Are you talking about offline gambling? If yes, then if you can check every customers ID before placing a bet (if you can evaluate his age by looking on him), then such casino should stop operating. Its not possible or impossible to check, its a duty to check age. As to online gambling, then yes, its totally impossible to check everyones ID. In fact, rare online casino try to check ID during registration. They usually allow everyone to register freely.
physical casinos will require an ID for anyone suspected to be a minor before they can enter the premise, not before placing bets. They should never be allowed to be inside a casino in the first place, so right in front of the entrance they will already be filtered out.
As for the online casinos, there are a lot of different ways the minors can by-pass that policy. So, there's not much an online casino can do with these regards. The least thing they can do is to impose the KYC verification upon registration, but that only discourage a potential client.