Changed hotels, and next hotel (different chain than one previous) had same room number.
I think I've had that happen before once.

It seems like it should be awfully infrequent, and the probability should be something like winning the lottery. 2 random numbers being the same?
Though I guess it could be more frequent than thought (like 2 in room sharing a birthday) because of other factors.

Maybe ElevatorEnthusiast knows, given changing hotels nightly?

I'm sure certain factors can increase the likelihood of this happening. I.e. say you tend to request first floors, and a given hotel has say, 30 rooms on the first floor. You then go to your next hotel where you again request a first floor room which again has 30 rooms. If done randomly, the odds of pulling the same room number twice in a row is 1 in 900. For back-to-back hotels if both hotels had 100 rooms, the odds are 1 in 10,000. Certainly not the highest odds, especially on the latter, but also given how many tens of thousands of people are checking into or out of a hotel on a given day, it does make sense that it would happen on occasion.

It means that you travel too much.

So if the hotel are of similar size it makes it easier. But the numbering system also matters. And in certain small hotels you get numbers like 5, which will never be possible in a big hotel.

I don't know if there is a uniform numbering system around the world, but it seems in the US you put the floor number and then 2 digits for room number. Properties which have multiple buildings often have a building number as the first digit (and then 3 more), but I don't know if that is normal. In the US hotels also run up the numbers, but I've seen in other places numbers run up and also run down (eg 2199, but on that floor there aren't 99 rooms) depending on which direction in the building you are going.

I'd guess if you always booked suites or corner rooms your chances would be higher, as corners should be more often 01.

Anyway, in my case I don't request first floors and both properties were 250-300 rooms, and not newly built.

FWIW I’ve been assigned rm 606 in three different hotels from separate chains in separate countries for some reason beyond me.

I mean, if you change the middle number that could make sense ...

The math is off. For 30 rooms on the same floor, the probability of having the same one is 1/30. Similar for two hotels with 100 rooms - it is 1/100. The lower 1/900 and 1/10,000 are the probably of having the same in room in both hotels and that room being specific number.