How does high altitudes effect tire pressure?

The amount of air in the tire stays the same.The outside pressure drops about 3psi or 0,2 bar, when you are at about 2000 meters or 6000 feet. So you would expect that the pressure you measure is higher. But on 2000 meters height there is mostly a lower temperature, this lowers the pressure in the tire a bit. So it would not be strange if you measure the same pressure.