I like abstract strategy games, but I don't like heavy memorization. Chess is popular so it's easy to find opponents, but memorizing the opening book is necessary if you want to get good. It's also very easy for weaker players to lose the game from a single blunder, which is unsatisfying for everybody. Arimaa was designed to be difficult for computers because of the very high branching factor, and that same property also makes it interesting for humans.
Arimaa can be played on a Chess board, and the rules are simple. Memorization is completely useless. You're forced to use intuition, in a way more like Go than Chess. There are no draws. Comebacks from inferior material are much more common than in Chess. It feels like Chess without the boring bits. It's still too new to tell if it's a truly great abstract strategy game, but people are already playing it at a very high level with no obvious flaw in the rules. I recommend trying it:
Lend money to a bad debtor and he will hate you.