Expected value, implied probability, vig and fair price
Short answer. Expected value (EV) is the average result of a bet per dollar staked if you could place it again and again. Sportsbooks build a margin into every price, so the average is normally below zero. A parlay multiplies that margin, one leg at a time.
Take a made-up two-way market, such as a point spread, with both sides at -110. These prices are hypothetical. Each side's implied probability is 52.38%, and the two add up to 104.76%. The extra 4.76 points is the overround. The sides are identical, so the fair chance of each is 50% and the fair price is +100. The hold is 4.76 divided by 104.76, which is 4.55%.
A $100 bet at -110 returns $190.91 if it wins, stake included. At the fair price it would return $200.00. If each side really wins half the time, the $9.09 gap applies only on a win, so the average loss is $4.55 per $100, which is the hold.
| Legs | Offered price | Fair price | Pays on $100, offered vs fair | Average loss per $100 |
|---|---|---|---|---|
| 1 | -110 | +100 | $190.91 vs $200.00 | $4.55 |
| 2 | +264 | +300 | $364.46 vs $400.00 | $8.88 |
| 3 | +596 | +700 | $695.79 vs $800.00 | $13.03 |
Each added leg multiplies the offered price and the fair price alike, but each leg's return falls short of its fair return by the same 4.55%, and the shortfalls multiply. Two legs lose about $8.88 per $100 and three about $13.03, assuming each leg's fair chance is 50%. At 10 legs of the same hypothetical, about $62.80 of every $100 comes back on average. The margin does not average out as legs are added. It stacks.
A bet has positive EV only when its price beats the fair price, which means you know the true chance better than the market does or you found a book whose number is off. Books adjust their prices and can limit accounts that beat them, so such bets are scarce. Even then EV is an average over many bets, not a promise about the next one. Can you beat the sportsbooks?
Parlotto makes no prediction about any game, shows no expected value on a ticket and claims no edge. It reads the prices sportsbooks publish and, for each book, builds the combination of real lines that reaches the biggest payout that book's own rules allow on one ticket, favoring lines that carry less margin. Every ticket still has the margin in it, so treat the entry as the price of a long shot. How Parlotto works
No. EV is an average over many repeats of the same bet. Any single bet either wins or loses. A positive EV bet still loses often, and a negative EV bet sometimes wins, which is why people play them for fun.
It means you stake $110 to win $100 in profit, or $1.10 to win $1. It is the American way of writing decimal odds of 1.909, and it is the usual price on a point spread or a total.
Yes. Remove the vig from both sides of the same market to estimate a fair probability, multiply it by the decimal odds, and subtract 1. A quoted price's implied probability still has the vig inside it, so using it directly overstates the chance. The fair probability is the hard part, and the arithmetic cannot tell you whether your estimate is right.
Play responsibly. You must be 21 or older, and only where sports betting is legal. Parlotto is not a sportsbook and never takes a bet. If gambling stops being fun, call 1-800-GAMBLER.
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