I wonder if there are passenger flights that would reach cruise altitudes higher than 40,000 ft (i.e. reach 41,000 ft for instance) more likely than others. It also depends on the plane of course, but assuming one gets a plane that can fly higher than 40k ft, e.g. the B777 or the B787 Dreamliner, are there other factors contributing to the likelihood of flying at higher altitudes?
The highest I think I've ever been is 38,000 ft, this was on a flight from Djerba to Central Europe in a B737 I think, but I'm unsure whether I didn't reach 39,000 ft on a transatlantic flight once in a B747 (it's too long ago to remember well). Then I've flown on many flights where there weren't those onboard screens where you can read altitude, speed and temperature but the captain announces the cruise altitude sometimes. However, I'm quite sure I've never flown above 40k ft (12.2 km). Are north-south flights more likely to fly at higher altitudes than west-east flights and/or are there other factors that may contribute to flying higher?
Edit: Following the revelations here I'm now sure that the flight from Djerba reached FL370, not 380 (it went slightly eastwards), and the transatlantic flight which was westwards to America probably reached FL380. So 38,000 ft MSL is really the highest I've ever been unless I don't remember correctly or haven't looked on a screen while a plane was higher or have been higher in some flight without those onboard screens and without the captain mentioning the cruise altitude.