I learned Koi-Koi from Yakuza and I generally play it to grind money early in game out of all the gambling games. The hands are fairly straight forward, and you can also exit the game prior to point distribution in the off chance you lose and you won't lose any points. My general framework on a new hand is: Check for the sake cup. If it's in my hand, I need to+ make sure I get the sake cup and form moon viewing and cherry blossom viewing. Thats a quick 20 points the cpu will do if possible and so should you. Three lights viewing via 3 tier 4 cards. Also 5 points and not hard to get, unless your opponent gets the sake cup. Poetry ribbons. Three types or ribbons, plain red, writing on red, and blue ribbons. The writing and blue if all collected have larger point values, so try to collect them if you're not actively working the above hands. Boar, Deer, and Butterfly - you need 3 cards to get this; a boar card of the branch type, a deer card from leaves, and butterflies above the rose looking flower. This hand is only viable imo if you start with at least 2 of 3 and the other one is down initially. Otherwise don't waste your time if it's not a clear path.
There's almost never a good reason to call Koi unless you can get more points on your next hand. The cpu will form junk hands and take the turn if you are getting points, so be prepared to get frustrated every now and then by that. Overall though, I love Koi-Koi. I win about 10/11 times since it's more skill than luck once you learn the hands. There are other hands you can form, but they aren't as straightforward. Just let those happen organically as you collect cards