Definition of Odds-on
Even money is a gambling term referring to a bet with even odds: the winning bettor stands to earn as much as the losing bettor stands to lose, minus the vig. In wider usage, even money refers to an even chance, which is different.
Odds-on, a term coined in the late 1800s, refers to odds that are less than even money. A sportsbook loses on a successful odds-on wager because the winner wins more than the loser loses, and the book covers the difference.
Over time, odds-on came to refer to wagers that did not involve much risk or had a better than even chance to win. The common term odds-on favorite often refers to the horse or team that is most likely to win the race or match.
In the gambling world, there is a subtle distinction. An odds-on favorite is a horse or a team that is so favored by the betting public that the odds are less than even. In other words, the betting public is preventing balance of the wager.
In order to appreciate this, it is important to recognize that sportsbooks generate profit from the vigorish alone, and they attempt to minimize risk by balancing wagers. Las Vegas can take big losses on an odds-on winner.
Often, books will sell and buy wagers to other books when possible in order to reduce the risk.