The amount of luck involved definitely helps with casual play. You can face much stronger players without being completely obliterated. But that also means, for tournament play, that you need a sufficient number of games for statistically better players to come out on top. So tournaments typically last 2–3 days, totaling 8–12 90 minute games.
Tenhou is rigged though. IIRC, if you are a non-paying member (and possibly use a non-Japanese IP - a claim I haven't verified), the game will steer you towards a maximum of 25% 1st places. I have seen good (non-paying) players with thousands of games and they did indeed reach only that percentage. Of course, there are ways to minimize the rigging (basically never riichi if you are 5-dan or higher) but those only help so much.
I've played tenhou before... until I moved, didn't play for a few months and my account expired. I should give it another try at some point.
I did not know about mahjongsoul, perhaps I'll give it a try.
I learned against bots and then humans using "mahjong fight club ds wi-fi taiou", a seriously slick ds implementation. It's in Japanese, but English guides covering its interface are easy to find.
Is this correct? I don't have a pair: https://files.catbox.moe/p651pq.png
1 & 1 bamboo pair.
1, 2, 3 bamboo straight.
Oh I see, the bird is a bamboo. Thanks!
MahjongSoul was recently translated to English (https://mahjongsoul.game.yo-star.com/). The heavy anime-girl theming can be a bit unfortunate but it's an excellent implementation of the game and allows you to play matches against bots to learn the game.
Tenhou is the more classic and staid online implementation, and there are browser extensions for Chrome and Firefox to translate it to english. (http://tenhou.net/)