To lay the odds is to back an outcome where you stake more than you stand to win, which is typical when you bet on a clear favourite. Risking 100 to win 75 is laying the odds. The reverse is taking the odds: risking 100 to win more than 100, even 100.01, as you might when backing an underdog. The phrase is most common among sports bettors, but casino players use it too.
In craps, players betting against the shooter on don’t pass or don’t come can lay odds behind their bet once a point is set. This lay bet pays at true odds, so it carries no house edge. On betting exchanges, to lay means to act as the bookmaker and bet that an outcome will not happen. For sportsbook operators, knowing which side customers tend to back is central to pricing and liability management.