There are a number of stories about persons with exact look alikes. In general this seems to be a rather rare phenomenon. But if you assume more and more humans it should become also more likely that somewhere out there is a doppelganger. My personal rationale is that all humans come from the same ancestors there is a somehow limited number of genes that can be combined - at some point there will need to be duplicates.
So the question is: are there any numbers principles that would help estimate how many humans it would need for more people having a doppelganger than not?
To specify doppelganger I would consider a look alike person, same height, similar age, same gender, hair colour, eye colour, skin colour. They should look and sound very similar - like identical twins. Although I would ignore, haircut, tatoos, scars and any other cosmetic alteration. Especially I don't care if they are genetically identical - looks and sounds alone is enough. For this question I want to ignore cloning and twins. Also lets assume between the distant human groups there is no evolution or mutation that would separate them into different ethnics. Also no "mirror worlds".
Just by pure luck this story was featured today. Does anyone understand the maths well enough whether this applies to my question? Are we already enough humans?
After the first answers pouring in I see I should clarify some points. I am looking for cases that would be good lookalikes. As there are already a few around - a guess would be at least 100 (looakalikes so spooky close that I would classify them as doppelganger) for the 10 billion people we are. The answers based purely on genetics seem way to conservative as it would be near impossible to have a single doppelganger pair. I think it will be necessary to adjust for.
From mathematics the point to the birthday paradox is very valuable. But the birthday paradox calculates how likely it is for at least one pair to share a birthday. The number i am looking for is the probability for at least half of the people share the "birthday" (look in this case). I had a go at the equation - but I personally I think this problem needs to be tackled very different and is not trivial enough for me.
I know I'm new here so let me know if you think these clarifications "break" the question and should be stated as new one.