The average amount you can expect to win or lose per bet over time.
Expected Value (EV) is the most important concept in gambling mathematics. It represents the average outcome of a bet if it were placed an infinite number of times. A positive EV (+EV) means the bet is profitable long-term; a negative EV (-EV) means the house has the edge.
EV is calculated by multiplying each possible outcome by its probability, then summing the results. Every casino game has a negative EV for players (that's how casinos make money), but sports bettors can find +EV opportunities when a sportsbook's odds don't reflect true probabilities.
Understanding EV is what separates recreational gamblers from advantage players. Rather than focusing on individual wins or losses, sharp bettors evaluate every wager by its expected value.
FanDuel posts the Chiefs at +150 to cover +3.5 against the Ravens. Your model (backed by the Pinnacle consensus line) pegs the true cover probability at 45%. American odds of +150 imply only a 40% break-even rate, so each dollar wagered carries positive expectation.
The math: (0.45 × $150) − (0.55 × $100) = +$12.50 per $100 risked. Across 100 identical wagers you would expect roughly $1,250 in profit, though variance means any single week can swing wildly in either direction. Sharps size these with fractional Kelly — typically a quarter or half stake — to ride out inevitable cold streaks without cratering the bankroll.
EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)<p>FanDuel posts the Chiefs at <strong>+150</strong> to cover +3.5 against the Ravens. Your model (backed by the Pinnacle consensus line) pegs the true cover probability at <strong>45%</strong>. American odds of +150 imply only a 40% break-even rate, so each dollar wagered carries positive expectation.</p><p>The math: (0.45 × $150) − (0.55 × $100) = <strong>+$12.50 per $100 risked</strong>. Across 100 identical wagers you would expect roughly <strong>$1,250 in profit</strong>, though variance means any single week can swing wildly in either direction. Sharps size these with fractional Kelly — typically a quarter or half stake — to ride out inevitable cold streaks without cratering the bankroll.</p>
The mathematical advantage the casino has over players, expressed as a percentage of each bet.
The probability of an outcome as implied by the betting odds, including the bookmaker's margin.
The actual mathematical probability of an outcome, without any bookmaker margin.
The difference between the odds you bet at and the final odds at market close.
The average amount you can expect to win or lose per bet over time.
EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)
<p>FanDuel posts the Chiefs at <strong>+150</strong> to cover +3.5 against the Ravens. Your model (backed by the Pinnacle consensus line) pegs the true cover probability at <strong>45%</strong>. American odds of +150 imply only a 40% break-even rate, so each dollar wagered carries positive expectation.</p><p>The math: (0.45 × $150) − (0.55 × $100) = <strong>+$12.50 per $100 risked</strong>. Across 100 identical wagers you would expect roughly <strong>$1,250 in profit</strong>, though variance means any single week can swing wildly in either direction. Sharps size these with fractional Kelly — typically a quarter or half stake — to ride out inevitable cold streaks without cratering the bankroll.</p>
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