I'm not an eye doctor but I did stay at a Holiday Inn Express last night.
A lack of depth perception doesn't mean objects look different to your eyes.
It means the brain for some reason can't process clues,
clues that tell the viewer how far away stuff is.
The clues are always there, but some people just can't read them.
There are several clues we use.
If you are in a moving car, close things move faster and far things move slower.
Another is stereo vision, our eye sees
2 angles of the same object and then
the brain mashes them together into one image.
Another basic clue is just
how familiar we are with the size of certain objects from experience.
Like we know a pool ball is 2.25 inches or so. We know how tall those balls are supposed
to look relative to the height of the rails, and subconsciously we compare them to the rails diamonds etc.
A person with normal depth perception immediately would know if you swapped the 8 ball with
the black snooker ball, even though you can't see shadows on that ball.
A person with depth perception problems (and maybe less experience in pool),
might not know for sure if that black ball looks small because it's actually smaller,
or because it's just further away.
Unfortunately I can't show you side-by-side images of what good and bad
depth perception look like because they don't look any different.
It shows up most when things are moving. A person with bad depth perception
might see moving traffic and have a hard time judging if the gap is big enough for him to merge.
Or they might have difficulty catching a ball because they don't automatically know
when it's close enough to reach out and touch.
Bad depth perception is not the end of the world for a pool player, my buddy has double vision
that plays hell on his depth perception, and he must concentrate to keep everything together.
But he can play OK and was even a good marksman,
he was picked to teach his rifle team in high school. He can manage because he's firing at stationary targets
and with enough experience you can tell where you need to aim to hit those targets.
Then you just need the steady hands to deliver the cue ball (or bullet) to the intended spot.