Expected value is what a bet is worth on average if you could place it an unlimited number of times. It is the single number that separates a good bet from a bet that happened to win.
Odds format:
Expected value is the average result of a bet across every possible outcome, weighted by how likely each outcome is. A positive number means the bet makes money over the long run. A negative number means it loses money over the long run, no matter what happens on any single occasion. A winning bet can have been a bad bet and a losing bet can have been a good one.
Multiply your win probability by the profit if it wins, then subtract the probability of losing multiplied by the stake. At decimal odds of 1.91 with a 55% estimate on a $100 stake, that is 0.55 x $91 minus 0.45 x $100, which comes to $5.05. Over a large number of identical bets you would expect to average just over five dollars per bet.
This is the uncomfortable part. The arithmetic is trivial; the input is not. If your 55% is really 51%, the same bet has negative expected value and the calculator will have confirmed a loser with full confidence. Expected value is a tool for evaluating your estimates, not a substitute for making good ones. The honest use is to find out how accurate your estimate needs to be to make a bet worthwhile.
The most defensible starting point is the no-vig market price, because it aggregates everything the market knows. Your own estimate should begin there and move only when you have a specific reason: an injury the market has not priced, a weather factor, a situational angle. Starting from scratch and arriving at a number far from the market usually means you are wrong, not early.
A 2% edge sounds like nothing. Over a thousand bets at $100 it is $2,000, and it compounds if you are staking proportionally. This is also why giving away margin by not shopping for the best line is so costly: half a point on a spread can be worth more than the edge you worked to find.
Anything consistently positive is good. Professionals often operate on edges of 1 to 3%. Anyone claiming routine double-digit edges on main lines is either mistaken or selling something.
Constantly. Expected value describes the long-run average, not any individual result. A 55% bet loses 45% of the time, and losing streaks within that are normal rather than evidence the estimate was wrong.
Only within a staking plan your bankroll can absorb. Positive expectation with reckless sizing still goes broke, which is what the Kelly calculator addresses.
More tools: No-Vig CalculatorKelly Criterion CalculatorBreak-Even Win Rate CalculatorHedge CalculatorArbitrage CalculatorBetting ROI and Units CalculatorClosing Line Value Calculator
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