How actually probable is to "meet" other people in No Man's Sky?

Solution 1:

The odds are actually pretty high that you will eventually "meet" somebody, as you can see. The odds of you being on the same planet at the same time and in the same place are where the odds drop like a rock unless you put in the effort and materials.

This is actually a version of the Birthday Paradox. With enough people involved the odds of two people having seen the same planet goes up VERY quickly.

Solution 2:

On PS4, the 4th system I visited had already been discovered and named by another player. I sent him a message on PSN and he told me that the 2nd system he visited happened to be the 2nd system I had visited. (We were not previously acquainted.)

I have not read anything online about how frequently this is happening, but my suspicion is that the developers decided to make encounters more likely by deciding on a few million possible starting "areas" (i.e. clusters of 100-1000 stars) and then assigning each new player to one of those areas randomly. Either that or they badly screwed up their randomizer. :)

Note that in this case the birthday paradox is not too helpful; sure, the principle is the same, but 1/365 is a massive number compared to 1/18,000,000,000,000,000,000. Every time you place one birthdate on the calendar, you're taking away a sizeable chunk of the possible dates for other people. In No Man's Sky, on the other hand, you could place 10 million (or 100 million, or 1 billion) players on the map and not even notice them. It's like finding the probability of two among 30 people born at the same picosecond.

Now, the fact that players can travel around definitely makes meeting folks way more likely. But this early in the game it still seems weird to me. That's why I feel the developers must have manipulated the starting locations on purpose (or screwed up :).

::edit:: Ok, I missed one of your points about how we're apparently starting in a galaxy that's much much smaller than the total star count. I didn't know that, and if true then it changes the math quite a bit. If there are only 100 billion stars in the starting galaxy then the birthday paradox definitely begins to matter.