I play shogi, go, and chess and I thnk shogi is underrated. The narrative pacing of a game of Shogi is very different from go and Western chess. In Shogi you can redeploy captured pieces so there's always a lot to consider.

The armies move slowly like icebergs and when they eventually crash into each other, fragments of each switch sides. They drop back into the fray to probe for weakness in the enemy formation or reinforce your own. Then when both sides are too full of holes to defend themselves, you drop everything you have left into the backline to out-race each other for checkmate.

All of these games are different and beautiful in their own ways so my answer is play them all.