A coin flip at −110 costs −$4.55 per $100 — your edge is what a price pays over fair.
Your price pays $2.23 more on $100 than fair would — that gap is the edge. Grey dot: the standard −110, $90.91.
01 · The cost of doing business
Vigorish is rent
Vigorish — the vig, the juice, the hold — is the commission a sportsbook bakes into a price so it profits regardless of which side wins. On a standard −110 / −110 market you risk $110 to win $100 on either side. If a book balanced $110 on each side and paid out the winner, it collects $220 and returns $210. The $10 it keeps on $220 of handle is the rent: 4.55%.
That is why beating sports betting is not a coin-flip problem. You are not trying to win 50% of your bets; you are trying to win more often than the price implies after the rent is stripped out. Everything downstream — fair lines, edge, expected value — is bookkeeping on that one idea.
As the book prices it
adds up to 104.8%Fair, cut removed
adds up to 100%4.76% over 100% is the book’s cut — 4.55% of everything staked, if the action is balanced.
02 · From odds to probability
Implied probability
Implied probability is the win rate a price assumes. American odds convert with two formulas — one for favorites (negative), one for underdogs (positive).
A −110 favorite implies 110 ÷ 210 = 52.38%. A +120 underdog implies 100 ÷ 220 = 45.45%. Add the two sides of a −110 / −110 market and you get 104.76%. That total is the overround: it sums to more than 100% precisely because the vig is the extra 4.76%.
03 · Removing the rent
De-vigging to a fair line
De-vigging removes the commission so both implied probabilities add back to exactly 100%. The everyday method is proportional (multiplicative): divide each side’s implied probability by the overround.
For the −110 / −110 market: 52.38% ÷ 104.76% = 50.00% each side. The vig vanishes; the fair line is a true coin flip. Sharper methods exist — additive and power correct for favorites and longshots carrying vig differently — but proportional is the workhorse and the right place to start. The no-vig calculator runs all three side by side.
04 · The whole point
Edge = price minus fair
Once you have a fair probability, your edge is the gap between what you believe (or what the sharpest consensus believes) and what the price you can actually bet implies. If a bet’s fair win probability is higher than the implied probability of the best available price, the difference is positive expected value.
Worked example · NBA rebounds prop
A center’s rebounds line sits at 24.5, priced Over −105 / Under −115.
- Over −105 → implied
- 51.22%
- Under −115 → implied
- 53.49%
- Overround
- 104.71%
- Fair Over (cut removed)
- 48.92%
- Fair Under (cut removed)
- 51.08%
The fair line says the Over hits 48.92% of the time. Now suppose your model projects him at 25.2 rebounds, nudging the true Over probability to about 49.7%. Your edge on the Over is 49.7% − 48.92% ≈ +0.8 points. Thin, real, and only visible because you de-vigged first.
05 · Turning edge into dollars
The EV expectation
Expected value is what a bet returns on average if you could place it infinitely many times. Multiply each outcome by its probability and add them up.
Worked example · A $100 bet at −110 with a real edge
You bet $100 on the Over at −110, which pays $90.91 profit on a win. Your de-vigged work says the true win probability is 53% — a genuine edge over the 52.38% the price implies.
- Win leg: 0.53 × $90.91
- +$48.18
- Lose leg: 0.47 × $100
- −$47.00
- Expected value per $100 staked
- +$1.18
That is a 1.18% return per bet. It looks like nothing. Across a thousand disciplined plays at the same edge it is the entire game — which is also why how much you stake matters as much as whether the edge exists. That is the Kelly staking problem.
06 · Try it
Your numbers, the calculators' engines
Drop in any two-way market to take the cut out, then any price and your own fair chance to read the edge. Both run the calculator wall’s own engine.
The book's cut — the book keeps 4.55% of balanced action on this market.
As the book prices it
adds up to 104.8%Fair, cut removed
adds up to 100%4.76% over 100% is the book’s cut — 4.55% of everything staked, if the action is balanced.
Bet it — at −110 this is +1.2% expected value against your 53.0% fair — every reading clears the rounding of your 53.0% (+0.2% to +2.1%).
Your price pays $2.23 more on $100 than fair would — that gap is the edge. Grey dot: the standard −110, $90.91.
- Win leg: 53.0% × $90.91
- +$48.18
- Lose leg: 47.0% × $100
- −$47.00
- Expected value per $100 staked
- +$1.18
07 · The honest part
When EV breaks down
The math is exact. The inputs are not. Expected value is only as good as your win-probability estimate, and that estimate is shakiest exactly where it is tempting to trust it.
- Size down or pass. A fair line you cannot trust is a guess wearing a decimal point.
- Confirm it is live. Shop the lowest-vig price you can find, and check the number is still there before you fire.
Reference
Frequently asked
5 questions · tap one to unfold the answer
A fair line is a probabilistic estimate, not a decree — it shifts every time the market reprices, which on a liquid game is constantly. Dynatyze recomputes the de-vigged fair line on every refresh and shows it next to the best available price so you see the gap as it exists right now, not a stale snapshot that's already wrong.
No. Positive expected value is the gap between a price and a fair line you can't see with the naked eye, and that gap is usually a fraction of a percent. You either run the de-vig math yourself or let a tool do it — eyeballing -115 vs -110 will not tell you which side carries the edge.
A real, repeatable edge above the noise floor is usually 1% to 3% of expected value after de-vigging; anything north of 5% deserves a second look for a stale line or a number you've misread. Edge is probabilistic, so a 3% edge still loses plenty of individual bets — it only compounds across a large number of plays.
Expected value assumes your win probability is well-estimated, which breaks down on thin or volatile markets — a freshly posted prop, a player one tweet away from being scratched, or a market with two books quoting it. On those, the fair line is a guess dressed up as a number, and the honest move is to size down or pass.
Standard two-way de-vigging splits the hold evenly across both sides, which assumes the market is equally efficient on the over and the under. When one side is a public magnet and the other is where the sharp money sits, that assumption skews the fair line, and a more advanced de-vig (or a sharper reference book) is the correction.
Continue reading
Research and methodology only. Dynatyze is not a sportsbook and takes no wagers. Bet legally and within your means. Every figure here is the arithmetic of a stated price; the calculators run the same engine.