In the Ryder Cup, Solheim Cup and Presidents Cup, and other team-based match-play competitions, foursomes -- better known as alternate shot -- is a common format.
In foursomes, or alternate shot, two players on the same team alternate shots on each hole. Player A tees off with the tee shot. Player B hits the next shot, typically the approach shot (unless it's a par-3 hole). Player A then hits the third shot. This alternating pattern continues until the team holes the ball. The team score is the total number of strokes played by both players. The winning side on each hole is the team with the fewest total strokes. This is done until a team wins the match or the match is halved.
One of the quirks of foursomes, or alternate shot, though, is the One Ball Rule.
What is the One Ball Rule is foursomes and alternate shot match play?
In alternate-shot competitions, the One Ball Rule -- which is a local rule, whose implementation is up to the tournament committee putting on the event -- requires the players on the same team to use the same model of ball for the hole they are currently playing.
If the team starts the hole with a Titleist Pro V1, then they have to finish the hole with a Titleist Pro V1, even if there are penalty strokes or lost balls. If a team violates that rule, then there is what's called a "match adjustment," and the opposing team is awarded a hole -- without even having to play one. The maximum penalty for violating the rule is an adjustment of two holes.
However, under the rules of these events, players are able to change balls at the start of a new hole. This gives the teams an opportunity to switch balls to the preference of the player hitting the tee shot on each hole.
Typically, players with similar golf balls like to be partners, but that's not necessarily a given or a priority over an existing friendship or partnership.