As-salaamu `alaykum
If Yu-Ghi-Oh is about magic and fictitious monsters like I think it is, then remember that magic is a type of shirk. It is simply letting your child get attached and grow fond of shirk, just through another one of it's shades. As for the cards, then of course, they contain pictures and animation. Hence the angels wouldn't enter the homes which holds these images.
Remember, Islaam began as something strange, and will return strange just as it began. So glad tidings to the strangers! (Saheeh Muslim) So yes, while all the other kids; disbelievers and non-practicing/some Muslims are allowing this sort of entertainment for their children, the believers are distinguished. We are seen as strange, and don't need a shirky cartoon for our kids. There are many halaal ways of having fun, yet we ignore them and look to what is haraam. There are many good ways one can raise children, yet we always relax and turn our eyes to some of the crap that is fed to the masses, feeding it to our kids as well.
Maa shaa' Allaah, I know a brother whose children have never seen a cartoon in their life! They know what they are through their understanding, but have never actually seen one on screen. This is strange to the kuffaar, extreme to the negligent, but good to us.
Raising children is definitely a hard battle, but I must say, that the best of children I've seen (even those who have reached adulthood now) are those whose parents took utmost care with their upbringing. So they home-schooled them fearing Allaah (despite the bogus claims that this blocks there sense of cohesion etc), they taught them what is good for them and prevented them from what is harmful to them. Yet, they didn't go to extremes and deprive their children from fun (like some claim and sadly, some do). Rather, they weeded out the haraam fun for what is halaal...
Anyway, I hope I haven't offended anyone with this. But instead of arguing halaal and haraam, we should look at the harms/benefits, and the obvious factors that would help us determine if these sort of programs are sound under an Islamic framework. Wallaahi, I don't see any excuse for this program, and most of those you find today.