If you liked Death Note, the following anime are also recommended:

• Code Geass (tactical warfare and intelligent use of a supernatural power; be warned of some plot contrivances)

• One Outs (if Light Yagami was a baseball pitcher)

• The Promised Neverland (season one is a battle of wits just like Death Note, although the manga it is adapted from is better)

• Talentless Nana (despite the OP advertising it, the cat and mouse game between Nana and Kyoya is not the series' best point; it is watching Nana puzzle out what the Talented's supernatural powers are, their weaknesses and finding a clever way to kill them. Also, the first episode disguises the series' true nature, so watch the first two episodes to find out if it is for you. Be warned that the finale is utter garbage.)

• No Game No Life (some of the plots were ridiculous, but some were really impressive; I should also warn you of heavy fanservice)

• Kaiji (gambling)

• Akagi (mah-jong)

• Moriarty The Patriot (I have heard this is a battle of wits but have never watched it, will do so soon)

• Hyouka (a mystery show with a completely different tone from Death Note but good mysteries)

I'll link you to here, here, here, here and here.

By the way, although it is not an anime, I would highly recommend you read the Liar Game manga. Read it scanlated online, for it is not available for purchase in English.