Yeah, its without a shadow of a doubt the worst mini game to ever be put into a Yakuza game. But there is a method to its madness, its just buried under a load of rubbish.
First off, unfortunately there is still a certain degree of luck to it. I don't think its possible to win 100% of the time.
Secondly, when choosing a girl to bet on, pay attention to the little bits of text that scroll on the menu screen. It'll usually say stuff like "X didn't get any sleep", "her favourite blue pen broke", "had a good day" etc. This is usually a good indicator of which girl to pick. So choose the one that sounds the most positive, but also keep in mind the girls your going up against in your bracket (as going up against a girl who also has good morale can be problematic). I've no idea how much this really helps though...
Otherwise the blonde with glasses (Jennifer is it?) is a good all round solid bet. Her stats and special are good.
Now for the super hard part. The girls actually go have patterns, but you have to look really hard to see them. I don't remember what they were now for the life of me but its usually either - picking their strongest attack, trying to counter pick your last attack, trying to counter pick your strongest attack etc. stuff like that. Its really hard to pick up while playing, the only way I figured it out at the time was playing it for a couple of hours continuous so that I started seeing the patterns. Or I went completely mental and started imagining it.
Also, even if you do everything right, you can still be messed up with that stupid counter finisher that hits you after you win. That's just flat out stupid.