, "expectation" refers to the expected value (EV) of a bet or game, which is a measure of the average outcome you can anticipate if you were to repeat the same bet or game many times. It is calculated by multiplying each possible outcome by the probability of that outcome occurring and then summing all those values.
The formula for expected value is:
[ \text{EV} = (P_1 \times V_1) + (P_2 \times V_2) + ... + (P_n \times V_n) ]
Where:
- ( P ) represents the probability of each outcome.
- ( V ) represents the value (or payoff) of each outcome.
In gambling, a positive expectation means that, on average, you can expect to win money over time, while a negative expectation means you can expect to lose money. Understanding expectation helps players make informed decisions about which games to play and how to manage their bets.
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