Seven ads breached the new rules, including six out of 56 TV ads and one out of 344 internet pop-up ads.
Four of the TV ads were from the same advertiser, which the ASA did not name but can be deduced as Intercasino. The ASA said it considered the ads, which included dwarves dressing up in dice costumes and rolling down a hill, were contrary to the code because they had particular appeal for children.
Since the new rules were introduced, the ASA has had cause to formally investigate complaints about one ad, for Ladbrokes featuring former footballers Ally McCoist and Ian Wright. It rejected the complaints, which alleged the ad encouraged bravado and persuaded young people to gamble.
Christopher Graham, director-general of the ASA, argued the survey showed the self-regulation model was sound.
He said: "The results of this compliance survey are confirmation that advertising self-regulation is working effectively and that advertisers in the gambling sector are demonstrating a proper concern for social responsibility in their marketing communications."
The gambling regulator, the Gambling Commission, said the survey "demonstrates the widespread commitment of licensed gambling operators to the advertising rules".