DNA twins

[Whickerman]

Just curious - what's the chances of having a DNA twin? What are the odds of two people having the same DNA, and at what stage is it a certainty that there's another with the same DNA pattern?

(Background: you hear that there's a one in xxxxnumber chance of DNA match being wrongly applied, yet surely a finite number of options must be reached as populations grow, and then taking race into account the odds must get slashed? If at all possible, a statistical answer would be appreciated, thanks)

[Whickerman]

Sorry - meant to specify, I mean where two people aren't, say, twin siblings...