If the batter swings and misses and the catcher catches the cap, then the batter is out. If a fielder catches a cap on the fly, that too is an out. Otherwise four hits equals a run, and each additional hit in an inning is a run. Three outs and inning. Nine inning games.
Most runs win.
The White House bottle cap court was not only central to Dogtown in the 30s and 40s, but I spent a good deal of my own youth playing there in the 50s as well. Jack Moser related how at that time beer was 10 cents a bottle. Games were played for beer, with an even number of players on each team. Each member of the losing team purchased a beer for the player on the winning team playing the same position. We lived next door to a Gasthaus and the Frau there provided us with an unending supply of bottle caps.