If you liked the Yu-Gi-Oh! Duel Monsters anime, the Anime-Planet community thinks you'd like:
Twelve-year-old Shobu Kirifuda has one goal: to become a top-ranking player at the game of Duel Masters, a card game in which players use spells and summon monsters to break through their opponents' shield cards and subsequently defeat them. Shobu believes he's a great player, but he soon discovers that there is more to the game than he originally thought; true Duel Masters, he learns, are able to make the monsters on the cards manifest themselves during a duel. A mysterious group has taken a keen interest in Shobu, although their reasons are as mysterious as the group itself. Now Shobu and his friends not only have to win the championship, but also try to figure out who these people are and why they're so interested in Shobu.
While examining an old Go board in his grandfather's basement, twelve-year-old Shindo Hikaru is possessed by the restless spirit of Sai, an ancient Go master who has waited for over one thousand years to play the Hand of God: the perfect move. Sai convinces Hikaru to act as a vessel for making his moves, but it is soon clear that Hikaru also enjoys Go and wants to play his own games. Moreover, the rules of Go have changed since Sai's time, and Go players from all over the world are now much stronger, having had the benefit of hundreds of years of evolution and experimentation by the masters before them. Can this unlikely pair form a successful partnership and rise to the top of Japan's Go community, and can Sai finally play the Hand of God and find some peace?
The main simiarity are main characters. Both of them posess "inner" self that they can talk to and that are a masters in Card game/Go. Both anime tell the story of these characters as they learn more about the games and about themselves.
Takamine Kiyomaro is a junior high school student who thinks he’s too smart for school, to the disappointment of his mother. On his 14th birthday a surprise literally crashes through Kiyomaro’s window, in the form of… a small naked child?! His name is Gash Bell and his goal is simple: be a mentor for Kiyomaro, at the request of Kiyomaro’s departed father. In return, Kiyomaro must help discover the secrets behind Gash Bell’s amnesia and his past, with only a red book as a clue. As if things weren’t crazy enough, Kiyomaro soon discovers that Gash Bell is a demon -- one of many on Earth -- who can be forced back to the demon world if its corresponding book is burned. Armed with the power of the red book, Kiyomaro must now help Gash Bell defend himself against other demons who want to vanquish him from the Earth, lest his newfound friend vanish forever!
Yu-Gi-Oh! and Zatch Bell are very similar in the fact that there is battling within the show and the basis is the battling. The only difference is that ZatchBell is little monster things and Yu-Gi-Oh! has cards.
Tachibana Riku is an orphan who lives with his adoptive grandfather. Other than school and homework, Riku has to put up with lessons from his grandfather, teaching him seemingly meaningless hand signals and signs; meaningless, that is, until Riku is violently introduced to the world of 'shikigamis', fighting beasts with human owners. After witnessing his grandfather defend against a shikigami assault on their home shrine, Riku obtains his own Drive device to summon his own shikigami, Kogenta, and it turns out the hand signals give the shikigamis special powers. With his newly obtained powers, and a shikigami as a companion and friend, what adventures await Tachibana Riku? Do his powers have any relation to his parents' disappearance?
If you like one, you will like the other.
They also share the same kind of feel to the main villain, being some kind of huge evil corporation. And the fact that they utilize "monsters" to do battle.
Some time ago, Jin Mitaka lost his memories when battling against Count Pythagoreas. Now that the Orpheus Order has been defeated, Kaito, Nonoha and Rook are determined to restore the man to his former self by bringing him to familiar locations, and soon arrive at the Fool’s Puzzle from their past. But things escalate when a mysterious girl named Raetsel ambushes them in the puzzle’s chambers; she works for an organization called Master Brain, and she’s come to steal Jin away. And not only does Jin recognize the girl, but she also claims that Master Brain’s goal is to rid the world of puzzlers at Jin’s request! Now, it’s up to the Children of Phi Brain to discover the truth and put a stop to the organization’s nefarious plans.
These are both shounen anime where the characters get involoved with games they enjoy on a much larger and more dangerous scale. Phi Brain is about solving puzzles and Yu-Gi-Oh is about a card game, but at their heart they are both shounen anime with all the usual cliches and character archetypes. Both anime have characters matching wits with villains through either puzzles or the card game.
In both these shows there is at least some attempt to have strategy and tactics play a role in the puzzles or the games, but don't expect anything too complicated from either of them. If you are looking for a stereotypical shounen anime then either of these should suit your needs.