Pegfinity

Pegfinity keeps your upgrades while changing the board. The official description says every board is randomly generated and every upgrade persists. What you have unlocked and what is in front of the next shot can therefore develop on different schedules.

The effects have concrete advertised forms. An atomic-bomb peg hits everything; other listed possibilities include electric pegs, portals and balls that shatter. The bomb is a useful example of an effect whose reach differs from an ordinary single contact, although the description does not say how those hits score or guarantee that the peg appears on a particular board.

That pairing gives persistence a particular meaning. You are accumulating possible interventions without receiving a promise that the same layout will be waiting next time. A previous successful arrangement is a reference rather than an exact repeatable route. If this kind of score chasing interests you, the question is how the effects you have gained apply to the board you received—not only how much larger the next multiplier becomes.