Correlated parlays are two or more bets from the same game that rely on a closely related outcome: for example, betting that a football (soccer) team might both score more than three goals in a match, and also win the match.
These are not independent events, as a team that scores more than three goals is also very likely to win the match.
A naive application of odds that treated these events as uncorrelated would not accurately reflect the probability of the linked bet.
However, with the rise of sports betting through mobile gambling apps in the late 2010s–2020s, this traditional hesitance has weakened.
While these systems usually prefer to lean heavily in the house's favor, the increased volatility from these bundles has resulted in some notable cases where bettors have found favorable odds.
This isn't always a windfall for the bettors, though, as these newer-style sportsbooks have sometimes simply refused to pay out in those cases if the parlay comes through.
[1] Parlays were introduced into New York-area racetrack gambling in 1988, but a 1989 newspaper article indicated that they still weren't very popular, perhaps due to the large surcharges and fees charged by off-track betting (OTB) parlors.
For instance, a common two-team NFL parlay based entirely on the spread generally has a payout of 2.64:1.
In reality, however, if one assumes that each single game bet is 50/50, the true payout should instead be 3:1.