Learn Russian: Шар не упадёт в лузу без того, чтобы не отскочить от борта. - The ball won't fall into the pocket without bouncing off the board.

The phrase без того, чтобы не is a set structure used to express 'without doing something'. When the main clause is negative (like не упадёт), Russian requires this double negative to show that the first action cannot happen without the second action also happening.

Why do we use the infinitive отскочить instead of the past tense?

We use the infinitive because the subject performing both actions is exactly the same: the ball (шар). If the entity performing the action in the second clause were different from the main subject, you would have to use the past tense instead.

Why is отскочить perfective here instead of imperfective?

The perfective aspect focuses on the completion of a specific, single result. The ball needs to successfully complete one bounce off the board for it to fall into the pocket. If we were describing a continuous or repeated action, we would use the imperfective отскакивать.

Why does луза take the accusative case (в лузу) here rather than the prepositional?

The verb упадёт (will fall) describes active motion toward a destination. Even though we might say 'fall in' in English, Russian requires the accusative case to show the direction of movement into the pocket, rather than the prepositional case which would describe being in a static location.