Horses are regarded as stable horses when they have the same trainer. Stable horses are common in America, French, and Italian races. When you place a bet on a horse, which happens to be a stable horse, the punter automatically bets on all horses in the same stable. Thus, if the second stable horse wins, the punter wins the bet.
In the United States of America, this is applied to all betting types. In France and Italy, this only applies to win bets placed at starting price (SP).
Stable horses are marked with a corresponding number on the race page.