During a galactic merger, the gravitational forces at play are immense, yet the actual impact on individual star systems is surprisingly subtle. Stars are separated by vast distances relative to their own sizes. When two galaxies merge, their gravitational fields interact, causing stars to follow new orbital paths. This process can shift the position of a star within its local neighborhood, but it rarely causes a radical disruption of a solar system's internal structure.
Regarding the mathematical odds of a direct stellar collision, the probability is extremely low. Because space is so vast, the chances of two stars physically hitting one another are nearly negligible. Astronomers estimate the likelihood of a direct collision between stars during a merger to be effectively zero for most systems. Instead of collisions, the primary effect is the redistribution of stars into a new galactic shape, such as an elliptical galaxy.
While stars will certainly move to new locations, the planetary systems orbiting them are expected to remain intact. The gravitational tugging is generally too gentle to strip planets away from their host stars or force stars into one another.