It just dawned on me that we should be calculating the number of possible public keys (not private keys) when illustrating the chances to steal someone's bitcoin. (The whole 'single atom in the universe' thing)

Since there are far fewer possible public keys than there are private keys, there is obviously a less-than 1:1 ratio between them, and therefore multiple private keys could clash and produce the same public key - and therefore would be able to spend the bitcoin associated with its UTXO set.

Am I wrong? 

 Isn’t there an infinite amount of public keys that are derived from each private key? 

 A public key string is shorter than a private key string, suggesting that there's some hashing that happens in the process. 

 I'm no expert, but the way you get a private key is with math. You know who has a really good explanation on this Andreas Antonopoulos  

 So you can't go backwards only foward and something about you add to the private key to get a public key or something like that so you cant get a private key randomly he explains it very very well  

 Yes. There's hashing involved in that case. 

 Yes so when you hash i take it as math 1+1 but its random numbers that never give the same outcome  

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 My point is, everything that uses SHA256, will generate an outcome of 1 in 2²⁵⁶, including any collisions. 

 I’d say you are not wrong 

 I wonder how many people are "address mining"

https://media.tenor.com/507BGTQ64ZkAAAAC/bh187-dumb-and-dumber.gif 

 Relatively expensive to do but I’m sure some are 

 Big incentive on some early addresses 

 In this section of videos your question will be answered. I forget which one was the exact video that he explains this 
https://youtube.com/playlist?list=PLPQwGV1aLnTtAmzmz6uVE0kTKXtaGX1zY&