Expected value: the only reason a bet is worth making

Imagine a friend offers to flip a fair coin. If you call it right, they pay you $120; if you miss, you pay them $100. You will win exactly half the time, so on an average flip you make $10. That is a +EV bet. Flip it a thousand times and you would expect to be up about $10,000, even though you lost roughly five hundred of them.

Now flip the deal: you win $100 on a correct call and pay $120 when you miss. Same coin, same skill, but each flip now costs you $10 on average. That is what a normal sportsbook price is: a fair-looking bet with the payout quietly trimmed so the house comes out ahead.

Sportsbooks do not need to predict games better than you. They set prices so that whichever side wins, they keep a small margin. That margin is called the vig (or juice). On a typical -110 / -110 line, both sides together add up to more than 100%, and that extra few percent is the book's cut on every dollar wagered.

• Fair price — what the bet would pay if nobody took a cut.
• Vig — the gap between the fair price and what the book actually pays.
• +EV — a price that is better than fair, so the margin is working for you instead of against you.

No single sportsbook is +EV on purpose. Edges appear because dozens of books price the same game independently and sometimes disagree. When most of the market has a player at +200 to score and one book is still posting +260, that one book is paying more than the real chance deserves. Bet it there, and you have a +EV bet without predicting anything yourself.

This is why EV bettors shop lines across many sportsbooks instead of being loyal to one. The edge is in the comparison, not in the pick.

• You will lose often — a +EV bet at +260 still loses about 70% of the time. The edge shows up over hundreds of bets, not one weekend.
• Real edges are small — a few percent is normal. A bet showing +40% is far more likely to be a stale or mistaken price than a gift.
• Books notice — accounts that only take +EV prices get limited. Spreading action across many books helps.

American odds are a payout, but they are also a statement of probability. A -110 price implies the book thinks the side wins about 52.4% of the time; +200 implies 33.3%. Converting every price to a probability is what lets you compare them.

Add the implied probabilities of both sides of a market and you get more than 100%. A -110 / -110 line sums to 104.8%; the extra 4.8% is the vig. Devigging scales the two sides back down so they sum to exactly 100%, which gives you the book's real opinion of each side without its margin.

One book's devigged line is one opinion. The market's fair probability is a blend of several books' devigged lines, which is more stable than trusting any single book, and the number everything else is measured against.

Knowing a bet is +EV tells you to bet; it does not tell you how much. The Kelly criterion sizes a stake to the edge and the odds so that your bankroll grows fastest without risking ruin. Full Kelly is aggressive, so most bettors use a fraction of it.

Results are noisy for a long time, so bettors judge themselves by closing line value (CLV): did the price you took beat the price the market closed at? A bettor who consistently beats the close is getting better prices than the market's final, sharpest opinion, and profit tends to follow. A bettor whose bets close worse than they bought them is likely betting -EV no matter how last month went.

The +EV strategy only uses books that quote both sides of a market, because a one-sided price cannot be devigged. Each qualifying book is devigged on its own quote, and the board's fair probability is the median of those per-book fair probabilities, not the mean.

• Pure methods — multiplicative (scale both sides by their sum), additive (subtract an equal share of the overround from each side), power (find the exponent k that makes Σ implied^k = 1), and Shin (models the share of informed money).
• Worst case — the fair probability for each side is the minimum of multiplicative, additive and power. The two sides do not sum to 1 by design: each is the most conservative estimate available, so an edge has to survive the least generous method. Shin is deliberately excluded from the floor on the board (the free Vig Remover includes it).
• Median across books — one bad quote should not own the fair value. The case that forced this: one -700 quote against four books near +500 moved a mean-based fair from about +600 to +256 and manufactured a +54% EV. With two books the median is their midpoint; with one, it is that book.
• N-way markets — soccer three-way lines need all three sides from the same book before that book counts.

By default the benchmark set is DraftKings, FanDuel, Caesars, Hard Rock, ESPN BET, Pinnacle and Circa: the deep retail books plus the two sharpest. You can swap in a saved Compare Against blend of your own books. Derived feeds (prices built from other books) and DFS operators are never allowed to set fair value.

• Price families — BetRivers, BallyBet and BetParX run the same Kambi model and post the same number within a rounding step (on 42 of 42 same-game parlay quotes, mean difference −0.3%). Every calculation counts the family once at its best price, so three copies of one opinion are not three votes.
• fairBookCount — the number of book pairs that entered the median, shown on each row. The built-in minimum is one; the Min books filter lets you demand more.
• Market width — an optional filter on how wide each benchmark book's own two-sided quote is, in cents (-110 / -110 is a 20-cent line). Wide lines are weaker evidence of a fair price.

Before fair value is computed, every price is checked against a consensus of the plain sportsbooks on that side: the median implied probability, one vote per price family, with exchanges, derived feeds and DFS operators never voting. A line that fails stays visible with a marker but drops out of fair value, best price and arbitrage legs. Nothing is silently deleted.

• Leave-one-out — a book is never measured against a consensus it helped set; its own vote is removed before the comparison.
• Ratio test — the implied probability may not be more than 4× the consensus in either direction. This catches a -1329 exchange ask on a +1000 prop, or Hard Rock at -700 on a fighter the other seven books had near +500.
• Logit test, one-tailed — the ratio goes blind mid-market (65% vs 20% is only 3.3×), so a logit distance is checked as well: at most 0.65 logits when the price is shorter than consensus, 1.8 logits when it is longer. The asymmetry is deliberate; see the Outlier Detection page.
• Who gets judged — a sportsbook is only gated when at least three other sportsbooks vote, so two books cannot gate each other. Exchanges are judged against any non-empty sportsbook consensus.
• Exchange liquidity — an exchange line whose maximum bet is $5 or less (or unknown) is marked LOW_LIQUIDITY. A separate Min exchange liquidity filter re-quotes an exchange line at the depth that fills your stake.
• Exchange width — an exchange whose two sides add up to more than a 12-point overround is marked WIDE_MARKET on both sides and leaves the devig. Two stale asks far apart are a spread, not a market, and their midpoint is not a fair value.
• Split board — an outlier is a minority. If half or more of the voting books would be flagged, the flags are dropped and the side passes ungated.

A separate swap detector runs on every surface. For each book quoting both sides, it measures the logit distance of the book's prices to consensus as posted and with the sides swapped; when the swapped reading is less than half the distance and the as-posted distance exceeds 0.3 logits, the book is marked SWAPPED_SIDES. It needs at least three clean books, runs two passes, and never corrects the price by swapping it back.