As a parent you have to decide what are your goals as a parent regarding to laws, right and wrong, morale and ethics. No one follows the law completely. You might drive slightly over the limit, you might watch copyrighted material and so on. And no one is perfect with morale and ethics (as it is impossible too). We all lie.
So when your underaged child want to use your ID, it all comes down to what you want to teach your kid. Is it ok to break the rules and law? Is it harmful to play for money when underaged? There are a lot of researches about teenage brains and gaming/gambling.
It's not an easy thing to do. If the kid is 10y old, it's a lot easier than when he is 17,5y old and very mature.
My own approach (we have 15y and 8y old ones) is that our job as parents is to teach what is right and wrong, and mold their morale and ethics as good as we can. And the general rule is that you should be honest and obey the rules and laws. And sometimes you don't do things you would like just for the reason that it is wrong. I don't tell them all the thing I have done in the past and as a kid, as they can't understand the whole world yet. I can't say "you can't do it because it is wrong, but I did it when I was a kid". They learn so much from our example.
If 15y (soon 16y) would be interested in poker, I could talk about probabilities with him and maybe play with chips at home. Approach the game from strategic point of view. But at the same time explain why he can't and shouldn't play with money. How the brains of teenager work and what are the dangers and problems in it. He is pretty smart kid and understands that.
Last summer he was on a boat trip and there are hundreds of slot machines on that boat (all Finns and Swedes know this). They are forbidden from underaged but in reality 15-17y old kids play them a lot. He wanted to play them too and got really upset when I said no. When I explained the reason, he took it a lot better and understood it. For 8y old simple no is enough, she can live with the explanation "cos it's forbidden, that's why".
I did my practical learning in my studies for Bachelor of Social Services in a resource center for gambling addicts. I talked and worked a lot with former and current addicts and pretty much all of them started playing when underaged.