The Genjintchi game is similar to to Forestgotchi in that there are 4 holes and you have to guess which bone it is in. Frankly, there's a 25% chance of selecting the correct hole at random. Rather than having to constantly select a different hole, just continue to guess hole #1 (far left) and spam that. It's much more efficient and far easier to just spam the first hole and win a bunch of games. Great if you don't want to pay much attention and help your tama lose a bunch of weight :)
While care levels do matter, such as keeping hunger and happiness full, cleaning up poop, and giving medicine when necessary, the Evolution Meter matters far more when it comes to the character you get. Also, your Genjintchi will not call for more "discipline" after it reaches 100% Evolution Meter, so you can relax after you fill it to full if you want.