When I used to run games, I'd make some dice rolls behind my screen and some right in front of the players. I'd also make it look seeingly random, but in actuality, for those rare times that things weren't going the players' way, I'd fudge things to help them. Since I'd boucne back and forth in my dice rolls, they never noticed. Also, the fact that I was a rather evil GM (not trying to kill PC's, just making them hate me at times), they never realized they were being helped those rare times.
Of course, playing solo or same-side, you're 100% at the mercy of the dice. One of the first times playing All Things Zombies, my character ended up surrounded by zombies 30 seconds into the game. He escaped into a building, only for zombies to come flying out of the closet. He killed them all, but then ran into two people who began arguing at the top of their lungs, attracting more zombies. He nearly made it to the edge of the board when a car alarm when off. The poor guy just had one mishap after another and ended up losing every single person who joined his group.