What are the odds of someone having the same DNA as you?

1 in billions. The only people who have the same DNA are identical twins, and they don't even have exactly the same DNA because of random mutations that occur during the splitting of the ovum and development. The chance of identical twins are about 1 in 285 but the chances of one of them not developing a benign mutation somewhere in their DNA is very very unlikely. There is likely nobody in the world who shares their DNA with anybody.