Watching stars on earth's poles

We know that the the galaxies are all shaped like discs, so if we are on the north or south pole, we should see very few stars as compared to what we would see on the equator

well first of all you gotta know which side of the galaxy you are facing when you are standing in the poles given the fact that the earth is rotating.... also you gotta understand that the density of the stars in terms of location is different in different places.....

so how do you come to conclusion about the number of stars visible.....

Quite a intresting observation..........it is absolutely correct what you are saying but the reason you are giving is not correct .

not really estimating the number of stars, just speculating that there should be a lesser number of them visible on poles than on the equator.

and I don't really know if it is correct, I've never been to the poles.

We are located roughly half-way out from the center of our galaxy in one of its spiral arms. The few thousand individual stars we see with our naked eye are all relatively close to us, mostly within 1000 light years. Our galaxy is several times thicker than that. That's why, no matter which way we look with our eyes, we see pretty much the same density of scattered stars.

The situation changes when you use a telescope. Look along the plane of our galaxy and you'll see a huge number of dim distant stars. They are too faint to resolve with the naked eye, but together they form that band of ghostly light called the Milky Way. The Milky Way appears brightest towards the center of our galaxy, in the direction of Sagittarius.

Earth's axis and our galaxy's axis point in different directions. That's why the Milky Way's glow is tilted relative to Earth's equator.

People living in light-polluted cities almost never see the Milky Way. The 1994 Northridge earthquake in California knocked out the electricity in much of southern California. The suddenly brilliant stars and Milky Way actually frightened some people.

Not all galaxies are disk-shaped.

Over the course of a year, people living on the equator see almost all the stars. People living at the pole (a few shivering scientists I guess) see only half of them.

the basic thing is there are too many factors to be considered..... so you cant be cent percent sure that there would be more stars at a particular direction....
for example you have to consider the earth's rotation, rotation of our solar system, rotation of those stars with respect to each other, their visibility to you etc etc etc.....

The original conjecture would be pretty much valid if the earth's axis of rotation was perpendicular to both the the galactic plane and it's own orbital plane about the sun (which they aren't). In that case, the Milky Way bands would remain pretty much overhead at the equator and barely visible (if at all), low on the horizon, at the poles.

Also, all the galaxies aren't shaped like disks.