These minigames are meant to give you some entertainment, plus the opportunity to win a nifty prize or two. It's not a big deal to complete them all, so be sure to get on it.
The rule is simple: hold right mouse button pressed (Geralt is avoiding enemy blows), and when the enemy throws a punch, release it and press the left button. Then press the right button again. And repeat. And repeat - until the enemy falls to the ground. You might want to spend one bronze talent on Brawl perk (Strength tree) to make things a bit easier.
You can't lower the entry fee, but you can double it.
Rolling the dice is always random, so there's no real recipe for success here. Just remember to save your game before the match in case you loose a lot of money.
Raise the starting bet as high as you can if you're after money, and as low as you can if you just want to win (to make progress in a quest).
Try to achieve three-of-a-kind each time you play. There's a high chance you'll win just by having it. You almost always have a pair, and if you do, just re-roll the three remaining dice. There's way above 50% chance you'll have three-of-a-kind. A simple method, but surprisingly effective.
Geralt has a relatively strong head and is able to drink more than most of his fellow drunks. However, there are some that you can't beat without a little cheat - Wives' Tears potion to be exact. You can buy it from a lumberjack at the swamps (M10.22) or from a waitress in New Narakort (M14.13). Just stop drinking for a while, drink the potion and get back to work - you'll start off fresh, and your opponent will be continuing what you started.