I like Tetra Master (and Final Fantasy IX). Square Enix even ran a Tetra Master Online version (formerly accessible along with Final Fantasy XI via playonline.com) until 2010. There has been at least one fan project to recreate a playable Tetra Master[1] though sadly it seems to be offline.
However Triple Triad (from Final Fantasy VIII) is perhaps a bit easier/saner to play, and is also included in (the MMO) Final Fantasy XIV. Two of my favorite Final Fantasy games. Triple Triad in particular is probably my favorite Final Fantasy minigame (FFIX jump rope and FFX lightning dodge being my least favorite).
[1] https://www.reddit.com/r/FinalFantasyIX/comments/139vs9o/ffi...
It causes a feeling in uncertainty, which is closer to a gambling game.
Randomness prevents the player to form strategies that allows him to win must of the time.
Uncertainty is a bit similar. If the player could figure everything out, there would be less suspense.
The players are frustrated because they naively expect that they should always be able to determine things in advance so they can be experts at the game and know if they can win or not.
Sprinkling some randomness at such game is smart game design.