The probability of an outcome implied by its betting odds.
Betting odds aren't just prices — they're predictions in disguise. Every quoted price corresponds to a specific probability of the outcome occurring. Implied probability is the conversion.
For American odds, the math has two cases. Positive odds (+150) convert via 100 / (odds + 100). +150 implies 100/250 = 40%. Negative odds (-150) convert via |odds| / (|odds| + 100). -150 implies 150/250 = 60%. The intuition: positive odds pay more than the stake, so the implied probability is below 50%; negative odds pay less, so the implied probability is above 50%.
Implied probability is the basis of every betting math calculation that follows. Expected value compares your estimated probability to the implied probability. Kelly stake size scales with the gap between the two. No-vig fair odds back out the implied probabilities and re-normalize them so they sum to exactly 100% — the cleanest estimate of the market's true belief.
The unstated wrinkle is that the implied probabilities of all possible outcomes in a market always sum to more than 100%. The excess is the vig — the sportsbook's built-in margin. A two-way market at -110/-110 implies 52.4% on each side, for a 104.8% total. The 4.8% overround is the book's edge, which has to be stripped out before any honest expected-value calculation.
Every probability the model emits is compared against the no-vig implied probability of the corresponding market price. The gap, scaled by stake, is the bet's expected value.